ECareers BB EL Manual XL PDF [PDF]

Zitiervorschau

e–Careers Limited Lean Six Sigma Black Belt

Third Edition

Lean Six Sigma Black Belt Third Edition Manual Based on Version 11.0XL Training Materials Utilizing SigmaXL Statistical Software

An e-Careers Limited Publication   10 Riverside Business Park Stony Common Road Stansted Mountfitchet Essex. CM24 8PL. United Kingdom Email: [email protected] (UK 0044) (0) 1279 799 444

© 2013 e-Careers Limited. All rights are reserved. Individual Copy. No portion of these materials may be reproduced, transmitted, stored in a retrieval system or translated into any language in any form or by any means.

Table of Contents Page Define Phase Understanding Six Sigma…………………………..………………………………..….…….… 1 Six Sigma Fundamentals………..………..………………………..………………..……..…. 22 Selecting Projects………………………….……………………………………..……..……… 42 Elements of Waste……………………..…………………………...……………………………64 Wrap Up and Action Items……………...………………………………………………….……77 Measure Phase Welcome to Measure……………………………………………………………….……..….....83 Process Discovery………………………..………………………………………………………86 Six Sigma Statistics…………………..………………….………………………………….….135 Measurement System Analysis…………….………………………………………………....168 Process Capability ………………………...………………………………………… ……….202 Wrap Up and Action Items …………………………………………………………………….223 Analyze Phase Welcome to Analyze……………………………………………………………………… .…..229 “X” Sifting………………………………….…...………..………………………….……….….232 Inferential Statistics………………………………….………………………..………….…….259 Introduction to Hypothesis Testing……………………………..……….…………………….274 Hypothesis Testing Normal Data Part 1……………………….……………..………………290 Hypothesis Testing Normal Data Part 2 ………………….…………………………….……333 Hypothesis Testing Non-Normal Data Part 1………………………………………….……362 Hypothesis Testing Non-Normal Data Part 2……………………………………………….389 Wrap Up and Action Items ………………………………………..…………………....……..409 Improve Phase Welcome to Improve…………………………….…………………….…………………...…..415 Process Modeling Regression…………………………………………………..…………….418 Advanced Process Modeling…………………….…………………………………………….436 Designing Experiments………………………….……………………………..………………464 Experimental Methods………………………….………………………………………………479 Full Factorial Experiments………………………..…………………………..……………..…494 Fractional Factorial Experiments………………...…………………….……………….……..524 Wrap Up and Action Items………………………………………………………..……………544 Control Phase Welcome to Control……………………………………………………………………………550 Advanced Experiments…………………………………………………………………….…..553 Advanced Capability……………………………..……………………………………………..563 Lean Controls……………………………………………………………………………………580 Defect Controls……………………………………………………………………….…………595 Statistical Process Control………………….………………………………………………….607 Six Sigma Control Plans…………………..….…………………………………..……………648 Wrap Up and Action Items………………..….……………………………..……………….…668 Glossary

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

1

Lean Six Sigma Black Belt Training

Define Phase Understanding Six Sigma

Welcome to the Black Belt Training Course. This course has been designed to build your knowledge and capability to improve the performance of processes and subsequently the performance of the business of which you are a part. The focus of the course is process centric. Your role in process performance improvement is to be through the use of the methodologies of Six Sigma, Lean and Process Management. By taking this course you will have a well rounded and firm grasp of many of the tools of these methodologies. We firmly believe this is one of the most effective classes you will ever take and it is our commitment to assure that this is the case. We begin in the Define Phase with “Understanding Six Sigma”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

2

Understanding Six Sigma Overview The core fundamentals of this phase are Definitions, History, Strategy, Problem Solving and Roles and Responsibilities.

Understanding Six Sigma Definitions History

We will examine the meaning of each of these and show you how to apply them.

Strategy Problem Solving Roles & Responsibilities Six Sigma Fundamentals Selecting Projects Elements of Waste Wrap Up & Action Items

Six Sigma Vocabulary In order to do something differently, we must first learn the vocabulary and understand the meaning of the various terms. Please read and be familiar with these terms.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

3

Understanding Six Sigma Definition of Six Sigma

Six Sigma represents a great deal to a business enterprise. At the basic level it is a process improvement tool set yet when linked to corporate strategy it becomes an operating philosophy of great assistance to the accomplishment of corporate objectives. What is Six Sigma…as a Methodology? As a methodology to be followed by practitioners Six Sigma is a standardized approach to problem solving or opportunity grasping. Following the DMAIC approach through a Six Sigma project creates a framework whereby one has the greatest probability of arriving at a true solution with associated means of retaining the gains. Additionally, with Six Sigma broadly based throughout the company it creates a standardized way for co-workers to communicate thereby improving understanding. Also, with its commitment to data and specific operating metrics a system is established whereby process performance can be tracked in a succinct manner. Should any process begin yielding out-of-spec performance it is known immediately. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

4

Understanding Six Sigma What is Six Sigma…as a Business Strategy? Six Sigma is also a business strategy that provides new knowledge and capability to employees so they can better organize the process activity of the business, solve business problems and make better decisions. Using Six Sigma is now a common way to solve business problems and remove waste resulting in significant profitability improvements. In addition to improving profitability, customer and employee satisfaction are also improved. This pictorial depicts the percentage of data which falls between Standard Deviations within a Normal Distribution. In this specific example, 99.73% of the data points fall within +/- 3 Standard Deviations of the Mean; this is Six Sigma performance. Those data points at the outer edge of the bell curve represent the greatest variation in our process. They are the ones causing customer dissatisfaction and we want to eliminate them. What is Six Sigma…as a Philosophy? As a philosophy of Operational Excellence, Six Sigma has a targeted quality performance level of no more than 3.4 defects per million opportunities. When an output of a process operates at this quality performance, it is said to be a “Six Sigma performing process.” It takes a great deal of effort and time to move through all the processes of a company. However, that effort is positively correlated to the operating performance of the company. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

5

Understanding Six Sigma What is Six Sigma…as a Process Measurement? Additionally, Six Sigma is a process measurement and management system that enables employees and companies to take a process oriented view of the entire business. Using the various concepts embedded in Six Sigma, key processes are identified, the outputs of these processes are prioritized, the capability is determined, improvements are made, if necessary, and a management structure is put in place to assure the ongoing success of the business. With key metrics identified for processes a commonality of measurement is established for all processes. What is Six Sigma…as a Benchmark? As you can see from this graphic, as the sigma performance level is improved the operating efficiency improves yielding lower costs for the same output and more customer satisfying products and services.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

6

Understanding Six Sigma What is Six Sigma…as a Tool? Six Sigma has not created new tools. It is the appropriate application of the tools that makes all the difference. This course teaches the use of these tools, equips a belt with the knowledge of which should be utilized when and what the desired results of their application is expected to be. Additionally, the use of the tools is additive; that is, information garnered from one leads to the use of another until such time as the sought after answers are obtained.

What is Six Sigma…as a Tool? This is a high level view of the approach used when conducting what is called a “Six Sigma Project”. A Six Sigma project is a specific effort to fix a defined problem. We will be studying this approach throughout most of this course.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

7

Understanding Six Sigma What is Six Sigma…as a Goal? To give you a better example the concept of the sigma level can be related to hanging fruit. The higher the fruit, the more challenging it is to obtain. And, the more sophisticated the tools necessary to obtain them.

Goal

highest level of process performance possible.

5+ Sigma

Sweet Fruit Design for Six Sigma Bulk of Fruit Process Characterization and Optimization

3 - 5 Sigma

3 Sigma

1 - 2 Sigma

Low Hanging Fruit Basic Tools of Problem Solving Ground Fruit Simplify and Standardize

History of Six Sigma

And so it begins….. • 

1984 Bob Galvin of Motorola articulated the first objectives of a Process Improvement Program –  10x levels of improvement in service and quality by 1989 –  100x improvement by 1991 –  Six Sigma capability by 1992 –  Bill Smith, an engineer from Motorola, is the person credited as the father of Six Sigma

• 

1984 Texas Instruments and ABB Work closely with Motorola to further develop Six Sigma

It continues….. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

8

Understanding Six Sigma History of Six Sigma (cont.) • 

1994 Application experts leave Motorola

• 

1995 AlliedSignal begins Six Sigma initiative as directed by Larry Bossidy –  Captured the interest of Wall Street

• 

1995 General Electric, led by Jack Welch, began the most widespread undertaking of Six Sigma even attempted

• 

1997 to Present: Six Sigma spans industries worldwide

Keeps getting better!! And, as you may well know, Six Sigma has been embraced worldwide as a powerful and effective process improvement methodology. Its history continues to be written…

The Phase Approach of Six Sigma Six Sigma created a realistic and quantifiable goal in terms of its target of 3.4 defects per million operations. It was also accompanied by a methodology to attain that goal. That methodology was a problem solving strategy made up of four steps: measure, analyze, improve and control. When GE launched Six Sigma they improved the methodology to include the Define Phase.

Today the Define Phase is an important aspect to the methodology. Motorola was a mature culture from a process perspective and didn’t necessarily have a need for the Define Phase. Most organizations today DEFINITELY need it to properly approach improvement projects. As you will learn, properly defining a problem or an opportunity is key to putting you on the right track to solve it or take advantage of it.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

9

Understanding Six Sigma

C h a m p io n / P ro ce s s   O w ner

DMAIC Phases Roadmap

Identify  Problem  A rea

D e fin e

Determine  A ppropria te  Project  Focus Estima te  C O PQ

A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

A n a ly z e

Mea sure

C harter  Project

Im p r o v e

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C o n tr o l

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Implement  C ontrol  Pla n  to  Ensure  Problem  Does  N ot  Return

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Verify  Financia l  Impact

This roadmap provides an overview of the DMAIC approach. Define Phase Deployment Business  C a se S elected

Here is a more granular look of the Define Phase.

N otify  Belts  and  S takeholders

This is what you will later learn to be a Level 2 Process Map.

C reate  H ig h-­‐Level  Process  Map

Determine  A ppropriate  Project  Focus (Pareto,  Project  Desirability) Define  &  C harter  Project (Problem  S tatement,  O bjective,  Primary  Metric,  S econdary  Metric) N

Estimate  C O PQ A pproved Project   Focus

Recommend  Project  Focus Y C reate  Team

C harter  Team

Rea dy  for   Mea sure

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

10

Understanding Six Sigma Define Phase Deliverables The Define Phase deliverables listed above are discussed throughout the Define course. By the end of this course, you should understand what would be necessary to provide these deliverables in a presentation.

Deliverables: –  Charter Benefits Analysis –  Team Members (Team Meeting Attendance) –  Process Map – high level –  Primary Metric –  Secondary Metric(s) –  Lean Opportunities –  Stakeholder Analysis –  Project Plan –  Issues and Barriers

Six Sigma Strategy Six Sigma places the emphasis on the Process –  Using a structured, data driven approach centered on the customer Six Sigma can resolve business problems where they are rooted, for example: §  Month end reports §  Capital expenditure approval §  New hire recruiting Six Sigma is a Breakthrough Strategy –  Widened the scope of the definition of quality §  includes the value and the utility of the product/service to both the company and the customer.

Success of Six Sigma depends on the extent of transformation achieved in each of these levels. Six Sigma as a breakthrough strategy to process improvement. Many people mistakenly assume that Six Sigma only works in manufacturing type operations. That is categorically untrue. It applies to all aspects of either a product or service based business. Wherever there are processes, Six Sigma can improve their performance. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

11

Understanding Six Sigma Conventional Strategy Conventional definitions of quality focused on conformance to standards. Requirement or LSL

Bad

Target

Requirement or USL

Good

Bad

Conventional strategy was to create a product or service that met certain specifications. §  Assumed that if products and services were of good quality then their performance standards were correct. §  Rework was required to ensure final quality. §  Efforts were overlooked and unquantified (time, money, equipment usage, etc). The conventional strategy was to create a product or service that met certain specifications. It was assumed that if products and services were of good quality, then their performance standards were correct irrespective of how they were met. Using this strategy often required rework to ensure final quality or the rejection and trashing of some products and the efforts to accomplish this “inspect in quality” were largely overlooked and unquantified. You will see more about this issues when we investigate the Hidden Factory. Problem Solving Strategy

Th e   P r o b le m   S o lv in g   M e th o d o lo g y   fo cu s e s   o n : • • • •

Understa nding  the  rela tionship  between  independent  va ria bles   a nd  the  dependa nt  va ria ble. Identifying  the  vita l  few  independent  va ria bles  tha t  effect  the   dependa nt  va ria ble. O ptimiz ing  the  independent  va ria bles  so  a s  to  control  our   dependa nt  va ria ble(s). Monitoring  the  optimiz ed  independent  va ria ble(s).

Th e r e   a r e   m a n y   e x a m p le s   to   d e s cr ib e   d e p e n d a n t   a n d   in d e p e n d e n t   r e la tio n s h ip s . •

W e  describe  this  concept  in  terms  of  the  equa tion: •

This  equa tion  is  a lso  commonly  referred  to  a s  a  tra nsfer  function

Y=f (Xi) Th is   s im p ly   s ta te s   th a t   Y   is   a   fu n ctio n   o f   th e   X ’ s .     In   o th e r   w o r d s   Y   is   d icta te d   b y   th e   X ’ s .  

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

12

Understanding Six Sigma Problem Solving Strategy (contd) Y = f(x) is a key concept that you must fully understand and remember. It is a fundamental principle to the Six Sigma methodology. In its simplest form it is called “cause and effect”. In its more robust mathematical form it is called “Y is equal to a function of X”. In the mathematical sense it is data driven and precise, as you would expect in a Six Sigma approach. Six Sigma will always refer to an output or the result as a Y and will always refer to an input that is associated with or creates the output as an X. Another way of saying this is that the output is dependent on the inputs that create it through the blending that occurs from the activities in the process. Since the output is dependent on the inputs we cannot directly control it, we can only monitor it.

Example

Y=f (Xi) W h ich   p ro ce s s   v a ria b le s   (ca u s e s )   h a v e   critica l   im p a ct   o n   th e   o u tp u t   (e ffe ct)? Crusher Yield

Time to Close

Tool = f ( Feed, Speed,Material Type , Wear , Lubricant ) Correct Trial Sub Credit Entry = f (Balance ,Accounts,Accounts,Memos,Mistakes,X ) Applied

n

If we are so good at the X’s why are we constantly testing and inspecting the Y? Y=f(x) is a transfer function tool to determine what input variables (X’s) affect the output responses (Y’s). The observed output is a function of the inputs. The difficulty lies in determining which X’s are critical to describe the behavior of the Y’s. The X’s determine how the Y performs. In the Measure Phase we will introduce a tool to manage the long list of input variable and their relationship to the output responses. It is the X-Y Matrix or Input-Output Matrix.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

13

Understanding Six Sigma Y=f(X) Exercise

Exercise: Consider establishing a Y = f(x) equation for a simple everyday activity such as producing a cup of espresso. In this case our output or Y is espresso.

Espresso

=f

( X1 , X , X , X , X n 2 3 4

)

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

14

Understanding Six Sigma Six Sigma Strategy

We use a variety of Six Sigma tools to help separate the vital few variables effecting our Y from the trivial many. Some processes contain many, many variables. However, our Y is not effected equally by all of them.

(X1)

(X10)

(X8)

(X7)

By focusing on the vital few we instantly gain leverage.

(X4)

(X3)

(X5)

(X9) Archimedes said: Give me a lever big enough and fulcrum on which to place it and I shall move the world.

(X2)

(X6)

Archimedes not shown actual size!

As you go through the application of DMAIC you will have a goal to find the root causes to the problem you are solving. Remember that a vital component of problem solving is cause and effect thinking or Y=f(X). To aid you in doing so, you should create a visual model of this goal as a funnel a funnel that takes in a large number of the “trivial many contributors,” and narrows them to the “vital few contributors” by the time they leave the bottom. At the top of the funnel you are faced with all possible causes - the “vital few” mixed in with the “trivial many.” When you work an improvement effort or project, you must start with this type of thinking. You will use various tools and techniques to brainstorm possible causes of performance problems and operational issues based on data from the process. In summary, you will be applying an appropriate set of “analytical methods” and the “Y is a function of X” thinking, to transform data into the useful knowledge needed to find the solution to the problem. It is a mathematical fact that 80 percent of a problem is related to six or fewer causes, the X’s. In most cases it is between one and three. The goal is to find the one to three Critical X’s from the many potential causes when we start an improvement project. In a nutshell, this is how the Six Sigma methodology works.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

15

Understanding Six Sigma Breakthrough Strategy

P e rfo rm a n ce

Ba d

66-­‐S -­‐Sig igm maa BBre a k th ro re a k th rouugghh

UC UCLL

O ld   S ta n d a r d LC LCLL

UC UCLL

N e w   S ta n d a r d

LC LCLL

G ood

Tim e

Juran’s Q uality  Handbook by  Joseph  Juran

By utilizing the DMAIC problem solving methodology to identify and optimize the vital few variables we will realize sustainable breakthrough performance as opposed to incremental improvements or, even worse, temporary and non-sustainable improvement. The image above shows how after applying the Six Sigma tools, variation stays within the specification limits. VOC, VOB, VOE The foundation of Six Sigma requires Focus on the voices of the Customer, the Business, and the Employee which provides:

VOC is Customer Driven VOB is Profit Driven VOE is Process Driven

§  Awareness of the needs that are critical to the quality (CTQ) of our products and services §  Identification of the gaps between “what is” and “what should be” §  Identification of the process defects that contribute to the “gap” §  Knowledge of which processes are “most broken” §  Enlightenment as to the unacceptable Costs of Poor Quality (COPQ) Six Sigma puts a strong emphasis on the customer because they are the ones assessing our performance and they respond by either continuing to purchase our products and services or….by NOT! So, while the customer is the primary concern we must keep in mind the Voice of the Business – how do we meet the business’s needs so we stay in business? And we must keep in mind the Voice of the Employee how do we meet employees needs such that they remain employed by our firm and remain inspired and productive? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

16

Understanding Six Sigma Six Sigma Roles and Responsibilities There are many roles and responsibilities for successful implementation of Six Sigma.

MBB Black Belts Green Belts

§  §  §  §  §  § 

Executive Leadership Champion/Process Owner Master Black Belt Black Belt Green Belt Yellow Belt

Yellow Belts Just like a winning sports team, various people who have specific positions or roles have defined responsibilities. Six Sigma is similar - each person is trained to be able to understand and perform the responsibilities of their role. The end result is a knowledgeable and well coordinated winning business team. The division of training and skill will be delivered across the organization in such a way as to provide a specialist: it is based on an assistant structure much as you would find in the medical field between a Doctor, 1st year Intern, Nurse, etc. The following slides discuss these roles in more detail. In addition to the roles described herein, all other employees are expected to have essential Six Sigma skills for process improvement and to provide assistance and support for the goals of Six Sigma and the company. Six Sigma has been designed to provide a structure with various skill levels and knowledge for all members of the organization. Each group has well defined roles and responsibilities and communication links. When all individuals are actively applying Six Sigma principles, the company operates and performs at a higher level. This leads to increased profitability, and greater employee and customer satisfaction. Executive Leadership Not all Six Sigma deployments are driven from the top by executive leadership. The data is clear, however, that those deployments that are driven by executive management are much more successful than those that are not. §  Makes decision to implement the Six Sigma initiative and develop accountability method §  Sets meaningful goals and objectives for the corporation §  Sets performance expectations for the corporation §  Ensures continuous improvement in the process §  Eliminates barriers The executive leadership owns the vision for the business, they provide sponsorship and set expectations for the results from Six Sigma. They enable the organization to apply Six Sigma and then monitor the progress against expectations.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

17

Understanding Six Sigma Champion/Process Owner Champions identify and select the most meaningful projects to work on, they provide guidance to the Six Sigma Belt and open the doors for the belts to apply the process improvement technologies. §  Own project selection, execution control, implementation and realization of gains §  Own Project selection §  Obtain needed project resources and eliminates roadblocks §  Participate in all project reviews §  Ask good questions… §  One to three hours per week commitment Champions are responsible for functional business activities and to provide business deliverables to either internal or external customers. They are in a position to be able to recognize problem areas of the business, define improvement projects, assign projects to appropriate individuals, review projects and support their completion. They are also responsible for a business roadmap and employee training plan to achieve the goals and objectives of Six Sigma within their area of accountability.

Master Black Belt MBB should be well versed with all aspects of Six Sigma, from technical applications to Project Management. MBBs need to have the ability to influence change and motivate others. §  Provide advice and counsel to Executive Staff §  Provide training and support

MBB

- In class training - On site mentoring §  Develop sustainability for the business §  Facilitate cultural change

A Master Black Belt is a technical expert, a “go to” person for the Six Sigma methodology. Master Black Belts mentor Black Belts and Green Belts through their projects and support Champions. In addition to applying Six Sigma, Master Black Belts are capable of teaching others in the practices and tools. Being a Master Black Belt is a full time position.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

18

Understanding Six Sigma Black Belt Black Belts are application experts and work projects within the business. They should be well versed with The Six Sigma Technologies and have the ability to drive results.

Black Belts

§  Project team leader §  Facilitates DMAIC teams in applying Six Sigma methods to solve problems §  Works cross-functionally §  Contributes to the accomplishment of organizational goals §  Provides technical support to improvement efforts

A Black Belt is a project team leader, working full time to solve problems under the direction of a Champion, and with technical support from the Master Black Belt. Black Belts work on projects that are relatively complex and require significant focus to resolve. Most Black Belts conduct an average of 4 to 6 projects a year -- projects that usually have a high financial return for the company.

Green Belt Green Belts are practitioners of Six Sigma Methodology and typically work within their functional areas or support larger Black Belt Projects. •  Well versed in the definition & measurement of critical processes - Creating Process Control Systems

Green Belts

§  Typically works project in existing functional area §  Involved in identifying improvement opportunities §  Involved in continuous improvement efforts - Applying basic tools and PDCA §  Team members on DMAIC teams - Supporting projects with process knowledge & data collection

Green Belts are capable of solving problems within their local span of control. Green Belts remain in their current positions, but apply the concepts and principles of Six Sigma to their job environment. Green Belts usually address less complex problems than Black Belts and perform at least two projects per year. They may also be a part of a Black Belt’s team, helping to complete the Black Belt project.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

19

Understanding Six Sigma Yellow Belt

Yellow Belts

§  Provide support to Black Belts and Green Belts as needed §  May be team members on DMAIC teams - Supporting projects with process knowledge and data collection

Yellow Belts participate in process management activities. They fully understand the principles of Six Sigma and are capable of characterizing processes, solving problems associated with their work responsibilities and implementing and maintaining the gains from improvements. They apply Six Sigma concepts to their work assignments. They may also participate on Green and Black Belt projects. The Life of a Six Sigma Belt Training as a Six Sigma Belt can be one of the most rewarding undertakings of your career and one of the most difficult. You can expect to experience: §  §  §  §  §  §  §  § 

Hard work (becoming a Six Sigma Belt is not easy) Long hours of training Be a change agent for your organization Work effectively as a team leader Prepare and present reports on progress Receive mentoring from your Master Black Belt Perform mentoring for your team members ACHIEVE RESULTS!

You’re going places!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

20

Understanding Six Sigma Black & Green Belt Certification To achieve certification, Belts typically must:: §  Complete all course work: - Be familiar with tools and their application - Practice using tools in theoretical situations - Discuss how tools will apply to actual projects §  Demonstrate application of learning to training project: - Use the tools to effect a financially measurable and significant business impact through their projects - Show ability to use tools beyond the training environment §  Must complete two projects within one year from beginning of training

We’ll be watching!!

§  Achieve results and make a difference §  Submit a final report which documents tool understanding and application as well as process changes and financial impact for each project Organizational Behaviors All players in the Six Sigma process must be willing to step up and act according to the Six Sigma set of behaviors. §  Leadership by example: “walk the talk” §  Encourage and reward individual initiative §  Align incentive systems to support desired behaviors §  Eliminate functional barriers §  Embrace “systems” thinking §  Balance standardization with flexibility Six Sigma is a system of improvement. It develops people skills and capability for the participants. It consists of proven set of analytical tools, project-management techniques, reporting methods and management methods combined to form a powerful problem-solving and business-improvement methodology. It solves problems, resulting in increased revenue and profit, and business growth. The strategy of Six Sigma is a data-driven, structured approach to managing processes, quantifying problems, and removing waste by reducing variation and eliminating defects. The tactics of Six Sigma are the use of process exploration and analysis tools to solve the equation of Y = f(X) and to translate this into a controllable practical solution. As a performance goal, a Six Sigma process produces less than 3.4 defects per million opportunities. As a business goal, Six Sigma can achieve 40% or more improvement in the profitability of a company. It is a philosophy that every process can be improved, at breakthrough levels. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

21

Understanding Six Sigma At this point, you should be able to: §  Describe the objectives of Six Sigma §  Describe the relationship between variation and sigma §  Recognize some Six Sigma concepts §  Recognize the Six Sigma implementation model §  Describe the general roles and responsibilities in Six Sigma

You have now completed Define Phase – Understanding Six Sigma.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

22

Lean Six Sigma Black Belt Training

Define Phase Six Sigma Fundamentals

Now we will continue in the Define Phase with the “Six Sigma Fundamentals”. The output of the Define Phase is a well developed and articulated project. It has been correctly stated that 50% of the success of a project is dependent on how well the effort has been defined. There’s that Y=f(X) thinking again.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

23

Six Sigma Fundamentals Overview The core fundamentals of this phase are Process Maps, Voice of the Customer, Cost of Poor Quality and Process Metrics.

U n d e r s ta n d in g   S ix   S ig m a S ix   S ig m a   Fu n d a m e n ta ls PPro roce cessss    M Maa ppss

We will examine the meaning of each of these and show you how to apply them.

VV ooice ice    oof  f  th thee    CCuussto tom m eerr CCoosst  t  oof  f  PPoooor   r  Q Q uuaa lity lity PPro roce cessss    M Meetr trics ics S e le ctin g   P r o je cts Ele m e n ts   o f   W a s te W ra p   U p   &   A ctio n   Ite m s

What is a Process?

W h y   h a v e   a   p ro ce s s   fo cu s ? – So  we  can  understand  how  and  why  work  g ets  done – To  characteriz e  customer  &  supplier  relationships – To  manag e  for  maximum  customer  satisfaction  while  utiliz ing   minimum  resources – To  see  the  process  from  start  to  finish  as  it  is   cu rr e n tly being   performed – Blame  the  process,  n o t the  people proc•ess  (pros′es)  n. proc•ess  (pros′es)  n. –– AA  rep  rep eetitiv titiv ee    aa nndd    ssyy sste tem m aa tic tic series   series   of  s te p s   o r   a ctiv itie s where  in p u ts are  modified  to  achieve   of  s te p s   o r   a ctiv itie s where  in p u ts are  modified  to  achieve   a  value-­‐ a  value-­‐aadded  o dded  ouutp tp uutt What is a Process? Many people do or conduct a process everyday but do you really think of it as a process? Our definition of a process is a repetitive and systematic series of steps or activities where inputs are modified to achieve a value-added output. Usually a successful process needs to be well defined and developed. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

24

Six Sigma Fundamentals Examples of Processes We go thru processes everyday. Below are some examples of processes. Can you think of other processes within your daily environment? §  Injection molding §  Recruiting staff §  Decanting solutions §  Processing invoices §  Filling vial/bottles §  Conducting research §  Crushing ore §  Opening accounts §  Refining oil §  Reconciling accounts §  Turning screws §  Filling out a timesheet §  Building custom homes §  Distributing mail §  Paving roads §  Backing up files §  Changing a tire §  Issuing purchase orders Process Maps

Purpose: –  Identify the complexity of the process –  Communicate the focus of problem solving

Living documents: –  They represent what is currently happening, not what you think is happening. –  They should be created by the people who are closest to the process

t

Remember that a process is a blending of inputs to produce some desired output. The intent of each Start task, activity and step is to add value, as perceived by the customer, to the product or service we are producing. You cannot discover if this is the case until you have adequately mapped the process.

Process Map

Step A

Step B

Step C

In sp ec

Process Mapping, also called flowcharting, is a technique to visualize the tasks, activities and steps necessary to produce a product or a service. The preferred method for describing a process is to identify it with a generic name, show the workflow with a Process Map and describe its purpose with an operational description.

Step D

Finish

There are many reasons for creating a Process Map: - It helps all process members understand their part in the process and how their process fits into the bigger picture. - It describes how activities are performed and how the work effort flows, it is a visual way of standing above the process and watching how work is done. In fact, Process Maps can be easily uploaded into model and simulation software allowing you to simulate the process and visually see how it works. - It can be used as an aid in training new people. - It will show you where you can take measurements that will help you to run the process better. - It will help you understand where problems occur and what some of the causes may be. - It leverages other analytical tools by providing a source of data and inputs into these tools. - It identifies many important characteristics you will need as you strive to make improvements. The individual processes are linked together to see the total effort and flow for meeting business and customer needs. In order to improve or to correctly manage a process, you must be able to describe it in a way that can be easily understood. Process Mapping is the most important and powerful tool you will use to improve the effectiveness and efficiency of a process. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

25

Six Sigma Fundamentals Process Map Symbols

Standard symbols for Process Mapping: (available in Microsoft Office™, Visio™, iGrafx™ , SigmaFlow™ and other products)

A RECTANGLE indicates an activity. Statements within the rectangle should begin with a verb

A PARALLELAGRAM shows that there are data

A DIAMOND signifies a decision point. Only two paths emerge from a decision point: No and Yes

An ELLIPSE shows the start and end of the process

An ARROW shows the connection and direction of flow

1

A CIRCLE WITH A LETTER OR NUMBER INSIDE symbolizes the continuation of a flowchart to another page

There may be several interpretations of some of the process mapping symbols; however, just about everyone uses these primary symbols to document processes. As you become more practiced you will find additional symbols useful, i.e. reports, data storage etc. For now we will start with just these symbols. High Level Process Map At a minimum a high level Process Map must include; start and stop points, all process steps, all decision points and directional flow. Also be sure to include Value Categories such as Value Added (Customer Focus) and Value Enabling (External Stakeholder focus).

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

26

Six Sigma Fundamentals Process Map Example B

START

LOGON TO PC & APPLICATIONS

SCHEDULED PHONE TIME?

E

Z

N

Y

WALK-IN N

CALL

PROVIDE RESPONSE PHONE& NOTE DATA ENDS

PUT ON HOLD, REFER TO REFERENCES

PHONE DATA CAPTURE BEGINS

ANSWER?

DETERMINE WHO IS INQUIRING

Y

ANSWER?

N

C

Y

OFF HOLD AND ARRANGE CALL BACK PHONE DATA ENDS

B

F

ENTER APPROPRIATE SSAN (#,9s,0s)

CREATE A CASE INCL CASE TYPE DATE/TIME, & NEEDED BY

N

Y UPDATE ENTRIES INCL OPEN DATE/TIME

Y

AUTO ROUTE

ROUTE

N

Y CASE CLOSED

N CASE TOOL RECORD?

ACCESS CASE TOOL

OLD CASE

N

DETERMINE NATURE OF CALL & CONFIRM UNDERSTANDING

A

N

IF EMP DATA NOT POPULATED, ENTER

QUERY INTERNAL HRSC SME(S)

ACCESS CASE TOOL

D

EXAMINE NEXT NOTE OR RESEARCH ITEM

IMMEDIATE RESPONSE AVAILABLE?

Y CALL or WALK-IN?

Z

TRANSFER CALL

N LOGON TO PHONE

PHONE TIME

Y

TRANSFER APPROPRIATE?

Y

SCHEDULED PHONE TIME?

Y

A

D

LOGOFF PHONE, CHECK MAIL,E-MAIL,VOICE MAIL

C

N

Call Center Process Map

Z

REVIEW CASE TOOL HISTORY & TAKE NOTES

ADD TO RESEARCH LIST

N TAKE ACTION or DO RESEARCH

Y

CLOSE CASE W/ DATE/TIME

E

GO TO F or E DEPENDING ON CASE

E NEXT

F

Cross Functional Process Map When multiple departments or functional groups are involved in a complex process it is often useful to use cross functional Process Maps. –  Draw in either vertical or horizontal Swim Lanes and label the functional groups and draw the Process Map

G eneral   A ccounting

Bank

Financial   A ccounting

Vendor

Department

These are best S e n d in g   Fu n d   Tra n s fe r s used in transactional A C H  – A utomated A ttach  A C H Request C lea ring  House. form  to Sta rt transfer processes or Invoice   where the Fill  out  A C H Receive No Produce  an process involves End enrollment pa yment Invoice form several departments. Match  ag ainst Ma inta in  da ta ba se Vendor bank  batch to  ba la nce  A C H Input  info  into Yes info  in tra nsfers and  daily  cash The lines drawn web  interface FRS? batch   horizontally A ccepts  transactions, across the map transfer  money,  and provide  batch  total represent different Review  and 2 1 .0 3 .0 Process departments in Bank Journey  Entry transfer  in Reconciliation FRS the company and are usually referred to as Swim Lanes. By mapping in this manner one can see how the various departments are interdependent in this process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

27

Six Sigma Fundamentals Process Map Exercise

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

28

Six Sigma Fundamentals Do you know your Customer?

Knowing your customer is more than just a handshake. It is necessary to clearly understand their needs. In Six Sigma we call this understanding the CTQ s or critical to customer characteristics.

Voice Of the Customer

Critical to Customer Characteristics

An important element of Six Sigma is understanding your customer. This is called VOC or Voice of the Customer. By doing this allows you to find all of the necessary information that is relevant between your product/process and customer, better known as CTQ’s (Critical to Quality). The CTQ’s are the customer requirements for satisfaction with your product or service. Voice of the Customer Do you feel confident that you know what your customer wants? There of four steps that can help you in understanding your customer. These steps focus on the customer’s perspective of features, your company’s integrity, delivery mechanisms and perceived value versus cost.

LSS Black Belt Manual XL v11

Voice of the Customer or VOC seems obvious; after all, we all know what the customer wants. Or do we?? 1.  Features Does the process provide what the customers expect and need? How do you know?

2. Integrity Is the relationship with the customer centered on trust? How do you know?

3. Delivery Does the process meet the customer s time frame? How do you know?

4. Expense Does the customer perceive value for cost? How do you know?

© 2013 e-Careers Limited

29

Six Sigma Fundamentals What is a Customer? Every process has a deliverable. The person or entity who receives this deliverable is a customer. There are two different types of customers; External and Internal. People generally forget about the Internal customer and they are just as important as the customers who are buying your product.

There  are  different  types  of  customers  which  dictates  how  we  interact   with  them  in  the  process,  in  order  to  identify  customer  and  supplier   requirements  we  must  first  define  who  the  customers  are: Ex te r n a l – Direct:  those  who  receive  the  output  of  your  services,  they  g enerally  are   the  source  of  your  revenue – Indirect:  those  who  do  not  receive  or  pay  for  the  output  of  your services   but  ha ve  a  vested  interest  in  wha t  you  do  (g overnment  ag encies)

In te r n a l -­‐ those  within  your  org aniz ation who  receive  the  output  of  your work  

Value Chain

The relationship from one process to the next in an organization creates a

Value Chain of suppliers and receivers of process outputs. Each process has a contribution and accountability to the next to satisfy the external customer. External customers needs and requirements are best met when all process owners work cooperatively in the Value Chain.

Careful – each move has many impacts!! The disconnect from Design and Production in some organizations is a good example. If Production is not fed the proper information from Design how can Production properly build a product? Every activity (process) must be linked to move from raw materials to a finished product on a store shelf. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

30

Six Sigma Fundamentals What is a CTQ?

Example: Making an Online Purchase Reliability – Correct amount of money is taken from account Responsiveness – How long to you wait for product after the Merchant receives their money Security – is your sensitive banking information stored in secure place

Developing CTQ’s The steps in developing CTQ’s are identifying the customer, capturing the Voice of the Customer and finally validating the CTQ’s.

Step 1

Step 2

Step 3

LSS Black Belt Manual XL v11

Identify Customers •  Listing •  Segmentation •  Prioritization Validate CTQ s •  Translate VOC to CTQ s •  Prioritize the CTQ s •  Set Specified Requirements •  Confirm CTQ s with customer Capture VOC •  Review existing performance •  Determine gaps in what you need to know •  Select tools that provide data on gaps •  Collect data on the gaps

© 2013 e-Careers Limited

31

Six Sigma Fundamentals Cost of Poor Quality (COPQ) Another important tool from this phase is COPQ, Cost of Poor Quality. COPQ represents the financial opportunity of your team’s improvement efforts. Those opportunities are tied to either hard or soft savings. COPQ, is a symptom measured in loss of profit (financial quantification) that results from errors (defects) and other inefficiencies in our processes. This is what we are seeking to eliminate!

•  COPQ stands for Cost of Poor Quality •  As a Six Sigma Belt, one of your tasks will be to estimate COPQ for your process •  Through your process exploration and project definition work you will develop a refined estimate of the COPQ in your project •  This project COPQ represents the financial opportunity of your team s improvement effort (VOB) •  Calculating COPQ is iterative and will change as you learn more about the process

No, not that kind of cop queue!!

You will use the concept of COPQ to quantify the benefits of an improvement effort and also to determine where you might want to investigate improvement opportunities. The Essence of COPQ

• C O PQ  helps  us  understand  the  financial  impact  of  problems  created   by  defects. • C O PQ  is  a  s y m p to m ,   not  a d e fe ct – Projects  fix  defects  with  the  intent  of  improving  symptoms.

• The  concepts  of  traditional  Q uality  C ost  are  the  foundation  for   C O PQ . – Externa l,  Interna l,  Prevention,  A ppra isa l

• A  sig nificant  portion  of  C O PQ  from  any  defect  comes  from  effects that  are  difficult  to  quantify  and  must  be  estimated.

There are four elements that make up COPQ; External Costs, Internal Costs, Prevention Costs and Appraisal Costs. Internal Costs are opportunities of error found in a process that is within your organization. Whereas, External Costs are costs associated to the finish product associated with the internal and external customer.

Prevention Costs are typically cost associated to product quality, this is viewed as an investment that companies make to ensure product quality. The final element is Appraisal costs, these are tied to product inspection and auditing. This idea was of COPQ was defined by Joseph Juran and is a great point of reference to gain a further understanding. Over time and with Six Sigma, COPQ has migrated towards the reduction of waste. Waste is a better term, because it includes poor quality and all other costs that are not integral to the product or service your company provides. Waste does not add value in the eyes of customers, employees or investors. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

32

Six Sigma Fundamentals COPQ - Categories

Internal COPQ

Prevention •  •  •  • 

•  Quality Control Department •  Inspection •  Quarantined Inventory •  Etc…

Error Proofing Devices Supplier Certification Design for Six Sigma Etc…

Detection

External COPQ •  Warranty •  Customer Complaint Related Travel •  Customer Charge Back Costs •  Etc…

•  •  •  • 

Supplier Audits Sorting Incoming Parts Repaired Material Etc…

COPQ - Iceberg Generally speaking COPQ can be classified as tangible (easy to see) and intangible (hard to see). Visually you can think of COPQ as an iceberg. Most of the iceberg is below the water where you cannot see it.

W a r r a n ty

In s p e ctio n

R e co d e

R e je cts

V is ib le   C o s ts Lo s t   s a le s

En g in e e r in g   ch a n g e   o r d e rs Tim e   v a lu e   o f   m o n e y M o r e   S e t-­‐u p s W o r k in g   C a p ita l   a llo ca tio n s

Rew o rk

(le s s   o b v io u s )

La te   d e liv e ry

Ex p e d itin g   co s ts

Ex ce s s   in v e n to r y Lo n g   cy cle   tim e s

Similarly the tangible Ex ce s s iv e   Ma te r ia l O rd e r s / P la n n in g quality costs are H id d e n   C o s ts Lo s t   C u s to m e r   Lo y a lty costs the organization is rather conscious of, may be measuring already or could easily be measured. The COPQ metric is reported as a percent of sales revenue. For example tangible costs like inspection, rework, warranty, etc can cost an organization in the range of 4 percent to 10 percent of every sales dollar it receives. If a company makes a billion dollars in revenue, this means there are tangible wastes between 40 and 100 million dollars. Even worse are the intangible Costs of Poor Quality. These are typically 20 to 35% of sales. If you average the intangible and tangible costs together, it is not uncommon for a company to be spending 25% of their revenue on COPQ or waste. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

33

Six Sigma Fundamentals COPQ and Lean

W a s te   d o e s   n o t   a d d ,   s u b tr a ct   o r   o th e r w is e   m o d ify   th e   th r o u g h p u t   in   a   w a y   th a t   is   p e rce iv e d   b y   th e   cu s to m e r   to   a d d   v a lu e . •

In  some  cases,  waste  may be   necessary,  but  should  be   recog niz ed  and  explored: – –

• •

Le a n   En te rp ris e S e v e n   Ele m e n ts   o f   W a s te   *

Inspection,  C orrection,  W a iting   in  suspense Decision  dia monds,  by   definition,  a re  non-­‐va lue  a dded

u u u u u u u

O ften,  waste  can  provide   opportunities  for  additional  defects   to  occur. W e  will  discuss  Lean  in  more   detail  later  this  week.

C orrection Processing C onveya nce Motion W a iting O verproduction Inventory

Implementing Lean fundamentals can also help identify areas of COPQ. Lean will be discussed later.

COPQ and Lean

While hard savings are always more desirable because they are easier to quantify, it is also necessary to think about soft savings. COPQ – Hard Savings •  •  •  •  • 

Labor Savings Cycle Time Improvements Scrap Reductions Hidden Factory Costs Inventory Carrying Cost

LSS Black Belt Manual XL v11

COPQ – Soft Savings •  •  •  •  • 

Gaining Lost Sales Missed Opportunities Customer Loyalty Strategic Savings Preventing Regulatory Fines

© 2013 e-Careers Limited

34

Six Sigma Fundamentals COPQ Exercise

Ex e rcis e   o b je ctiv e :   Identify  current  C O PQ   opportunities  in  your  direct  area. 1 . Brainstorm  a  list  of  C O PQ  opportunities. 2 . C ateg oriz e  the  top  3  sources  of  C O PQ  for  the   four  classifications: • • • •

Interna l Externa l Prevention Detection Use Excel file “Define Templates.xls”, COPQ Brainstorm

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

35

Six Sigma Fundamentals The Basic Six Sigma Metrics

The previous slides have been discussing process management and the concepts behind a process perspective. Now we begin to discuss process improvement and the metrics used. Some of these metrics are: DPU: defects per unit produced. DPMO: defects per million opportunities, assuming there is more than one opportunity to fail in a given unit of output. RTY: rolled throughput yield, the probability that any unit will go through a process defect-free. Cycle Time Defined

Th in k   o f   C y cle   Tim e   in   te rm s   o f   y o u r   p ro d u ct   o r   tra n s a ctio n   in   th e   e y e s   o f   th e   cu s to m e r   o f   th e   p ro ce s s : – It  is  the  time  required  for  the  product  or  transaction  to  g o  throug h  the   entire  process,  from  beg inning  to  end – It  is  not  simply  the  “touch  time” of  the  value-­‐a dded  portion  of  the  process

W h a t   is   th e   cy cle   tim e   o f   th e   p ro ce s s   y o u   m a p p e d ? Is   th e re   a n y   v a ria tio n   in   th e   cy cle   tim e ?     W h y ? Cycle time includes any wait or queue time for either people or products. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

36

Six Sigma Fundamentals Defects Per Unit (DPU) DPU or Defects per Unit quantifies individual defects on a unit and not just defective units. A returned unit or transaction can be defective and have more than one defect. Defect: A physical count of all errors on a unit, regardless of the disposition of the unit. EXAMPLES: An error in a Online transaction has (typed wrong card number, internet failed). In this case one online transaction had 2 defects (DPU=2).

Six  Sig ma  methods  quantify  individual  defects  and  not  just  defectives – Defects  account  for  all  errors  on  a  unit • A  unit  may  have  multiple  defects • A n  incorrect  invoice  may  have  the  wrong  amount  due   and  the  wrong   due  date – Defectives  simply  classifies  the  unit  bad • Doesn’t  matter  how  many  defects  there  are • The  invoice  is  wrong ,  ca uses  are  unknown – A  unit: • Is  the  measure  of  volume  of  output  from  your  area. • Is  observable  and  countable.    It  has  a  discrete  start  and  stop  p oint. • It  is  an  individua l  measurement  and  not  an  averag e  of   measurements. Tw o   D e fects

O n e   D e fectiv e  

A Mobile Computer that has 1 broken video screen, 2 broken keyboard keys and 1 dead battery, has a total of 4 defects. (DPU=4) Is a process that produces 1 DPU better or worse than a process that generates 4 DPU? If you assume equal weight on the defects, obviously a process that generates 1 DPU is better; however, cost and severity should be considered. However, the only way you can model or predict a process is to count all the defects. First Time Yield Traditional metrics when chosen poorly can lead the team in a direction that is not consistent with the focus of the business. Some of the metrics we must be concerned about would be FTY FIRST TIME YIELD. It is very possible to have 100% FTY and spend tremendous amounts in excess repairs and rework. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

37

Six Sigma Fundamentals Rolled Throughput Yield

Instead of relying on FTY - First Time Yield, a more efficient metric to use is RTY-Rolled Throughput Yield. RTY has a direct correlation (relationship) to Cost of Poor Quality. In the few organizations where data is readily available, the RTY can be calculated using actual defect data. The data provided by this calculation would be a binomial distribution since the lowest yield possible would be zero. As depicted here, RTY is the multiplied yield of each subsequent operation throughout a process (X1 * X2 * X3…) RTY Estimate Sadly, in most companies there is not enough data to calculate RTY in the long term. Installing data collection practices required to provide such data would not be cost effective. In those instances, it is necessary to utilize a prediction of RTY in the form of edpu (e to the negative dpu).

• In  many  org aniz ations  the  long  term  data  required  to   calculate  RTY  is  not  availa ble,  we  can  however  estimate   RTY  using  a  known  DPU  as  long  as  certain  conditions  are   met. • The  Poisson  distribution  g enerally  holds  true  for  the   random  distribution  of  defects  in  a  unit  of  product  and  is   the  basis  for  the  estimation. – The  best  estimate  of  the  proportion  of  units  containing   no  defects,  or  RTY  is:

When using the e-dpu equation to pu RTY  =  e-­‐-­‐ddpu calculate the probability of a The mathematical constant e is the base of the natural logarithm. product or service moving through e ≈ 2.71828 18284 59045 23536 02874 7135 the entire process without a defect, there are several things that must be held for consideration. While this would seem to be a constraint, it is appropriate to note that if a process has in excess of 10% defects, there is little need to concern yourself with the RTY. In such extreme cases, it would be much more prudent to correct the problem at hand before worrying about how to calculate yield. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

38

Six Sigma Fundamentals Deriving RTY from DPU The  Binomial  distribution  is  the  true  model  for  defect  data,  but the  Poisson  is  the   convenient  model  for  defect  data.    The  Poisson  does  a  g ood  job  of  predicting   when  the  defect  rates  are  low. Poisson Poisson VS VS Binomial Binomial (r=0,n=1) (r=0,n=1)

120% 120% 100% 100%

Yield(RTY) (RTY) Yield

Yield Yield (Binomial) (Binomial) Yield Yield (Poisson) (Poisson)

80% 80% 60% 60% 40% 40% 20% 20% 0% 0% 0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

Probability Probabilityof ofaadefect defect

0.7 0.7

0.8 0.8

0.9 0.9

1.0 1.0

Probability Yield Probability Yield of ofaadefect defect (Binomial) (Binomial) 0.0 100% 0.0 100% 0.1 90% 0.1 90% 0.2 80% 0.2 80% 0.3 70% 0.3 70% 0.4 60% 0.4 60% 0.5 50% 0.5 50% 0.6 40% 0.6 40% 0.7 30% 0.7 30% 0.8 20% 0.8 20% 0.9 10% 0.9 10% 1.0 0% 1.0 0%

Yield Yield (Poisson) (Poisson) 100% 100% 90% 90% 82% 82% 74% 74% 67% 67% 61% 61% 55% 55% 50% 50% 45% 45% 41% 41% 37% 37%

% %Over Over Estimated Estimated 0% 0% 0% 0% 2% 2% 4% 4% 7% 7% 11% 11% 15% 15% 20% 20% 25% 25% 31% 31% 37% 37%

B in o m ia l n  =  number  of  units r  =  number  of  predicted  defects p  =  probability  of  a  defect  occurrence q  =  1  -­‐ p

P o is s o n

For  low  defect  rates  (p  <  0.1 ),  the  Poisson  approximates  the  Binomial  fairly  well.

Our goal is to predict yield. For process improvement, the “yield” of interest is the ability of a process to produce zero defects (r=0). Question: What happens to the Poisson equation when r=0? Deriving RTY from DPU - Modeling

To what value is the P(0) converging? Note: Ultimately, this means that you need the ability to track all the individual defects which occur per unit via your data collection system.

U n it O p p o rtu n ity •

•

B a s ic   Q u e s tio n :     W hat  is  the  likelihood  of   producing  a  unit  with  z ero  defects?

For  the  unit  shown  a bove  the  following   da ta  wa s  g a thered:   – 6 0  defects  observed – 6 0  units  processed   W ha t  is  the  DPU?

•

W ha t  is  probability  tha t  any  g iven   opportunity  will  be  a  defect?

•

W ha t  is  the  proba bility  tha t  any  g iven   opportunity  will  N O T  be  a  defect  is:

•

The  proba bility  tha t  a ll  1 0  opportunities   on  sing le  unit  will  be  defect-­‐free  is:

RTY RTY for for DPU DPU = = 11

0.368 0.368 0.364 0.364

Yield Yield

Given a probability that any opportunity is a defect = # defects / (# units x # opps per unit):

0.36 0.36 0.356 0.356 0.352 0.352 0.348 0.348 10 10

Opportunities 10 100 1000 10000 100000 1000000

100 100

P(defect) 0.1 0.01 0.001 0.0001 0.00001 0.000001

1000 1000

10000 10000

Chances Chances Per Per Unit Unit P(no defect) 0.9 0.99 0.999 0.9999 0.99999 0.999999

100000 100000

1000000 1000000

RTY (Prob defect free unit) 0.34867844 0.366032341 0.367695425 0.367861046 0.367877602 0.367879257

If  we  extend  the  concept  to  an  infinite  number   of  opportunities,  all  at  a  DPU  of  1 .0 ,  we  will   approach  the  value  of  0 .3 6 8 .

Probability that an opportunity is a defect = 0.1 Probability that an opportunity is not a defect = 1 - 0.1 = 0.9 Probability that all 10 opportunities are defect-free = 0.910 = 0.34867844 LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

39

Six Sigma Fundamentals RTY Prediction — Poisson Model

When r = 1, this equation simplifies to: (dpu)*edpu

•

Use  the  binomial  to  estimate  the  probability  of  a  discrete  event (g ood/ bad)  when  sampling  from  a  relatively  larg e  population,   n  >  1 6 ,  &    p  <  0 .1 .

•

W hen  r= 0 ,  we  compute  the  probability  of  finding  z ero  defects  per unit  (called  “rolled  throug hput  yield”).

•

The  table  to  the  rig ht  shows  the  proportion  of  product  which  will   have

Y=

–

0  defects  (r= 0 )

–

1  defect  (r= 1 )                                W h e n   D P U = 1

–

2  defects  (r= 2 ),  etc…

•

W hen,  on  averag e,  we  have  a  process,  with  1  defect  per  unit,   then  we  say  there  is  a  3 6 .7 9 %  cha nce  of  finding  a  unit  with  z ero defects.  There  is  only  a  1 .5 3 %  chance  of  finding  a  unit  with  4   defects.

•

W hen  r= 1 ,  this  equation  simplifies  to:

•

To  predict  the  %  of  units  with  z ero  defect  (i.e.,  RTY ): –

count  the  number  of  defects  found

–

count  the  number  of  units  produced

–

compute  the  dpu  and  enter  it  in  the  dpu  equa tion:

(d p u ) r e – d p u r r! p [r] 0 1 2 3 4 5 6 7 8

0 .3 6 7 9 0 .3 6 7 9 0 .1 8 3 9 0 .0 6 1 3 0 .0 1 5 3 0 .0 0 3 1 0 .0 0 0 5 0 .0 0 0 1 0 .0 0 0 0

The point of this slide is to demonstrate the mathematical model used to predict the probability of an outcome of interest. It has little practical purpose other than to acquaint the Six Sigma Belt with the math behind the tool they are learning and let them understand that there is a logical basis for the equation. Six Sigma Metrics – Calculating DPU The  DPU  for  a  g iven  operation  can  be  calculated  by  dividing  the  number  of   defects  found  in  the  operation  by  the  number  of  units  entering  the  operational   step. 1 0 0   p a rts   b u ilt 2   d e fe cts   id e n tifie d   a n d   co r re cte d d p u   =   0 .0 2 S o   R TY   fo r   th is   s te p   w o u ld   b e   e -­‐.0 2   (.9 8 0 1 9 9 )   o r   9 8 .0 2 % . R TY 1 = 0 .9 8 d p u   =   .0 2

R TY 2 = 0 .9 8 d p u   =   .0 2

R TY 3 = 0 .9 8 d p u   =   .0 2

R TY 4 = 0 .9 8 d p u   =   .0 2

R TY 5 = 0 .9 8 d p u   =   .0 2

RRTY = 0 .9 0 TY TO TO TT = 0 .9 0 44 ddppuuTO =   .1 TO TT =   .1

If  the  process  had  only  5  process  steps  with  the  same  yield  the   process   RTY  would  be:    0 .9 8  *  0 .9 8  *  0 .9 8  *  0 .9 8  *  0 .9 8  =  0 .9 0 3 9 2 1  or  9 0 .3 9 %.    Since  our   metric  of  primary  concern  is  the  C O PQ  of  this  process,  we  can  sa y  that  in  less  tha n  9 %  of   the  time  we  will  be  spending  dollars  in  excess  of  the  pre-­‐d etermined  standard  or  value   added  amount  to  which  this  process  is  entitled.

N o te :   R TY ’ s   m u s t   b e   m u ltip lie d   a cro s s   a   p ro ce s s ,   D P U ’ s   a re   a d d e d   a cro s s   a   p ro ce s s .

When the number of steps in a process continually increase, we then continue to multiply the yield from each step to find the overall process yield. For the sake of simplicity let’s say we are calculating the RTY for a process with 8 steps. Each step in our process has a yield of .98. Again, there will be a direct correlation between the RTY and the dollars spent to correct errors in our process. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

40

Six Sigma Fundamentals Focusing our Effort – FTY vs. RTY

Assume we are creating two products in our organization that use similar processes.

Product B FTY = 80% Product A FTY = 80%

How do you know what to work on? *None of the data used herein is associated with the products shown herein. Pictures are no more than illustration to make a point to teach the concept.

If we chose only to examine the FTY in our decision making process, it would be difficult to determine the process and product on which our resources should be focused. As you have seen, there are many factors behind the final number for FTY. That’s where we need to look for process improvements. Focusing our Effort – FTY vs. RTY

Answer Slide questions. Now we have a better idea of: “What does a defect cost?” “What product should get the focus?”

Let s look at the DPU of each product assuming equal opportunities and margin… Product B Product A dpu 100 / 100 = 1 dpu

dpu 200 / 100 = 2 dpu

Now, can you tell which to work on? The product with the highest DPU? …think again! More questions to answer How much more time and/or raw material are required? How much extra floor space do we need? How much extra staff or hours are required to perform the rework? How many extra shipments are we paying for from our suppliers? How much testing have we built in to capture our defects? *None of the data used herein is associated with the products shown herein. Pictures are no more than illustration to make a point to teach the concept.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

41

Six Sigma Fundamentals At this point, you should be able to: §  Describe what is meant by “Process Focus” §  Generate a Process Map §  Describe the importance of VOC, VOB and VOE, and CTQ’s §  Explain COPQ §  Describe the Basic Six Sigma metrics §  Explain the difference between FTY and RTY §  Explain how to calculate “Defects per Unit” (DPU)

You have now completed Define Phase – Six Sigma Fundamentals. Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

42

Lean Six Sigma Black Belt Training

Define Phase Selecting Projects

Now we will continue in the Define Phase with the “Selecting Projects”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

43

Selecting Projects Overview The core fundamentals of this phase are Selecting Projects, Refining and Defining and Financial Evaluation. The output of the Define Phase is a well developed and articulated project. It has been correctly stated that 50% of the success of a project is dependent on how well the effort has been defined.

U n d e r s ta n d in g   S ix   S ig m a S ix   S ig m a   Fu n d a m e n ta ls S e le ctin g   P r o je cts Selecting Selecting  Projects  Projects Refining Refining  &  Defining  &  Defining     Fina Financial  Evaluation ncial  Evaluation Ele m e n ts   o f   W a s te W ra p   U p   &   A ctio n   Ite m s

Approaches to Project Selection Here are three approaches for identifying projects. Do you know what the best approach is? The most popular process for generating and selecting projects is by holding “brainstorming” sessions. In brainstorming sessions a group of people get together, sometimes after polling process owners for what “blatantly obvious” problems are occurring, and as a team try to identify and refine a list of problems that MAY be causing issues in the organization. Furthermore in an organization that does not have an intelligent problem-solving methodology in-place, such as Six Sigma, Lean or even TQM, what follows the project selection process brainstorm is ANOTHER brainstorming session focused on coming up with ideas on how to SOLVE these problems. Although brainstorming itself can be very structured it falls far short of being a systematic means of identifying projects that will reduce cost of poor quality throughout the organization. Why…for several reasons. One, it does not ensure that we are dealing with the most important high-impact problems, but rather what happens to be the recent fire fight initiatives. Two, usually brainstorming does not utilize a data based approach, it relies on tribal knowledge, experience and what people THINK is happening. As we know what people THINK is happening and what is ACTUALLY happening can be two very different things. In this module we are going to learn about establishing a structured approach for Project Selection.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

44

Selecting Projects Project Selection – Core Components

With every project there must be a minimum of 3 deliverables: Business Case Project Charter Benefits Analysis Project Selection - Governance

R e s p o n s ib le P a rty

R e s o u r ce s

B u s in e s s Ca se

C hampion (Process  O wner)

Business  Unit Members

N/A

P ro je ct C h a rte r

Six  Sig ma  Belt

C hampion  (Process   O wner)  &   Master  Black  Belt

O ng oing

B e n e fits A n a ly s is

Benefits  C apture Ma nag er  or   Unit  Fina ncial  Rep

C hampion  (Process   O wner)  &   Six  Sig ma  Belt

O ng oing  / D,M,A ,I,C

LSS Black Belt Manual XL v11

Fre q u e n cy   o f   U p d a te

© 2013 e-Careers Limited

45

Selecting Projects A Structured Approach – A Starting Point These are some examples of Business Metrics or Key Performance Indicators. What metric should you focus on…it depends? What is the project focus? What are your organizations strategic goals?

The Starting Point is defined by the Champion or Process Owner with the Business Case is the output. –  The tree diagram is used to facilitate the process of breaking down the metric of interest.

!  EBIT !  Cycle time

Level 2

!  Defects !  Cost

Level 2 Level 1

!  Revenue

Level 2

Are Cost of Sales !  Complaints preventing growth? Level 2 Are customer !  Compliance complaints resulting in lost !  Safety earnings? Are excess cycle times and yield issues eroding market share? Is the fastest growing division of the business the refurbishing department? It depends because the motivation for organizations vary so much and all projects should be directly aligned with the organizations objectives. Answer the question: What metrics are my department not meeting? What is causing us pain? A Structured Approach - Snapshot Once a metric point has been determined another important question needs to be asked - What is my metric a function of? In other words what are all of the things that affect this metric?

Th e   K P I’ s   n e e d   to   b ro k e n   d o w n   in to   a ctio n a b le   le v e ls . B u s in e s s   M e a s u re s K e y   P e rfo rm a n ce   In d ica to rs   (K P Is )

A ctio n a b le   Le v e l

Le v e l   2 Le v e l   3 A ctiv itie s P ro ce s s es We utilize the Tree Diagram to facilitate Le v e l   1 the process of Le v e l   4 Le v e l   2 A ctiv itie s P ro ce s s es breaking down the metric of interest. When creating the tree diagram you will eventually run into activities which are made up of processes. This is where projects will be focused because this is where defects, errors and waste occur.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

46

Selecting Projects Business Case Components – Level 1

P rim a ry   B u s in e s s   M e a s u re   o r   K e y   P e rfo rm a n ce   In d ica to r   (K P I)

Le v e l   2

Le v e l   3

A ctiv itie s

P ro ce s s es

Le v e l   2

Le v e l   4

A ctiv itie s

P ro ce s s es

Le v e l   1

– Focus  on  one prima ry  business  mea sure  or  KPI. – Prima ry  business  mea sure  should  bea r  a  direct  line  of  site  with   the   org a niz a tions  stra teg ic  objective. – A s  the  C ha mpion  na rrows  in  on  the  g rea test  opportunity  for   improvement,  this  provides  a  clea r  focus  for  how  the  success  will  be   mea sured. Be sure to start with higher level metrics, whether they are measured at the Corporate Level, Division Level or Department Level, projects should track to the Metrics of interest within a given area. Primary Business Measures or Key Performance Indicators (KPI’s) serve as indicators of the success of a critical objective. Business Case Components – Business Measures

Primary Business Measure

Business Measure

Business Measure

Activities

Processes

Business Measure

Business Measure

Activities

Processes

Unless you can measure it…. You can t do much about it!!

Post business measures (product/service) of the primary business measure are lower level metrics and must focus on the end product to avoid internal optimization at expense of total optimization.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

47

Selecting Projects Business Case Components - Activities

P rim a ry   B u s in es s   M e a s u re

B u s in e s s   M e a s u re

B u s in e s s   M e a s u re

A ctiv itie s

P ro ce s s es

B u s in e s s   M e a s u re

B u s in e s s   M e a s u re

A ctiv itie s

P ro ce s s es

Y   =   f (x 1 ,   x 2 ,   x 3 … x n ) 1 st C all  Resolution  =  f (C alls,  O perators,  Resolutions… x n ) Black  Box  Testing  =  f   (Specifications,  Simulation,  Eng ineering … x n ) Business measures are a function of activities. These activities are usually created or enforced by direct supervision of functional managers. Activities are usually made up of a series of processes or specific processes. Business Case Components - Processes

P rim a ry   B u s in es s   M e a s u re

B u s in e s s   M e a s u re

B u s in e s s   M e a s u re

A ctiv itie s

P ro ce s s es

B u s in e s s   M e a s u re

B u s in e s s   M e a s u re

A ctiv itie s

P ro ce s s es

Y   =   f (x 1 ,   x 2 ,   x 3 … x n ) Resolutions  =  f (N ew  C ustomers,  Existing  C ustomers,  Defective  Products… x n ) S imula tion  =  f (Desig n,  Da ta ,  modeling … x n ) The processes represent the final stage of the matrix where multiple steps result in the delivery of some output for the customer. These deliverables are set by the business and customer and are captured within the Voice of the Customer, Voice of the Business or Voice of the Employee. What makes up these process are the X’s that determine the performance of the Y which is where the actual breakthrough projects should be focused.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

48

Selecting Projects What is a Business Case? The Business Case is created to ensure the strategic need for your project. It is the first step in project description development.

The Business Case communicates the need for the project in terms of meeting business objectives. The components are: –  Output unit (product/service) for external customer –  Primary business measure of output unit for project –  Baseline performance of primary business measure –  Gap in baseline performance of primary business measure from business objective

Let s get down to business!!

Business Case Example

During FY 2005, the 1st Time Call Resolution Efficiency for New Customer Hardware Setup was 89% . This represents a gap of 8% from the industry standard of 93% that amounts to US $2,000,000 of annualized cost impact.

Here is an example of an Business Case. This defines the problem and provides evidence of the problem.

As you review this statement remember the following format of what needs to be in a Business Case: WHAT is wrong, WHERE and WHEN is it occurring, what is the BASELINE magnitude at which it is occurring and what is it COSTING me? You must take caution to avoid under-writing a Business Case. Your natural tendency is to write too simplistically because you are already familiar with the problem. You must remember that if you are to enlist support and resources to solve your problem, others will have to understand the context and the significance in order to support you. The Business Case cannot include any speculation about the cause of the problem or what actions will be taken to solve the problem. It’s important that you don’t attempt to solve the problem or bias the solution at this stage. The data and the Six Sigma methodology will find the true causes and solutions to the problem. The next step is getting project approval.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

49

Selecting Projects The Business Case Template

Fill   in   th e   B la n k s   fo r   Y o u r   P r o je ct: During  ___________________________________  ,  the  ____________________    for (P e r io d   o f   tim e   fo r   b a s e lin e   p e rfo r m a n ce )     (P rim a ry   b u s in e s s   m e a s u re )

________________________  was  _________________  .     (A   k e y   b u s in e s s   p r o ce s s )   (B a s e lin e   p e rfo r m a n ce ) This  g ap  of  ____________________________ (B u s in e s s   o b je ctiv e   ta rg e t   v s .   b a s e lin e )

from  ___________________  represents  ____________________  of  cost impact.   (B u s in e s s   o b je ctiv e ) (C o s t   im p a ct   o f   g a p )

You need to make sure that your own Business Case captures the units of pain, the business measures, the performance and the gaps. If this template does not seem to be clicking use your own or just free form your Business Case ensuring that its well articulated and quantified. Business Case Exercise

Using the Excel file ‘Define Templates.xls’, Business Case, perform this exercise. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

50

Selecting Projects What is a Project Charter? The Charter expands on the Business Case, it clarifies the projects focus and measures of project performance and is completed by the Six Sigma Belt. Components: • The  Problem • Project  Scope • Project  Metrics • Prima ry  &  Secondary • G ra phical  Displa y  of  Project  Metrics • Prima ry  &  Secondary • Sta nda rd  project  informa tion • Project,  Belt  &  Process  O wner   na mes • Sta rt  da te  &  desired  End  da te • Division  or  Business  Unit • Supporting  Ma ster  Bla ck  Belt   (Mentor)   • Team  Members

The Project Charter is an important document – it is the initial communication of the project. The first phases of the Six Sigma methodology are Define and Measure. These are known as “Characterization” phases that focus primarily on understanding and measuring the problem at hand. Therefore some of the information in the Project Charter, such as primary and secondary metrics, can change several times. By the time the Measure Phase is wrapping up the Project Charter should be in its final form meaning defects and the metrics for measuring them are clear and agreed upon. As you can see some of the information in the Project Charter is self explanatory, especially the first section. We are going to focus on establishing the Problem Statement and determining Objective Statement, scope and the primary and secondary metrics. Project Charter - Definitions •

P ro b le m   S ta te m e n t -­‐ A rticula tes  the  pa in  of  the  defect or  error in  the   process.

•

O b je ctiv e   S ta te m e n t – S ta tes  how  much  of  a n  improvement  is  desired   from  the  project.

•

S co p e – A rticula tes  the  bounda ries  of  the  project.

•

P rim a ry   M e tric – The  a ctua l  mea sure of  the  defect  or  error  in  the  process.

•

S e co n d a ry   M e tric(s ) – Mea sures  of  potentia l  consequences  (+  /   -­‐)  a s  a   result  of  cha ng es  in  the  process.

•

C h a rts – G raphica l  displa ys  of  the  Prima ry  a nd  S econda ry  Metrics  over  a   period  of  time.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

51

Selecting Projects Project Charter - Problem Statement Migrate the Business Case into a Problem Statement…

First the Business Case will serve as the Problem Statement, as the Belt learns more about the process and the defects that are occurring.

Project Charter – Objective & Scope Consider the following for constructing your Objective & Scope: What represents a significant improvement? §  X amount of an increase in yield §  X amount of defect reduction §  Use Framing Tools to establish the initial scope A project’s main objective is to solve a problem! The area highlighted is for articulating how much of a reduction or improvement will yield a significant impact to the process and business. This is the starting point creating your project’s Objective Statement.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

52

Selecting Projects Pareto Analysis Assisting you in determining what inputs are having the greatest impact on your process is the Pareto Analysis approach.

The 80:20 Rule Examples

•

2 0 %  of  the  time  expended  produced  8 0 %  of  the  results

•

8 0 %  of  your  phone  calls  g o  to  2 0 %  of  the  na mes  on  your  list

•

2 0 %  of  the  streets  ha ndle  8 0 %  of  the  traffic

•

8 0 %  of  the  meals  in  a  restaurant  come  from  2 0 %  of  the  menu

•

2 0 %  of  the  paper  ha s  8 0 %  of  the  news

•

8 0 %  of  the  news  is  in  the  first  2 0 %  of  the  article

•

2 0 %  of  the  people  cause  8 0 %  of  the  problems

•

2 0 %  of  the  features  of  an  application  are  used  8 0 %  of  the  time

LSS Black Belt Manual XL v11

Here are some examples of the 80:20 Rule. Can you think of any other examples?

© 2013 e-Careers Limited

53

Selecting Projects Pareto Chart - Tool Multi level Pareto Charts are used in a drill down fashion to get to Root Cause of the tallest bar.

The Pareto Charts are often referred to as levels. For instance the first graph is called the first level, the next the second level and so on. Start high and drill down. Let’s look at how we interpret this and what it means.

Let’s look at the following example. By drilling down from the first level we see that Department J makes up approximately 60% of the scrap and part Z101 makes up 80% of Dept J’s scrap. See how we are creating focus and establishing a line of sight? You many be eager to jump into trying to fix the problem once you have identified it, BE CAREFUL. This is what causes rework and defects in the first place. Follow the methodology, be patient and you will eventually be led to a solution.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

54

Selecting Projects Pareto Chart - Example

Open the “Define Data Sets.xls” file and go to the “Call Center” sheet. Select “Graphic Tools>Basic Pareto Chart”. Select Failure Mode for “Pareto Category (X)” and Count for the “Optional Numeric Count (Y)”. You may also choose to add a title to your chart. When you hit “Next” you are brought to the “Basic Pareto” options. Take this time now to select the defaults you will be using. Cum Sum Line should be set to “On Top of First Bar”. Under the “Chart Options tab” select only “Data Table” for Data Labels. Finally select “Percent” for “Secondary Y Axis”. If you wish you may modify the “Gap Width” between the bars. Ensure “Save Defaults” is checked and click “Finish”. When your Pareto shows up like this your focus is probably too broad. A good indication of having too broad of a focus is when your Pareto looks flat. It’s telling you that there is no one or two inputs that are impacting your process. Multiple inputs are having similar effects. You need to reduce the scope of the project to get to a more granular level.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

55

Selecting Projects Pareto Chart – Example (Cont.) Let’s look at the problem a little differently… - Using a higher level scope for the first Pareto may help in providing focus. - Create another Pareto as shown below.

This gives a better picture of which product category produces the highest defect count.

Now we’ve got something to work with. Notice the 80% area…. draw a line from the 80% mark across to the cumulative percent line (Red Line) in the graph as shown here. Which cards create the highest Defect Rates? Now you are beginning to see what needs work to improve the performance of your project. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

56

Selecting Projects Pareto Chart – Example (cont.)

Remember to keep focused on finding the biggest bang for the buck.

This does not mean there is NO opportunity for improvements to be had; it simply means nothing obvious is sticking out at this level. So let’s keep looking. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

57

Selecting Projects Project Charter – Primary Metric Moving on to the next element of the Project Charter…, Using the Excel file ‘Define Templates.xls’, Project Charter, perform the following exercise: Since we will be narrowing in on the defect thru the Measure Phase it is common for the Primary Metric to change several times while we struggle to understand what is happening in our process of interest. The Primary Metric also serves as the gauge for when we can claim victory with the project. SigmaXL® also has a Project Charter template. You can access it through, “SigmaXL>Templates and Calculators>DMAIC and DFSS Templates>Team/Project Charter”. Project Charter – Secondary Metrics Consider a project focused on improving duration of call times (cycle time) in a call center. If we realize a reduction in call time you would want to know if anything else was effected. Think about it…did overtime increase / reduce, did labor increase / reduce, what happened to customer satisfaction ratings? These are all things that should be measured in order to accurately capture the true effect of the improvement. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

58

Selecting Projects Project Charter – Metric Charts The Project Charter template includes the graphing capabilities shown here. It is OK to not use this template but in any case ensure you are regularly measuring the critical metrics.

Project Charter Exercise Using the Excel file ‘Define Templates.xls’, Project Charter, perform this exercise.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

59

Selecting Projects What is the Financial Evaluation?

The Financial Evaluation establishes the value of the project. The components are: –  Impact •  Sustainable •  One-off

–  Allocations •  Cost Codes / Accounting System

–  Forecast •  Cash flow •  Realization schedule

OK, let s add it up!! Standard financial principles should be followed at the beginning and end of the project to provide a true measure of the improvement’s effect on the organization. A financial representative of the firm should establish guidelines on how savings will be calculated throughout the Six Sigma deployment. Benefits Capture - Calculation “Template”

W h a tev er   y o u r   o rg a n iz a tio n ’ s   p ro to co l   m a y   b e   th es e   a s p e cts   s h o u ld   b e   a cco u n ted   fo r   w ith in   a n y   im p ro v em en t   p ro ject.

I M P A C T

C O S T C O D E S

Sustainable Impact

Reduced Costs

F O R E C A S T

LSS Black Belt Manual XL v11

There  are  two  types  of   Impact,  O ne  O ff &   Sustainable

“One-Off” Impact

Increased Revenue

Costs

Realization Schedule (Cash Flow)

Implementation

Capital

C ost  C odes allocate  the   impact  to  the   appropriate  area  in  the   “Books” Forecasts allow  for   proper  manag ement  of   projects  and  resources

By Period (i.e. Q1,Q2,Q3,Q4)

© 2013 e-Careers Limited

60

Selecting Projects Benefits Capture - Basic Guidelines

When calculating project benefits you should follow these steps.

Benefits Capture - Categorization Here is an example of how to categorize your project’s impact.

A •  Projects directly impact the Income Statement or Cash Flow Statement. B •  Projects impact the Balance Sheet (working capital).

C•  Projects avoid expense or investment due to known or expected events in the future (cost avoidance). D•  Projects are risk management, insurance, Safety, Health, Environment and Community related projects which prevent or reduce severity of unpredictable events.

You don t want to take this one home!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

61

Selecting Projects Benefits Calculation Involvement & Responsibility

P ro je ct   S e le ctio n

D -­‐M -­‐A -­‐I-­‐C

Im p le m e n ta tio n

6   M o n th   A u d it

Fina ncial   Representative

Fina ncial   Representative

Fina ncial   Representative

Fina ncial   Representative

C ha mpion   & Process  O wner

Black  Belt

C ha mpion   & Process  O wner

Process  O wner

It is highly recommended that you follow the involvement governance shown here.

Benefits Capture - Summary

•  Performance tracking for Six Sigma Projects should use the same discipline that would be used for tracking any other high-profile projects. •  The A-B-C-D categories can be used to illustrate the impact of your project or a portfolio of projects. •  Establish The Governess Grid for Responsibility & Involvement.

It s a wrap!! Just some recommendations to consider when running your projects or program.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

62

Selecting Projects Benefits Calculation Template

The Benefits Calculation Template facilitates and aligns with the aspects discussed for Project Accounting. The Excel file ‘Define Templates.xls’, BENEFITS CALCULATION TEMPLATE.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

63

Selecting Projects At this point, you should be able to: §  Understand the various approaches to project selection §  Articulate the benefits of a “Structured Approach” §  Refine and Define the business problem into a Project Charter to display critical aspects of an improvement project §  Make initial financial impact estimate

You have now completed Define Phase – Selecting Projects.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

64

Lean Six Sigma Black Belt Training

Define Phase Elements of Waste

Now we will continue in the Define Phase with “Elements of Waste”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

65

Elements of Waste Overview The core fundamentals of this phase are the 7 components of waste and 5S. We will examine the meaning of each of these and show you how to apply them.

U n d e r s ta n d in g   S ix   S ig m a S ix   S ig m a   Fu n d a m e n ta ls S e le ctin g   P r o je cts Ele m e n ts   o f   W a s te 77    CCoom m ppoonneennts ts    oof  f  W W aa sste te 55 SS W ra p   U p   &   A ctio n   Ite m s

Definition of Lean

“Lean  Enterprise  is  based  on  the  premise  that  anywhere   work  is  being  done,  waste  is  being  generated. The  Lean  Enterprise  seeks  to  organiz e  its  processes  to  the   optimum  level,  through  the  continual  focus  on  the   identification  and  elimination  of  waste.” -­‐-­‐ B a rb a ra   W h e a t

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

66

Elements of Waste Lean – History 1885 Craft Production

1913 Mass Production

- Machine then harden - Fit on assembly - Customization - Highly skilled workforce - Low production rates - High Cost

- Part inter-changeability - Moving production line - Production engineering - "Workers don't like to think" - Unskilled labor - High production rates - Low cost - Persistent quality problems - Inflexible models

1955 - 1990 Toyota Production System - Worker as problem solver - Worker as process owner enabled by: -- Training -- Upstream quality -- Minimal inventory -- Just-in-time - Eliminate waste - Responsive to change - Low cost - Improving productivity - High quality product

1993 Lean Enterprise - "Lean" applied to all functions in enterprise value stream - Optimization of value delivered to all stakeholders and enterprises in value chain - Low cost - Improving productivity - High quality product - Greater value for stakeholders

Lean Manufacturing has been going on for a very long time, however the phrase is credited to James Womac in 1990. A small list of accomplishments are noted in the slide above primarily focused on higher volume manufacturing. Lean Six Sigma The essence of Lean is to concentrate effort on removing waste while improving process flow to achieve speed and agility at lower cost. The focus of Lean is to increase the percentage of value-added work performed by a company. Lean recognizes that most businesses spend a relatively small portion of their energies on the true delivery of value to a customer. While all companies are busy, it is estimated for some companies that as little as 10% of their time is spent on value-added work, meaning as much as 90% of time is allocated to non value-added activities, or waste. Forms of waste include: Wasted capital (inventory), wasted material (scrap), wasted time (cycle time), wasted human effort (inefficiency, rework) and wasted energy (energy inefficiency). Lean is a prescriptive methodology for relatively fast improvements across a variety of processes, from administrative to manufacturing applications. Lean enables your company to identify waste where it exists. It also provides the tools to make improvements on the spot.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

67

Elements of Waste Lean Six Sigma (cont.) Lean focuses on what calls the Value Stream, the sequence of activities and work required to produce a product or to provide a service. It is similar to a Linear Process Flow Map, but it contains its own unique symbols and data. The Lean method is based on understanding how the Value Stream is organized, how work is performed, which work is value added vs. non-value added and what happens to products and services and information as they flow through the Value Stream. Lean identifies and eliminates the barriers to efficient flow through simple, effective tools. Lean removes many forms of waste so that Six Sigma can focus on eliminating variability. Variation leads to defects, which is a major source of waste. Six Sigma is a method to make processes more capable through the reduction of variation. Thus the symbiotic relationship between the two methodologies.

Project Requirements for Lean

•  Perhaps one of the most criminal employee performance issues in today s organizations is generated not by a desire to cheat one’s employer but rather by a lack of regard to waste. •  In every work environment there are multiple opportunities for reducing the non-value added activities that have (over time) become an ingrained part of the standard operating procedure. •  These non-value added activities have become so ingrained in our process that they are no longer recognized for what they are, WASTE. •  waste (v.) Anything other than the minimum amount of time, material, people, space, energy, etc needed to add value to the product or service you are providing. •  The Japanese word for waste is muda.

Get that stuff outta here!! Employees at some level have been de-sensitized to waste: “That’s what we’ve always done.” Lean brings these opportunities for savings back into focus with specific approaches to finding and eliminating waste.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

68

Elements of Waste Seven Components of Waste

Muda is classified into seven components: –  –  –  –  –  –  – 

Overproduction Correction (defects) Inventory Motion Overprocessing Conveyance Waiting

Sometimes additional forms of muda are added: –  Under use of talent –  Lack of safety

Being Lean means eliminating waste. Overproduction Overproduction is producing more than the next step needs or more than the customer buys. –  It may be the worst form of waste because it contributes to all the others. Examples are: ü Preparing extra reports ü Reports not acted upon or even read ü Multiple copies in data storage ü Over-ordering materials ü Duplication of effort/reports Waste of Overproduction relates to the excessive accumulation of work-in-process (WIP) or finished goods inventory.

Producing more parts than necessary to satisfy the customer’s quantity demand thus leading to idle capital invested in inventory. Producing parts at a rate faster than required such that a work-in-process queue is created – again, idle capital. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

69

Elements of Waste Correction Correction of defects are as obvious as it sounds. Examples are: ü Incorrect data entry ü Paying the wrong vendor ü Misspelled words in communications ü Making bad product

Eliminate erors!!!

ü Materials or labor discarded during production

Waste of Correction includes the waste of handling and fixing mistakes. This is common in both manufacturing and transactional settings.

Correcting or repairing a defect in materials or parts adds unnecessary costs because of additional equipment and labor expenses. An example is the labor cost of scheduling employees to work overtime to rework defects. Inventory Inventory is the liability of materials that are bought, invested in and not immediately sold or used. Examples are: ü Transactions not processed ü Bigger “in box” than “out box” ü Over-ordering materials consumed in-house ü Over-ordering raw materials – just in case Waste of Inventory is identical to overproduction except that it refers to the waste of acquiring raw material before the exact moment that it is needed.

Inventory is a drain on an organization’s overhead. The greater the inventory, the higher the overhead costs become. If quality issues arise and inventory is not minimized, defective material is hidden in finished goods. To remain flexible to customer requirements and to control product variation, we must minimize inventory. Excess inventory masks unacceptable change-over times, excessive downtime, operator inefficiency and a lack of organizational sense of urgency to produce product. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

70

Elements of Waste Motion Motion is the unnecessary movement of people and equipment. – 

This includes looking for things like documents or parts as well as movement that is straining.

Examples are: ü Extra steps ü Extra data entry ü Having to look for something

Waste of Motion examines how people move to ensure that value is added.

Any movement of people or machinery that does not contribute added value to the product, i.e. programming delay times and excessive walking distance between operations.

Overprocessing Overprocessing is tasks, activities and materials that don’t add value. – 

Can be caused by poor product or tool design as well as from not understanding what the customer wants. Examples are: ü Sign-offs ü Reports that contain more information than the customer wants or needs

Waste of Over-processing relates to over-processing anything that may not be adding value in the eyes of the customer.

ü Communications, reports, emails, contracts, etc that contain more than the necessary points (briefer is better) ü Voice mails that are too long

Processing work that has no connection to advancing the line or improving the quality of the product. Examples include typing memos that could be had written or painting components or fixtures internal to the equipment. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

71

Elements of Waste Conveyance Conveyance is the unnecessary movement of material and Goods. – 

Steps in a process should be located close to each other so movement is minimized.

Examples are: ü Extra steps in the process ü Distance traveled ü Moving paper from place to place

Waste of Conveyance is the movement of material.

Conveyance is incidental, required action that does not directly contribute value to the product. Perhaps it must be moved however, the time and expense incurred does not produce product or service characteristics that customers see. It’s vital to avoid conveyance unless it is supplying items when and where they are needed (i.e. just-in-time delivery). Waiting Waiting is nonproductive time due to lack of material, people, or equipment. – 

Can be due to slow or broken machines, material not arriving on time, etc. Examples are: ü Processing once each month instead of as the work comes in ü Showing up on time for a meeting that starts late ü Delayed work due to lack of communication from another internal group

Waste of Waiting is the cost of an idle resource.

Idle time between operations or events, i.e. an employee waiting for machine cycle to finish or a machine waiting for the operator to load new parts. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

72

Elements of Waste Waste Identification Exercise

Ex e rcis e   o b je ctiv e :   To  identify  waste  that  occurs  in   your  processes. W rite  an  example  of  each  type  of  muda  below: – – – – – – –

O verproduction C orrection   Inventory     Motion     O verprocessing   C onveyance   W aiting

___________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

73

Elements of Waste 5S – The Basics 5S is a process designed to organize the workplace, keep it neat and clean, maintain standardized conditions, and instill the discipline required to enable each individual to achieve and maintain a world class work environment.

Seiri - Put things in order Seiton - Proper Arrangement Seiso – Clean Seiketsu – Purity Shitsuke - Commitment

The term “5S” derives from the Japanese words for five practices leading to a clean and manageable work area. The five “S” are:

‘Seiri' means to separate needed tools, parts and instructions from unneeded materials and to remove the latter. 'Seiton' means to neatly arrange and identify parts and tools for ease of use. 'Seiso' means to conduct a cleanup campaign. 'Seiketsu' means to conduct seiri, seiton and seiso at frequent, indeed daily, intervals to maintain a workplace in perfect condition. 'Shitsuke' means to form the habit of always following the first four S’s. Simply put, 5S means the workplace is clean, there is a place for everything and everything is in its place. The 5S will create a work place that is suitable for and will stimulate high quality and high productivity work. Additionally it will make the workplace more comfortable and a place of which you can be proud. Developed in Japan, this method assume no effective and quality job can be done without clean and safe environment and without behavioral rules. The 5S approach allows you to set up a well adapted and functional work environment, ruled by simple yet effective rules. 5S deployment is done in a logical and progressive way. The first three S’s are workplace actions, while the last two are sustaining and progress actions. It is recommended to start implementing 5S in a well chosen pilot workspace or pilot process and spread to the others step by step.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

74

Elements of Waste English Translation There have been many attempts to force 5 English “S” words to maintain the original intent of 5S from Japanese. Listed below are typical English words used to translate: 1. Sort (Seiri) 2. Straighten or Systematically Arrange (Seiton) 3. Shine or Spic and Span (Seiso) 4. Standardize (Seiketsu) 5. Sustain or Self-Discipline (Shitsuke)

Place things in such a way that they can be easily reached whenever they are needed

Straighten Sort Identify necessary items and remove unnecessary ones, use time management

Self - Discipline Make 5S strong in habit. Make problems appear and solve them.

Shine

5S

Visual sweep of areas, eliminate dirt, dust and scrap. Make workplace shine.

Standardize Work to standards, maintain standards, wear safety equipment.

Regardless of which “S” words you use, the intent is clear: Organize the workplace, keep it neat and clean, maintain standardized conditions and instill the discipline required to enable each individual to achieve and maintain a world class work environment.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

75

Elements of Waste 5S Exercise

Ex e rcis e   o b je ctiv e :   :   To  identify  elements  of  5 S  in   your  workplace. W rite  an  example  for  each  of  the  5 S ’s  below: • • • • •

S ort S tra ig hten S hine S ta nda rdiz e S elf-­‐D iscipline

____________________ ____________________ ____________________   ____________________ ____________________

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

76

Elements of Waste At this point, you should be able to: §  Describe 5S §  Identify and describe the 7 Elements of Waste §  Provide examples of how Lean Principles can affect your area

You have now completed Define Phase – Elements of Waste.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

77

Lean Six Sigma Black Belt Training

Define Phase Wrap Up and Action Items

Now we will conclude the Define Phase with “Wrap Up and Action Items”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

78

Wrap Up and Action Items Define Phase Overview—The Goal

The goal of the Define Phase is to: •  Identify a process to improve and develop a specific Six Sigma project. –  Six Sigma Belts define critical processes, sub-processes and elaborate the decision points in those processes.

•  Define is the contract phase of the project. We are determining exactly what we intend to work on and estimating the impact to the business. •  At the completion of the Define Phase you should have a description of the process defect that is creating waste for the business. Goooooaaaaalllll!!!

Define Action Items

At this point you should all understand what is necessary to complete these action items associated with Define. –  Charter Benefits Analysis –  Team Members –  Process Map – high level –  Primary Metric –  Secondary Metric(s) –  Lean Opportunities –  Stakeholder Analysis –  Project Plan –  Issues and Barriers

LSS Black Belt Manual XL v11

Deliver the Goods!! © 2013 e-Careers Limited

79

Wrap Up and Action Items Six Sigma Behaviors

•  Being tenacious, courageous •  Being rigorous, disciplined •  Making data-based decisions •  Embracing change & continuous learning •  Sharing best practices

Walk the Walk!!

Each player in the Six Sigma process must be A ROLE MODEL for the Six Sigma culture. Define Phase — The Roadblocks

Look for the potential roadblocks and plan to address them before they become problems: –  No historical data exists to support the project. –  Team members do not have the time to collect data. –  Data presented is the best guess by functional managers. –  Data is communicated from poor systems. –  The project is scoped too broadly. –  The team creates the ideal Process Map rather than the as is Process Map.

Clear the road – I m comin through!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

80

Wrap Up and Action Items

Champion/ Process Owner

DMAIC Roadmap

Identify Problem Area

Define

Determine Appropriate Project Focus Estimate COPQ

Measure

Establish Team Assess Stability, Capability, and Measurement Systems

Improve

Analyze

Identify and Prioritize All X s

Prove/Disprove Impact X s Have On Problem

Identify, Prioritize, Select Solutions Control or Eliminate X s Causing Problems

Control

Implement Solutions to Control or Eliminate X s Causing Problems

Implement Control Plan to Ensure Problem Doesn t Return

Verify Financial Impact

Define Phase Deployment The importance of the Define Phase is to begin to understand the problem and formulate it into a project. Notice that if the Recommended Project Focus is approved the next step would be team selection.

Business  C ase S elected

N otify  Belts  and  S takeholders

C reate  Hig h-­‐Level  Process  Map

Determine  A ppropriate  Project  Focus (Pareto,  Project  Desirability) Define  &  C harter  Project (Problem  S tatement,  O bjective,  Primary  Metric,  S econdary  Metric) N A pproved Project   Focus

Estimate  C O PQ

Recommend  Project  Focus Y C reate  Team

C harter  Team

Ready  for  Measure

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

81

Wrap Up and Action Items Action Items Support List

Define Questions Step One: Project Selection, Project Definition And Stakeholder Identification Project Charter • What is the problem statement? Objective? • Is the business case developed? • What is the primary metric? • What are the secondary metrics? • Why did you choose these? • What are the benefits? • Have the benefits been quantified? It not, when will this be done? Date:____________________________ • Who is the customer (internal/external)? • Has the COPQ been identified? • Has the controller’s office been involved in these calculations? • Who are the members on your team? • Does anyone require additional training to be fully effective on the team? Voice of the Customer (VOC) and SIPOC defined • Voice of the customer identified? • Key issues with stakeholders identified? • VOC requirements identified? • Business Case data gathered, verified and displayed? Step Two: Process Exploration Processes Defined and High Level Process Map • Are the critical processes defined and decision points identified? • Are all the key attributes of the process defined? • Do you have a high level process map? • Who was involved in its development? General Questions • Are there any issues/barriers that prevent you from completing this phase? • Do you have adequate resources to complete the project? • Have you completed your initial Define report out presentation?

These are some additional questions to ensure all the deliverables are achieved.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

82

Wrap Up and Action Items At this point, you should: §  Have a clear understanding of the specific action items §  Have started to develop a project plan to complete the action items §  Have identified ways to deal with potential roadblocks §  Be ready to apply the Six Sigma method within your business

You have now completed Define Phase.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

83

Lean Six Sigma Black Belt Training

Measure Phase Welcome to Measure

Now that we have completed Define we are going to jump into the Measure Phase. Here you enter the world of measurement, where you can discover the ultimate source of problem-solving power: data. Process improvement is all about narrowing down to the vital few factors that influence the behavior of a system or a process. The only way to do this is to measure and observe your process characteristics and your critical-to-quality characteristics. Measurement is generally the most difficult and time-consuming phase in the DMAIC methodology. But if you do it well, and right the first time, you will save your self a lot of trouble later and maximize your chance of improvement. Welcome to the Measure Phase - will give you a brief look at the topics we are going to cover.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

84

Welcome to Measure Overview These are the modules we will cover in the Measure Phase.

Welc Welcome  to  Meas ome  to  Measure ure PProc roces esss  Dis  Disccovery overy SS ix  S ix  S ig igma  S ma  S tatis tatistic ticss Meas Measurement  S urement  S ys ys tem  Analys tem  Analys is is PProc roces esss  C  C apability apability Wrap  Up  &  Ac Wrap  Up  &  Action  Items tion  Items

C hampion/ Process  O wner

DMAIC Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

Here is the overview of the DMAIC process. Within measure we are going to start getting into details about process performance, measurement systems and variable prioritization. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

85

Welcome to Measure Measure Phase Deployment

Detailed Problem Statement Determined Detailed Process Mapping Identify All Process X’s Causing Problems (Fishbone, Process Map)

Select the Vital Few X’s Causing Problems (X-Y Matrix, FMEA) Assess Measurement System

N

Repeatable & Reproducible?

Y

Implement Changes to Make System Acceptable Assess Stability (Statistical Control) Assess Capability (Problem with Centering/Spread) Estimate Process Sigma Level Review Progress with Champion

Ready for Analyze

This provides a process look at putting “Measure” to work. By the time we complete this phase you will have a thorough understanding of the various Measure Phase concepts.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

86

Lean Six Sigma Black Belt Training

Measure Phase Process Discovery

Now we will continue in the Measure Phase with “Process Discovery”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

87

Process Discovery Overview

Welc Welcome  to  Meas ome  to  Meas ure ure PProc roces es ss  D  Dis is cc overy overy CC aus ause  &  E e  &  E ffect  D ffect  Diagram iagram D Detailed  P etailed  Proces rocesss  Mapping  Mapping CC aus ause  and  E e  and  E ffect  D ffect  Diagrams iagrams FFME ME A A

SS ix ix  S  S ig igma  S ma  S tatis tatis tic ticss Meas Meas urement  S urement  S ys ys tem  Analys tem  Analys is is PProc roces es ss  C  C apability apability Wrap  Up  &  Ac Wrap  Up  &  Action  Items tion  Items The purpose of this module is highlighted above. We will review tools to help facilitate Process Discovery. This will be a lengthy step as it requires a full characterization of your selected process. There are four key deliverables from the Measure Phase: (1) A robust description of the process and its workflow (2) A quantitative assessment of how well the process is actually working (3) An assessment of any measurement systems used to gather data for making decisions or to describe the performance of the process (4) A “short” list of the potential causes of our problem, these are the X’s that are most likely related to the problem. On the next lesson page we will help you develop a visual and mental model that will give you leverage in finding the causes to any problem..

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

88

Process Discovery Overview of Brainstorming Techniques

C aus e   a nd   E ffec t   D iag ram P eople

Machine

Method

The   Y The   o r   P roblem   roblem CPondition

The   X ’s (C aus es )

l Material

Measurement

E nvironment

C ateg ories

You will need to use brainstorming techniques to identify all possible problems and their causes. Brainstorming techniques work because the knowledge and ideas of two or more persons is always greater than that of any one individual. Brainstorming will generate a large number of ideas or possibilities in a relatively short time. Brainstorming tools are meant for teams, but can be used at the individual level also. Brainstorming will be a primary input for other improvement and analytical tools that you will use. You will learn two excellent brainstorming techniques, cause and effect diagrams and affinity diagrams. Cause and effect diagrams are also called Fishbone Diagrams because of their appearance and sometimes called Ishikawa diagrams after their inventor. In a brainstorming session, ideas are expressed by the individuals in the session and written down without debate or challenge. The general steps of a brainstorming sessions are: 1.  2.  3.  4.  5.  6.  7.  8. 

Agree on the category or condition to be considered. Encourage each team member to contribute. Discourage debates or criticism, the intent is to generate ideas and not to qualify them, that will come later. Contribute in rotation (take turns), or free flow, ensure every member has an equal opportunity. Listen to and respect the ideas of others. Record all ideas generated about the subject. Continue until no more ideas are offered. Edit the list for clarity and duplicates.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

89

Process Discovery Cause and Effect Diagram

A cause and effect diagram is a composition of lines and words representing a meaningful relationship between an effect, or condition, and its causes. To focus the effort and facilitate thought, the legs of the diagram are given categorical headings. Two common templates for the headings are for product related and transactional related efforts. Transactional is meant for processes where there is no traditional or physical product; rather it is more like an administrative process. Transactional processes are characterized as processes dealing with forms, ideas, people, decisions and services. You would most likely use the product template for determining the cause of burnt pizza and use the transactional template if you were trying to reduce order defects from the order taking process. A third approach is to identify all categories as you best perceive them. When performing a cause and effect diagram, keep drilling down, always asking why, until you find the root causes of the problem. Start with one category and stay with it until you have exhausted all possible inputs and then move to the next category. The next step is to rank each potential cause by its likelihood of being the root cause. Rank it by the most likely as a 1, second most likely as a 2 and so on. This make take some time, you may even have to create subsections like 2a, 2b, 2c, etc. Then come back to reorder the sub-section in to the larger ranking. This is your first attempt at really finding the Y=f(X); remember the funnel? The top X’s have the potential to be the critical X’s, those X’s which exert the most influence on the output Y. Finally you will need to determine if each cause is a control or a noise factor. This as you know is a requirement for the characterization of the process. Next we will explain the meaning and methods of using some of the common categories.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

90

Process Discovery Cause and Effect Diagram

Cause and Effect Diagram

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

91

Process Discovery Cause and Effect Diagram

Classifying the X’s

T he  C au s e  &  E ffec t  D iagram is  s imply  a  tool  to  g enerate  opinions   about  pos s ible  caus es  for  defects . F or  each  of  the  X ’s  identified  in  the  F is hbone  diagram  clas s ify  them   as  follows : – C ontrollable  – C  (K nowledg e) – P rocedural  – P  (P eople,  S ys tems ) – Nois e  – N  (E xternal  or  U ncontrollable)

T hink  of  procedural  as  a  s ubs et  of  controllable.    U nfortunately, many   procedures  within  a  company  are  not  well  controlled  and  can  caus e   the  defect  level  to  g o  up.    T he  clas s ification  methodolog y  is  us ed  to   s eparate  the  X ’s  s o  they  can  be  us ed  in  the  X -­‐Y  D iagram  and  the   F ME A  taug ht  later  in  this  module. WH IC H  X ’s  C A US E  D E F E C T S ? The Cause and Effect Diagram is an organized way to approach brainstorming. This approach allows us to further organize ourselves by classifying the X’s into controllable, procedural or noise types. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

92

Process Discovery Chemical Purity Example

Measurement Incoming QC (P)

Manpower

Materials Raw Materials (C)

Training on method (P)

Measurement Method (P) Measurement Capability (C)

Skill Level (P)

Insufficient staff (C)

Multiple Vendors (C) Specifications (C)

Adherence to procedure (P) Work order variability (N)

Startup inspection (P) Handling (P) Purification Method (P)

Room Humidity (N) RM Supply in Market (N) Shipping Methods (C)

Column Capability (C)

Chemical Purity

Nozzle type (C) Temp controller (C)

Data collection/feedback (P)

Methods

Mother Nature

Equipment

This example of the cause and effect diagram is of chemical purity. Notice how the input variables for each branch are classified as Controllable, Procedural and Noise. Cause & Effect Diagram – SigmaXL®

The Fishbone Diagram shown here for Surface Flaws was generated in SigmaXL®. We will now review the various steps for creating a Cause & Effect Diagram using the SigmaXL® statistical software package. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

93

Process Discovery Cause & Effect Diagram - SigmaXL®

Select “SigmaXL >Templates and Calculators>DMAIC and DFSS Templates>Cause & Effect (Fishbone) Template”. Take a few moments to study the worksheet. Notice the six groups are the classic bones for a Fishbone. Enter each Cause under the appropriate heading: People, Method, Material, Machine, Measurement, and Environment. You may enter up to 2 Sub-causes for each Cause.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

94

Process Discovery Cause & Effect Diagram - SigmaXL® (cont.)

Fill in the template as shown above. Click the “Fishbone Diagram” button to generate the Cause and Effect Diagram. You may modify the results to add data, however due to the simplicity of the template it is recommended that you add to the template and recreate the chart.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

95

Process Discovery Cause & Effect Diagram Exercise

Exercise objective: Create a Fishbone Diagram. 1.  Retrieve the high level Process Map for your project and use it to complete a Fishbone, if possible include your project team.

Don t let the big one get away!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

96

Process Discovery Overview of Process Mapping

In   o rd e r   to   co r re ctly   m a n a g e   a   p ro ce s s ,   y o u   m u s t   b e   a b le   to   d e s crib e   it   in   a   w a y   th a t   ca n   b e   e a s ily   u n d e rs to o d .

S te p   B

S te p   C

sp

S te p   A

S te p   D

Fin is h

In

S ta rt

ec

t

– The  preferred  method  for  describing  a  process  is   to  identify  it  with  a  g eneric  name,  show  the   workflow  with  a  Process  Map  and  describe  its   purpose  with  an  operational  description.   – The  first  activity  of  the  Measure  Phase  is  to   adequately  describe  the  process  under   investig ation.

Process Mapping, also called flowcharting, is a technique to visualize the tasks, activities and steps necessary to produce a product or a service. The preferred method for describing a process is to identify it with a generic name, show the workflow with a Process Map and describe its purpose with an operational description. Remember that a process is a blending of inputs to produce some desired output. The intent of each task, activity and step is to add value, as perceived by the customer, to the product or service we are producing. You cannot discover if this is the case until you have adequately mapped the process. There are many reasons for creating a Process Map: - It helps all process members understand their part in the process and how their process fits into the bigger picture. - It describes how activities are performed and how the work effort flows, it is a visual way of standing above the process and watching how work is done. In fact, process maps can be easily uploaded into model and simulation software where computers allow you to simulate the process and visually see how it works. - It can be used as an aid in training new people. - It will show you where you can take measurements that will help you to run the process better. - It will help you understand where problems occur and what some of the causes may be. - It leverages other analytical tools by providing a source of data and inputs into these tools. - It identifies and leads you to many important characteristics you will need as you strive to make improvements. Individual maps developed by Process Members form the basis of Process Management. The individual processes are linked together to see the total effort and flow for meeting business and customer needs. In order to improve or to correctly manage a process, you must be able to describe it in a way that can be easily understood, that is why the first activity of the Measure Phase is to adequately describe the process under investigation. Process Mapping is the most important and powerful tool you will use to improve the effectiveness and efficiency of a process. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

97

Process Discovery Information from Process Mapping These are more reasons why Process Mapping is the most important and powerful tool you will need to solve a problem. It has been said that Six Sigma is the most efficient problem solving methodology available. This is because work done with one tool sets up another tool, very little information and work is wasted. Later you will learn to how to further use the information and knowledge you gather from Process Mapping.

By mapping processes we can identify many important characteristics and develop information for other analytical tools: 1.  Process inputs (X’s) 2.  Supplier requirements 3.  Process outputs (Y’s) 4.  Actual customer needs 5.  All value-added and non-value added process tasks and steps 6.  Data collection points • Cycle times • Defects • Inventory levels • Cost of poor quality, etc. 7.  Decision points 8.  Problems that have immediate fixes 9.  Process control needs

Process Mapping

T here  are  us ually  three  views  of  a  proc es s :

1

2

3

What you THINK it is..

What it ACTUALLY is..

What it SHOULD be..

There are usually three views of a process: The first view is “what you think the process is” in terms of its size, how work flows and how well the process works. In virtually all cases the extent and difficulty of performing the process is understated.

It is not until someone Process Maps the process that the full extent and difficulty is known, and it virtually is always larger than what we thought, is more difficult and it cost more to operate than we realize. It is here that we discover the hidden operations also. This is the second view: “what the process actually is”. Then there is the third view: “what it should be”. This is the result of process improvement activities. It is precisely what you will be doing to the key process you have selected during the weeks between classes. As a result of your project you will either have created the “what it should be” or will be well on your way to getting there. In order to find the “what it should be” process, you have to learn process mapping and literally “walk” the process via a team method to document how it works. This is a much easier task then you might suspect, as you will learn over the next several lessons. We will start by reviewing the standard Process Mapping symbols. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

98

Process Discovery Standard Process Mapping Symbols

Standard symbols for Process Mapping: (available in Microsoft Office™, Visio™, iGrafx™ , SigmaFlow™ and other products) A RECTANGLE indicates an activity. Statements within the rectangle should begin with a verb

A PARALLELAGRAM shows that there are data

A DIAMOND signifies a decision point. Only two paths emerge from a decision point: No and Yes

An ELLIPSE shows the start and end of the process

An ARROW shows the connection and direction of flow

1

A CIRCLE WITH A LETTER OR NUMBER INSIDE symbolizes the continuation of a flowchart to another page

There may be several interpretations of some of the Process Mapping symbols; however, just about everyone uses these primary symbols to document processes. As you become more practiced you will find additional symbols useful, i.e. reports, data storage etc. For now we will start with just these symbols.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

99

Process Discovery Process Mapping Levels

L evel  1  – T he  Mac ro  P roc es s  Map,  s ometimes  c alled  a   Manag ement  level  or  viewpoint. C alls   for   O rder

C us tomer   Hungry

T ake   O rder

Make   P izza

C ook   P izza

P izza   C orrect

B ox   P izza

D eliver   P izza

C us tomer   E ats

L evel  2  – T he  P roc es s  Map,  s ometimes  c alled  the  Worker  level  or   viewpoint.  T his  example  is  from  the  pers pec tive  of  the  piz z a  c he f Pizza Dough

No Take Order from Cashier

Place in Oven

Add Ingredients

Observe Frequently

Check if Done

Yes

Remove from Oven

1

Start New Pizza

Scrap

No 1

Pizza Correct

Yes

Place in Box

Tape Order on Box

Put on Delivery Rack

L evel  3  – T he  Mic ro  P roc es s  Map,  s ometimes  c alled  the  Improvement   level  or  viewpoint.  S imilar  to  a  level  2,  it  will  s how  more  s tep s  and  tas ks   and  on  it  will  be  various  performanc e  data;  yields ,  c yc le  time,   value  and   non  value  added  time,  defec ts ,  etc . Before Process Mapping starts, you have to learn about the different level of detail on a Process Map and the different types of Process Maps. Fortunately these have been well categorized and are easy to understand. There are three different levels of Process Maps. You will need to use all three levels and you most likely will use them in order from the macro map to the micro map. The macro map contains the least level of detail, with increasing detail as you get to the micro map. You should think of and use the level of Process Maps in a way similar to the way you would use road maps. For example, if you want to find a country, you look at the world map. If you want to find a city in that country, you look at the country map. If you want to find a street address in the city, you use a city map. This is the general rule or approach for using Process Maps. The Macro Process Map, what is called the Level 1 Map, shows the big picture, you will use this to orient yourself to the way a product or service is created. It will also help you to better see which major step of the process is most likely related to the problem you have and it will put the various processes that you are associated with in the context of the larger whole. A Level 1 PFM, sometimes called the “management” level, is a high-level process map having the following characteristics: §  Combines related activities into one major processing step §  Illustrates where/how the process fits into the big picture §  Has minimal detail §  Illustrates only major process steps §  Can be completed with an understanding of general process steps and the purpose/objective of the process LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

100

Process Discovery Process Mapping Levels (cont.) The next level is generically called the Process Map. You will refer to it as a Level 2 Map and it identifies the major process steps from the workers point of view. In the pizza example above, these are the steps the pizza chef takes to make, cook and box the pizza for delivery. It gives you a good idea of what is going on in this process, but could can you fully understand why the process performs the way it does in terms of efficiency and effectiveness, could you improve the process with the level of knowledge from this map? Probably not, you are going to need a Level 3 Map called the Micro Process Map. It is also known as the improvement view of a process. There is however a lot of value in the Level 2 Map, because it is helping you to “see” and understand how work gets done, who does it, etc. It is a necessary stepping stone to arriving at improved performance. Next we will introduce the four different types of Process Maps. You will want to use different types of Process Maps, to better help see, understand and communicate the way processes behave.

Types of Process Maps There are four types of Process Maps that you will use. They are the Linear Flow Map, the deployment or Swim Lane Flow Map, the S-I-P-0-C Map (pronounced sigh-pock) and the Value Stream Map. T he  L inear-­‐F low  P roc es s  Map Customer Hungry

Calls for Order

Take Order

Make Pizza

Cook Pizza

Pizza Correct

Box Pizza

Deliver Pizza

Customer Eats

As  the  name  s tates ,  this  diag ram  s hows  the  proc es s  s teps  in  a  s e quential  flow,  g enerally  ordered   from  an  upper  left  c orner  of  the  map  towards  the  rig ht  s ide.

Customer Hungry

Calls for Order

Deliverer

Cook

Cashier

Customer

T he  D eployment-­‐F low  or  S wim  L ane  P roc es s  Map Customer Eats

Take Order

Make Pizza

Cook Pizza

Pizza Correct

Box Pizza

Deliver Pizza

T he  value  of  the  S wim  L ane  map  is  that  is  s hows  you  who  or  whic h department  is  res pons ible  for   the  s teps  in  a  proc es s .  T his  c an  provide  powerful  ins ig hts  in  th e  way  a  proc es s  performs .  A   timeline  c an  be  added  to  s how  how  long  it  takes  eac h  g roup  to  pe rform  their  work.  Als o  eac h   time  work  moves  ac ros s  a  s wim  lane,  there  is  a   “S upplier  – C us tomer” interac tion.  T his  is  us ually   where  bottlenec ks  and  queues  form.  

While they all show how work gets done, they emphasize different aspects of process flow and provide you with alternative ways to understand the behavior of the process so you can do something about it. The Linear Flow Map is the most traditional and is usually where most start the mapping effort. The Swim Lane Map adds another dimension of knowledge to the picture of the process: Now you can see which department area or person is responsible. You can use the various types of maps in the form of any of the three levels of a Process Map. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

101

Process Discovery Process Maps – Examples for Different Processes Linear Process Map for Door Manufacturing Begin

Prep doors

Inspect

A

Pre-cleaning

Return for rework Install into work jig

A

Mark for door handle drilling

Inspect finish

Light sanding

B

Rework

B

Drill holes

C

Scratch repair

De-burr and smooth hole

Apply part number

Final cleaning

Move to finishing

Apply stain and dry

Inspect

C

End

Inspect

Scrap

Prepare paperwork (CAAR & installation request)

Review & approve CAAR

Receive & use

Review & approve standard

Supplier Procurement Top Mgt/ Finance Corporate

I.T.

Business Unit

Swim Lane Process Map for Capital Equip Define Needs

Configure & install

Review & approve CAAR

Issue payment

Review & approve CAAR

Acquire equipment

Supplier Paid

Supplier Ships

21 days

6 days

5 days

15 days

17 days

7 days

71 days

50 days

Types of Process Maps The SIPOC diagram is especially useful after you have been able to construct either a Level 1 or Level 2 Map because it facilitates your gathering of other pertinent data that is affecting the process in a systematic way. It will help you to better see and understand all of the influences affecting the behavior and performance of the process.

The SIPOC Process Map Supplier – Input – Process – Output – Customer Suppliers

Inputs

Process

Outputs

See Below

Customers

Requirements

Price

Cook

Complete call < 3 min

Size

Order confirmation

Accounting

Order to Cook < 1 minute

TI Calculators

Quantity

Bake order

Complete bake order

NEC Cash Register

Extra Toppings

Data on cycle time

Correct bake order

Special orders

Order rate data

Correct address

Drink types & quantities

Order transaction

Correct Price

Other products

Delivery info

ATT Phones

Pizza type

Office Depot

Phone number Address Name Time, day and date Volume

Level 1 Process Map for Customer Order Process Call for an

Answer

Write

Confirm

Sets

Address &

Order to

You may also add a Cook Order Phone Order Order Price Phone requirements section to both the supplier side and the customer side to capture the expectations for the inputs and the outputs of the process. Doing a SIPOC is a great building block to creating the Level 3 Micro Process Map. The two really compliment each other and give you the power to make improvements to the process. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

102

Process Discovery Types of Process Maps

The Value Stream Map is a specialized map that helps you to understand numerous performance metrics associated primarily with the speed of the process, but has many other important data. While this Process Map level is at the macro level, the Value Stream Map provides you a lot of detailed performance data for the major steps of the process. It is great for finding bottlenecks in the process. Process Mapping Exercise – Going to Work

T he  purpos e  of  this  ex erc is e  is  to  develop  a  L evel  1  Mac ro,  L ine ar   P roc es s  F low  Map  and  then  c onvert  this  map  to  a  S wim  L ane  Map. R ead  the  following  bac kg round  for  the  ex erc is e:   Y ou  have  been  concerned   about  your  ability  to  arrive  at  work  on  time  and  als o  the  amount of  time  it  takes   from  the  time  your  alarm  goes  off  until  you  arrive  at  work.  T o  help  you  better   unders tand  both  the  variation  in  arrival  times  and  the  total  tim e,  you  decide  to   create  a  L evel  1  Macro  P roces s  Map.  F or  purpos es  of  this  exercis e,  the  s tart  is   when  your  alarm  goes  off  the  firs t  time  and  the  end  is  when  you   arrive  at  your   work  s tation. T as k  1 – Mentally  think  about  the  various  tas ks  and  activities  that  you   routinely   do  from  the  defined  s tart  to  the  end  points  of  the  exercis e. T as k  2 – Us ing  a  pencil  and  paper  create  a  linear  proces s  map  at  the  mac ro   level,  but  with  enough  detail  that  you  can  s ee  all  the  major  s te ps  of  your   proces s . T as k  3 – F rom  the  L inear  P roces s  Map,  create  a  s wim  lane  s tyle  P roces s  Map.   F or  the  lanes  you  may  us e  the  different  phas es  of  your  proces s ,   s uch  as  the   wake  up  phas e,  getting  prepared,  driving,  etc. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

103

Process Discovery A Process Map of Process Mapping Process Mapping follows a general order, but sometimes you may find it necessary, even advisable to deviate somewhat. However, you will find this a good path to follow as it has proven itself to generate significant results.

S elec t  the  proc es s

C reate  the  L evel  2   PFM

C reate  a  L evel  3   PFM

D etermine   approac h  to  map   the  proc es s

P erform  S IP O C

Add  P erformanc e   data

C omplete  L evel  1   P F M  works heet

Identify  all  X ’s  and   Y ’s

Identify  V A/NVA   s teps

C reate  L evel  1  P F M

Identify  c us tomer   requirements

On the lessons ahead we will always show you where you Identify  s upplier   D efine  the  s c ope   for  the  L evel  2  P F M requirements are at in this sequence of tasks for Process Mapping. Before we begin our Process Mapping we will first start you off with how to determine the approach to mapping the process. Basically there are two approaches: the individual and the team approach. Process Mapping Approach

S elec t  the   proc es s

D etermine   approac h  to   map  the   proc es s C omplete   L evel  1   P F M   works heet C reate   L evel  1   PFM D efine  the   s c ope  for   the  L evel  2   PFM

Us ing  the  Individual  A pproac h 1. S tart  with  the  L evel  1  Macro  P roces s  Map. 2. Meet  with  proc es s  owner(s )  /  manag er(s ).    C reate  a   L evel  1  Ma p  a nd  obtain  approval  to  interview   proces s  members . 3. S tarting  with  the  beg inning  of  the  proces s ,  pretend   you  are  the  product  or  s ervice  flowing  throug h  the   proces s ,  interview  to  g ather  information. 4. A s  the  interview  prog res s ,  as s emble  the  data  into  a   L evel  2  P F M. 5. V erify  the  accuracy  of  the  L evel  2  P F M  with  the   individuals  who  provided  input. 6. Update  the  L evel  2  P F M  as  needed. Us ing  the  T eam  A pproac h 1. F ollow  the  T eam  A pproac h  to  P roc es s  Mapping

If you decide to do the individual approach, here are a few key factors: You must pretend that you are the product or service flowing through the process and you are trying to “experience” all of the tasks that happen through the various steps. You must start by talking to the manager of the area and/or the process owner. This is where you will develop the Level 1 Macro Process Map. While you are talking to him, you will need to receive permission to talk to various members of the process in order to get the detailed information you need. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

104

Process Discovery Process Mapping Approach Process Mapping works best with a team approach. The logistics of performing the mapping are somewhat different, but it overall it takes less time, the quality of the output is higher and you will have more “buy-in” into the results. Input should come from people familiar with all stages of process.

S elec t  the   proc es s

Determine   approac h  to   map  the   proc es s C omplete   L evel  1   P F M   works heet C reate   L evel  1   PFM Define  the   s c ope  for   the  L evel  2   PFM

Us ing  the  T eam  Approac h 1. S tart  with  the  L evel  1  Macro  P roces s  Map. 2. Meet  with  proces s  owner(s )  /  manager(s ).    C reate  a   L evel  1  Map  and  obtain  approval  to  call  a  proces s   mapping  meeting  with  proces s  members  (S ee  team   works hop  ins tructions  for  details  on  running  the   meeting). 3. B ring  key  members  of  the  proces s  into  the  proces s   flow  works hop.  If  the  proces s  is  large  in  s cope,  hold   individual  works hops  for  each  s ubs ection  of  the   total  proces s .    S tart  with  the  beginning  s teps .   O rganiz e  meeting  to  us e  the  “pos t-­‐it  note  approach   to  gather  individual  tas ks  and  activities ,  bas ed  on   the  macro  map,  that  compris e  the  proces s . 4. Immediately  as s emble  the  information  that  has   been  provided  into  a  P roces s  Map.   5. V erify  the  P F M  by  dis cus s ing  it  with  proces s  owners   and  by  obs erving  the  actual  proces s  from  beginning   to  end.

Where appropriate the team should include line individuals, supervisors, design engineers, process engineers, process technicians, maintenance, etc. The team process mapping workshop is where it all comes together.

Select the process

Determine approach to map the process

T he  T eam  P roc es s  Mapping  Works hop 1. 2. 3.

Complete Level 1 PFM worksheet Create Level 1 PFM

Define the scope for the Level 2 PFM

4. 5. 6. 7.

A dd  to  and  agree  on  Macro  P roces s  Map. Us ing  8.5  X  11  paper  for  each  macro  proces s  s tep,   tape  the  proces s  to  the  wall  in  a  linear  s tyle. P roces s  Members  then  lis t  all  known  proces s  tas ks   that  they  do  on  a  P os t-­‐it  note,  one  proces s  tas k  per   note.   •Include  the  actual  time  s pent  to  perform  each   activity,  do  not  include  any  wait  time  or  queue   time.   •L is t  any  known  performance  data  that  des cribe   the  quality  of  the  tas k. P lace  the  pos t-­‐it  notes  on  the  wall  under  the   appropriate  macro  s tep  in  the  order  of  the  work  flow. R eview  proces s  with  whole  group,  add  additional   information  and  clos e  meeting. Immediately  cons olidate  information  into  a  L evel  2   P roces s  Map. Y ou  will  s till  have  to  verify  the  map  by  walking  the   proces s .

In summary, after adding to and agreeing to the Macro Process Map, the team process mapping approach is performed using multiple post-it notes where each person writes one task per note and, when finished, place them onto a wall which contains a large scale Macro Process Map. This is a very fast way to get a lot of information including how long it takes to do a particular task. Using the Value Stream Analysis techniques which you will study later, you will use this data to improve the process. We will now discuss the development of the various levels of Process Mapping. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

105

Process Discovery Steps in Generating a Level 1 PFM You may recall that the preferred method for C reating  a  L evel  1  P F M describing a process is to S elec t  the   proc es s 1.  Identify  a  generic  name  for  the  proces s :   identify it with a generic F or  ins tance:    “C us tomer  order  proces s ” name, describe its purpose 2.  Identify  the  beginning  and  ending  s teps  of  the  proces s : Determine   with an operational approac h  to   B eg inning -­‐ cus tomer  calls  in.  E nding – baked  piz z a  given  to   map  the   operations description and show the proc es s 3.  D es cribe  the  primary  purpos e  and  objective  of  the  proces s     workflow with a process (operational  definition):   C omplete   T he  purpos e  of  the  proces s  is  to  obtain  telephone  orders  for   L evel  1   map. When developing a piz z as ,  s ell  additional  products  if  pos s ible,  let  the  cus tomer   P F M   works heet Macro Process Map, always know  the  price  and  approximate  delivery  time,  provide  an   accurate  cook  order,  log  the  time  and  immediately  give  it  to  the add one process step in front piz z a  cooker. C reate   of and behind the area you 4.  Mentally  “walk” through  the  major  s teps  of  the  proces s  and   L evel  1   write  them  down:   PFM believe contains your R eceive  the  order  via  phone  call  from  the  cus tomer,  calculate   problem as a minimum. To the  price,  create  a  build  order  and  provide  the  order  to   Define  the   operations aid you in your start, we s c ope  for   5.  Us e  s tandard  flowcharting  s ymbols  to  order  and  to  illus trate   the  L evel  2   have provided you with a PFM the  flow  of  the  major  proces s  s teps . checklist or worksheet. You may acquire this data from your own knowledge and/or with the interviews you do with the managers / process owners. Once you have this data, and you should do this before drawing maps, you will be well positioned to communicate with others and you will be much more confident as you proceed. A Macro Process Map can be useful when reporting project status to management. A macro-map can show the scope of the project, so management can adjust their expectations accordingly. Remember, only major process steps are included. For example, a step listed as “Plating” in a manufacturing Macro Process Map, might actually consists of many steps: pre-clean, anodic cleaning, cathodic activation, pre-plate, electro-deposition, reverse-plate, rinse and spin-dry, etc. The plating step in the macro-map will then be detailed in the Level 2 Process Map. Exercise – Generate a Level 1 PFM

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

106

Process Discovery Exercise – Generate a Level 1 PFM (cont.) If necessary, you may look at the example for the Pizza order entry process.

1.  Identify  a  generic  name  for  the  proces s :  

2.  Identify  the  beginning  and  ending  s teps  of  the  proces s :

3.  D es cribe  the  primary  purpos e  and  objective  of  the  proces s     (operational  definition):  

4.  Mentally  “walk” through  the  major  s teps  of  the  proces s  and   write   them  down:  

5.  Us e  s tandard  flowcharting  s ymbols  to  order  and  to  illus trate   the  flow   of  the  major  proces s  s teps  on  a  s eparate  s heet  of  paper.

Exercise – Generate a Level 1 PFM Solution

1.

Identify  a  generic  name  for  the  proces s :   (I.E .  cus tomer  order  proces s ).

•

Identify  the  beginning  and  ending  s teps  of  the  proces s : (beg inning -­‐ cus tomer  calls  in,  ending – piz z a  order  given  to  the  chef).

•

D es cribe  the  primary  purpos e  and  objective  of  the  proces s    (operational   definition):  (T he  purpos e  of  the  proces s  is  to  obtain  telephone  orders  for   P iz z as ,  s ell  additional  products  if  pos s ible,  let  the  cus tomer  k now  the   price  and  approximate  delivery  time,  provide  an  accurate  cook  order,  log   the  time  and  immediately  give  it  to  the  piz z a  cooker).

•

Mentally  “walk” through  the  major  s teps  of  the  proces s  and  write  them   down: (R eceive  the  order  via  phone  call  from  the  cus tomer,  calculate  the  price,   create  a  build  order  and  provide  the  order  to  the  chef).

•

Us e  s tandard  flowcharting  s ymbols  to  order  and  to  illus trate  the flow  of   the  major  proces s  s teps  on  a  s eparate  s heet  of  paper.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

107

Process Discovery Defining the Scope of Level 2 PFM With a completed Level 1 PFM, you can now “see” where you have to go to get more detailed information. You will have the basis for a Level 2 Process Map. The improvements are in the details. If the efficiency or effectiveness of the process could be significantly improved by a broad summary analysis, the improvement would be done already. If you map the process at an actionable level, you can identify the source of inefficiencies and defects. But you need to be careful about mapping too little an area and missing your problem cause, or mapping to large an area in detail, thereby wasting your valuable time. The rules for determining the scope of the Level 2 Process Map: a) Look at your Macro Process Map, select the area which represents your problem. b) Map this area at a Level 2. c) Start and end at natural starting and stopping points for a process, in other words you have the complete associated process.

C us tomer   O rder   P roces s

S elect   the   proces s

C ustomer   Hungry

C alls   for   Order

Determine   approach   to   map   the   proces s

C us tomer   O rder   P roces s

Take   Order

Make   P izza

Deliver   P izza

C ustomer   E ats

No Take Order from Cashier

Place in Oven

Add Ingredients

Observe Frequently

Check if Done

Yes

Remove from Oven

1

Start New Pizza

Scrap

No Pizza Correct

1

Define   the   s cope   for   the   L evel   2   PF M

Box   P izza

Pizza Dough

C omplete   L evel   1   PF M   works heet C reate   L evel   1   PF M

C ook   P izza

Yes

Place in Box

Tape Order on Box

Put on Delivery Rack

The   rules   for   d etermining   the   L evel   2   P roces s   Map   s cope: •F rom   your   Macro   P rocess   Map,   s elect   the   a rea   which   represents   y our   problem.   •Map   this   a rea   a t   a   L evel   2 . •S tart   a nd   e nd   a t   natural   s tarting   a nd   s topping   points   for   a   process,   in   other   words   you   have   the   c omplete   a ssociated   process.  

C re a te   th e   Le v e l   2   P FM

Pizza Dough

No P e rfo rm   S IP O C

Take Order from Cashier

Place in Oven

Add Ingredients

Observe Frequently

Check if Done

Yes

Remove from Oven

1

Start New Pizza

Id e n tify   a ll   X ’ s   a n d   Y ’ s

Scrap

No Id e n tify   cu s to m e r   re q u ire m e n ts

1

Pizza Correct

Yes

Place in Box

Tape Order on Box

Put on Delivery Rack

When you perform the process Id e n tify   mapping workshop or do the s u p p lie r   re q u ire m e n ts individual interviews, you will determine how the various tasks and activities form a complete step. Do not worry about precisely defining the steps, it is not an exact science, common sense will prevail. If you have done a process mapping workshop, which you will remember we highly recommended, you will actually have a lot of the data for the Level 3 Micro Process Map. You will now perform a SIPOC and, with the other data you already have, it will position you for about 70 percent to 80 percent of the details you will need for the Level 3 Process Map. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

108

Process Discovery Building a SIPOC SIPOC diagram for customer-order process: Create the Level 2 PFM

Suppliers ATT Phones Office Depot TI Calculators NEC Cash Register

Perform SIPOC

Inputs

Process

See Below Pizza type Size Quantity Extra Toppings Special orders Drink types & quantities Other products Phone number

Outputs

Customers

Price Order confirmation Bake order Data on cycle time Order rate data Order transaction Delivery info

Cook Accounting

Requirements Complete call < 3 min Order to Cook < 1 minute Complete bake order Correct bake order Correct address Correct Price

Address Name Time, day and date Volume

Identify all X s and Y s

Identify customer requirements

Identify supplier requirements

Customer Order: Level 1 process flow diagram Call for an Order

Answer Phone

Write Order

Confirm Order

Sets Price

Address & Phone

Order to Cook

The tool name prompts the team to consider the suppliers (the 'S' in SIPOC) of your process, the inputs (the 'I') to the process, the process (the 'P') your team is improving, the outputs (the 'O') of the process and the customers (the 'C') that receive the process outputs. Requirements of the customers can be appended to the end of the SIPOC for further detail and requirements are easily added for the suppliers as well. The SIPOC tool is particularly useful in identifying: Who supplies inputs to the process? What are all of the inputs to the process we are aware of? (Later in the DMAIC methodology you will use other tools which will find still more inputs, remember Y=f(X) and if we are going to improve Y, we are going to have to find all the X’s. What specifications are placed on the inputs? What are all of the outputs of the process? Who are the true customers of the process? What are the requirements of the customers? You can actually begin with the Level 1 PFM that has 4 to 8 high-level steps, but a Level 2 PFM is even of more value. Creating a SIPOC with a process mapping team, again the recommended method is a wall exercise similar to your other process mapping workshop. Create an area that will allow the team to place post-it note additions to the 8.5 X 11 sheets with the letters S, I, P, O and C on them with a copy of the Process Map below the sheet with the letter P on it. Hold a process flow workshop with key members. (Note: If the process is large in scope, hold an individual workshop for each subsection of the total process, starting with the beginning steps). The preferred order of the steps is as follows: 1. Identify the outputs of this overall process. 2. Identify the customers who will receive the outputs of the process. 3. Identify customers’ preliminary requirements 4. Identify the inputs required for the process. 5. Identify suppliers of the required inputs that are necessary for the process to function. 6. Identify the preliminary requirements of the inputs for the process to function properly. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

109

Process Discovery Identifying Customer Requirements You are now ready to identify the customer requirements for the outputs you have defined. Customer requirements, called VOC, determine what are and are not acceptable for each of the outputs. You may find that some of the outputs do not have requirements or specifications. For a well managed process, this is not acceptable. If this is the case, you must ask/ negotiate with the customer as to what is acceptable. There is a technique for determining the validity of

C reate   the   L evel   2   P F M

Process Name

Operational Definition

PROCESS OUTPUT IDENTIFICATION AND ANALYSIS 1

3

4

5

Output Data Customer (Name)

P erform   S IP OC

Process Output - Name (Y)

Internal

External

Metric

6 7 Requirements Data Metric LSL

Target

8

9

USL

Measurement System (How is it Measured)

10 Measurement Data Frequency of Measurement

11

Performance Level Data

12 Value Data VA or NVA

13 General Data/Information

Comments

Identify   a ll   X ’s   and   Y ’s

Identify   c us tomer   requirements

Identify   s upplier   requirements

customer and supplier requirements. It is called “RUMBA” standing for: Reasonable, Understandable, Measurable, Believable and Achievable. If a requirement cannot meet all of these characteristics, then it is not a valid requirement , hence the word negotiation. We have included the process for validating customer requirements at the end of this lesson. The Excel spreadsheet is somewhat self explanatory. You will use a similar form for identifying the supplier requirements. Start by writing in the process name followed by the process operational definition. The operational definition is a short paragraph which states why the process exists, what it does and what its value proposition is. Always take sufficient time to write this such that anyone who reads it will be able to understand the process. Then list each of the outputs, the Y’s, and write in the customer’s name who receives this output, categorized as an internal or external customer. Next are the requirements data. To specify and measure something, it must have a unit of measure; called a metric. As an example, the metric for the speed of your car is miles per hour, for your weight it is pounds, for time it is hours or minutes and so on. You may know what the LSL and USL are but you may not have a target value. A target is the value the customer prefers all the output to be centered at; essentially, the average of the distribution. Sometimes it is stated as “1 hour +/- 5 minutes”. One hour is the target, the LSL is 55 minutes and the USL is 65 minutes. A target may not be specified by the customer; if not, put in what the average would be. You will want to minimize the variation from this value. You will learn more about measurement, but for now you must know that if something is required, you must have a way to measure it as specified in column 9. Column 10 is how often the measurement is made and column 11 is the current value for the measurement data. Column 12 is for identifying if this is a value or non value added activity; more on that later. And finally column 13 is for any comments you want to make about the output. You will come back to this form and rank the significance of the outputs in terms of importance to identify the CTQ’s.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

110

Process Discovery Identifying Supplier Requirements The supplier input or process input identification and analysis form is nearly identical to the output form just covered. Now you are the customer, you will specify what is required of your suppliers for your process to work correctly; remember RUMBA – the same rules apply. You will notice a new parameter introduced in column 2. It asks if the input is a controlled input or an uncontrolled input (noise). The next topic will discuss the meaning of these terms.

C reate   the   L evel   2   P F M

Process Name

Operational Definition

PROCESS INPUT IDENTIFICATION AND ANALYSIS 1

2 Input Data

3

4

5

6 7 Requirements Data Metric

Supplier (Name)

P erform   S IP OC

Controlled (C) Internal Process Input- Name (X) Noise (N)

External

Metric

LSL

Target

8

USL

9

10 Measurement Data

11

Measurement System (How is it Frequency of Performance Measured) Measurement Level Data

Value Data

12 General Data/Information

NV or NVA

Comments

Identify   a ll   X ’s   and   Y ’s

Identify   c us tomer   requirements

Identify   s upplier   requirements

Later you will come back to this form and rank the importance of the inputs to the success of your process and eventually you will have found the Critical X’s. Controllable vs. Noise Inputs For any process or process step input, there are two primary types of inputs: Controllable - we can exert influence over them Uncontrollable - they behave as they want to within some reasonable boundaries. Procedural - A standardized set of activities leading to readiness of a step. Compliance to GAAP (Generally Accepted Accounting Principals).

Screens in Place

P roc edural   Inputs

C ontrollable Inputs

Oven Clean Ingredients prepared

K ey  P roc es s Outputs

P roc es s

C orrec t  Ing redients R oom  T emp Mois ture  C ontent Ing redient  Variation

P izza  S ize

Nois e  Inputs

Ing redient  T ypes /Mixes

P roperly  C ooked Hot  P izza  >140  deg

Volume

E very  input  c an  be  either: C ontrollable (C ) -­‐ Inputs  can  be  adjus ted  or  controlled  while  the  proces s  is  running  (e.g.,  s peed,   feed  rate,  temperature,  and  pres s ure) P roc edural (P ) -­‐ Inputs  can  be  adjus ted  or  controlled  while  the  proces s  is  running  (e.g.,  s peed,   feed  rate,  temperature,  and  pres s ure) Nois e (N) -­‐ T hings  we  don’t  think  we  can  control,  we  are  unaware  of  or  s ee,  too  expens ive  or  too   difficult  to  control  (e.g.,  ambient  temperature,  humidity,  individual)

However, even with the inputs we define as controllable, we never exert complete control. We can control an input within the limits of its natural variation, but it will vary on its own based on its distributional shape - as you have previously learned. You choose to control certain inputs because you either know or believe they have an effect on the outcome of the process, it is inexpensive to do, so controlling it “makes us feel better” or there once was a problem and the solution (right or wrong) was to exert control over some input. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

111

Process Discovery Controllable vs. Noise Inputs (cont.) You choose to not control some inputs because you think you cannot control them, you either know or believe they don’t have much affect on the output, you think it is not cost justified or you just don’t know these inputs even exist. Yes, that’s right, you don’t know they are having an affect on the output. For example, what effect does ambient noise or temperature have on your ability to be attentive or productive, etc? It is important to distinguish which category an input falls into. You know through Y=f(X), that if it is a Critical X, by definition, that you must control it. Also if you believe that an input is or needs to be controlled, then you have automatically implied there are requirements placed on it and that it must be measured. You must always think and ask whether an input is or should be controlled or if it is uncontrolled. Exercise – Supplier Requirements

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

112

Process Discovery The Level 3 Process Flow Diagram Pizza Dough

No Take Order from Cashier

Place in Oven

Add Ingredients

Check if Done

Observe Frequently

Yes

Remove from Oven

1

Start New Pizza

Scrap

No 1 PROCESS STEP PROCESS STEP OUTPUT IDENTIFICATION AND ANALYSIS 1 3 4 5 ANALYSIS 6 7 OUTPUT IDENTIFICATION AND

Pizza Correct

Yes Process Name Process Name

8

9

Tape Order on Box

Place in Box

10 11 12 Data7 Measurement Data Value Data 1 Output Data 3 4 5 Requirements 6 8 9 10 11 12 Customer (Name) Metric Output Data Requirements Data Measurement Data Value Measurement VA Data Customer (Name) Metric System (How is it Frequency of or VA Measurement Internal External Metric LSL Target USL Process Output - Name (Y) Measured) NVA or System (How is itMeasurement Frequency of Performance Level Data Internal External Metric LSL Target USL Process Output - Name (Y) Measured) Measurement Performance Level Data NVA

Step Name/Number Step Name/Number 13 General Data/Information 13 General Data/Information Comments Comments

Put on Delivery Rack

PROCESS STEP PROCESS STEP INPUT IDENTIFICATION AND ANALYSIS 1 2 3 5 6 INPUT IDENTIFICATION AND4 ANALYSIS

Process Name

Process Name

7 8 9 10 11 12 Data 1 3 4 5Requirements 6 Data7 8 9 Measurement 10 11 Value Data 12 Metric Measurement Measurement Data VA Input Data Supplier (Name) Requirements Data Value Data Controlled (C) System (How is it Frequency of Performance or VA Supplier (Name) Metric Measurement Internal External Metric LSL Target USL Process Input- Name (X) Noise (N) (C) Measured) Data NVA or Controlled System (How isMeasurement it Frequency ofLevel Performance Internal External Metric LSL Target USL Process Input- Name (X) Noise (N) Measured) Measurement Level Data NVA Input Data2

Step Name/Number

Step Name/Number 13 General Data/Information 13

General Data/Information Comments

Comments

You have a decision at this point to continue with a complete characterization of the process you have documented at a Level 2 in order to fully build the process management system or to narrow the effort by focusing on those steps that are contributing to the problem you want solved. In reality, usually just a few of the process steps are the root cause areas for any given higher level process output problem. If your desire is the latter, there are some other Measure Phase actions and tools you will use to narrow the number of potential X’s and subsequently the number of process steps. To narrow the scope so it is relevant to your problem consider the following: Remember using the pizza restaurant as our example for selecting a key process? They were having a problem with overall delivery time and burnt pizzas. Which steps in this process would contribute to burnt pizzas and how might a pizza which was burnt so badly it had to be scrapped and restarted effect delivery time? It would most likely be the steps between “place in oven” to “remove from oven”, but it might also include “add ingredients” because certain ingredients may burn more quickly than others. This is how, based on the Problem Statement you have made, you would narrow the scope for doing a Level 3 PFM. For your project, the priority will be to do your best to find the problematic steps associated with your Problem Statement. We will teach you some new tools in a later lesson to aid you in doing this. You may have to characterize a number of steps until you get more experience at narrowing the steps that cause problems; this is to be expected. If you have the time you should characterize the whole process. Each step you select as the causal steps in the process must be fully characterized, just as you have previously done for the whole process. In essence you will do a “mini SIPOC” on each step of the process as defined in the Level 2 Process Map. This can be done using a Level 3 Micro Process Map and placing all the information on it or it can be consolidated onto an Excel spreadsheet format or a combination of both. If all the data and information is put onto an actual Process Map, expect the map to be rather large physically. Depending on the scope of the process, some people dedicate a wall space for doing this; say a 12 to 14 foot long wall. An effective approach for this is to use a roll of industrial LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

113

Process Discovery The Level 3 Process Flow Diagram (Cont.) grade brown package wrapping paper, which is generally 4 feet wide. Just roll out the length you want, cut it, place this on the wall and then build your Level 3 Process Map by taping and writing various elements onto the paper. The value of this approach is that you can take it off the wall, roll it up, take it with you and then put it back on any wall; great for team efforts. A Level 3 Process Map contains all of the process details needed to meet your objective: all of the flows, set points, standard operating procedures (SOPs), inputs and outputs; their specifications and if they are classified as being controllable or non-controllable (noise). The Level 3 PFM usually contains estimates of defects per unit (DPU), yield and rolled throughput yield (RTY) and value/non-value add. If processing cycle times and inventory levels (materials or work queues) are important, value stream parameters are also included. This can be a lot of detail to manage and appropriate tracking sheets are required. We have supplied these sheets in a paper and Excel spreadsheet format for your use. The good news is the approach and forms for the steps are essentially the same as the format for identifying supplier and customer requirements at the process level. A spreadsheet is very convenient tool and the output from the spreadsheet can then be fed directly into a C&E matrix and an FMEA (to be described later), also built using spreadsheets. You will find the work you have done up to this point in terms of a Level 1 and 2 Process Maps and the SIPOC will be of use, both from knowledge of the process and actual data. An important reminder of a previous lesson: You will recall when you were taught about project definition where it was stated that you should only try to solve the performance of only one process output, at any one time. Because of the amount of detail you can get into for just one Y, trying to optimize more than one Y at a time can become overwhelming. The good news is that you will have laid all the ground work to focus on a second and a third Y for a process by just focusing on one Y in your initial project. Process Inputs (X’s) and Outputs (Y’s) You are now down at the step level of the process, this is what we call the improvement view of a process. Now you do exactly the same thing as you did for the overall process, you list all of the input and output information for steps of the process you have selected for analysis and characterization to solve your problem. To help you comprehend what we are trying to accomplish we have provided you with visualization for the inputs and outputs of the Pizza restaurant.

LSS Black Belt Manual XL v11

Process Name

PROCESS STEP OUTPUT IDENTIFICATION AND ANALYSIS 1

C reate   a   L evel   3   P F M

3

4

5

Output Data Customer (Name) Process Output - Name (Y)

Internal

External

Metric

6 7 Requirements Data Metric LSL

Target

8

9

USL

Measurement System (How is it Measured)

10 Measurement Data Frequency of Measurement

Step Name/Number

11

Performance Level Data

12 Value Data VA or NVA

13 General Data/Information

Comments

Add   P erformanc e   data

Identify   VA/NVA   s teps

Process Name

PROCESS STEP INPUT IDENTIFICATION AND ANALYSIS 1

2 3 4 Input Data Supplier (Name) Controlled (C) Internal External Process Input- Name (X) Noise (N)

5

Metric

6 7 Requirements Data Metric LSL

Target

8

USL

Step Name/Number

9 10 11 12 Measurement Data Value Data Measurement VA System (How is it Frequency of Performance or Measured) Measurement Level Data NVA

13 General Data/Information

Comments

© 2013 e-Careers Limited

114

Process Discovery Process Inputs (X’s) and Outputs (Y’s) (cont.) Any process, even a pizza C  /N Inputs  (X s ) R equirements  or  S pecs . P roces s restaurant process can be characterized. This N/C 7”, 12”, 16” Size of Pizza visualization shows many N/C 12 meats, 2 veggies, 3 cheese Toppings N N/A Name of the inputs and outputs N Within 10 miles Address Take Order and their requirements. By N Within area code Phone N 11 AM to 1 AM Time using the process and the N 5 X 52 Day N MM/DD,YY Date process step input and output sheets, you get a C All fields complete Order very detail picture about C Per Spec Sheets Ingredients Make Pizza S.O.P Per Rev 7.0 Recipe how your process works. C As per recipe chart 3-1 in Oz. Amounts Now you have enough data to start making informed C All fields complete Order C Ingredients per order Raw Pizza decisions about the C 350F +/- 5F Oven Temp Cook Pizza process performance. The C 10 Min Time N 60 per hour max Volume next lesson pages will describe how you determine if a process task, activity or step is a value added step or not.

Ys Order

Raw Pizza

Cooked Pizza

•All  fields   c omplete

•S iz e •Weig ht   •Ing redients   c orrec t

•>140F •Ing redients   c orrec t •No  burns

Identifying Waste When we produce A products or services, we NV No A engage process-based NV No activities to transform Yes physical materials, ideas 1 2 No A and information into NV No 2 3 something valued by Yes A Yes customers. Some NV Yes C reate  a   activities in the process •E ac h  proc es s  ac tivity  c an  be  tes ted  for   1 L evel  3   its  value-­‐add  c ontribution P F M No generate true value, A •A s k  the  following  two  ques tions  to   NV others do not. The 3 identify  non-­‐value  added  ac tivity: A dd   –Is  the  form,  fit  or  function  of  the   expenditure of resources, P erformanc e   A OK data work  item  chang ed  as  a  res ult  of   NV capital and other this  activity? Not –Is  the  cus tomer  willing  to  pay  for   OK energies that do not Identify   this  activity? A VA /NVA   NV generate value is s teps considered waste. Value generation is any activity that changes the form, fit or function of what we are working on in a way that the customer is willing to pay for. The goal of testing for VA vs. NVA is to remove unnecessary activity (waste) from a process. Writes time on scratch pad

Call for an Order

Calculate price

Answer phone

Asks cook for time estimate

Greetings and mention specials

Inform customer of price/time

Request order from customer

Order still OK?

Writes on scratch pad

Gets address & phone #

Add to Order

Rewrite order

Asks for more?

Confirm order

Thanks customer & hangs up Writes time on scratch pad

Another call waiting

New order?

Completes order from from note pad

Give order to Cook

Verify with notes

Rewrite Order

Hint: If an action starts with the two letters “re” it’s a good chance that it’s a form of waste, i.e. rework, replace, review, etc. Some non-value activities cannot be removed; i.e., data collection is required to understand and plan production activity levels, data must be collected to comply with governmental regulations, etc. (even though the data have no effect on the actual product or service) On the process flow diagram we place a red X through the steps or we write NVA or VA by each step.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

115

Process Discovery Definition of X-Y Diagram The X-Y Diagram is a great tool to help us focus, again it is based on team experience and “Tribal” knowledge. At this point in the project that is great although it should be recognized that this is NOT hard data. As you progress through the methodology don’t be surprised if you find out through data analysis that what the team thought might be critical turns out to be insignificant. The great thing about the X-Y Diagram is that it is sort of an unbiased way to approach definition around the process and WILL give you focus.

• T he   X -­‐Y   diagram   is: – A   tool   used   to   identify/collate   potential   X ’s   a nd   a ssess   their   relative   impact   on   multiple   Y ’s   (include   a ll   Y ’s   that   a re   customer   focused) – Based   on   the   team’s   c ollective   “opinions” – C reated   for   e very   project – Never   c ompleted   – Updated  whenever   a   parameter   is   c hanged • T o   s ummarize,   the   X -­‐Y   is   a   team-­‐based   prioritization   tool   for   the   potential   X ’s • WAR NING !     T his   is   not   real   data,   this   is   organized   brainstorming!!     A t   the   c onclusion   of   the   project   y ou   may   realiz e   that   the   things   y ou   thought   were   c ritical   a re   in   fact   not   a s   important   a s   was   believed.

The Vital Few

A  S ix  S igma  B elt  does   n ot   jus t  dis cover   which  X ’s  are  important  in   a  proces s   ( the  vital  few). – T he  team   c ons iders   a ll  pos s ible  X ’s  that   c an   c ontribute  or   caus e   the   p roblem  obs erved. – T he  team  us es  3   p rimary   s ources  of  X  identification: • P roces s   Mapping • F is hbone  Analys is • B as ic  D ata  Analys is  – G raphical  and  S tatis tical – A  L is t  of  X ’s  is  es tablis hed   a nd   c ompiled. – T he  team  then  prioritiz es   which  X ’s  it   will  explore  firs t,   a nd   eliminates  the  “obvious ” low   impact  X ’s   from  further   cons ideration. T he  X -­‐Y  D iagram  is  this  P rioritiz ation  T ool!

This is an important tool for the many reasons we have already stated. Use it to your benefit, leverage the team and this will help you progress you through the methodology to accomplish your ultimate project goal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

116

Process Discovery The “XY Diagram”

This is the X-Y Diagram. You should have a copy of this template. If possible open it and get familiar with it as we progress through this section. Using the Classified X’s

• B reakthrough  requires   d ealing  primarily  with   c ontrollable  X ’s   impacting  the  “Y ”. • Us e  the   c ontrollable  X ’s  from  the  F is hbone  analys is  to  include  in  the   X -­‐Y  D iagram. • T he  goal  is  to  is olate  the  vital  few  X ’s  from  the  trivial  many  X ’s .     • P rocedures  and  Nois e  X ’s   will  be  us ed  in  the  F ME A  at  the   e nd   of   this  module.     H owever: – All  procedures  mus t  be  in  total  compliance. • T his  may  require  s ome  type  of  effectivenes s  meas ure. • T his  could  reduce  or  eliminate  s ome  of  the  defects  currently  s ee n  in   the  proces s  (allowing  focus  on  controllable  X ’s ).

– Nois e  type  inputs  increas e  ris k  of  defects  under   c urrent   technology  of  operation  and  therefore: • Increas e  R P N  on  the  F ME A  document  from  an  input. • Help  identify  areas  needing  inves tment  for  a  jus tified  R O I. *Risk Priority Number

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

117

Process Discovery X-Y Diagram: Steps

L is t  X ’s  from  F is hbone  D iag ram  in  horiz ontal  rows

Use your Fishbone Diagram as the source and type in the Inputs in this section, use common sense, some of the info from the Fishbone may not justify going into the X-Y inputs.

Enter your primary metric and any other secondary metrics across into this area. Weight these output variables (Y’s) on a scale of 1-10 you may find that some have the same weight which is just fine. If, at this time, additional metrics come to the surface, which is totally common, you may realize that you need to add secondary metrics to your project or even refine your primary metric.

LSS Black Belt Manual XL v11

L ist   Y ’s   in   c olumns   (including   P rimary   a nd   S econdary   metrics). Weight   the   Y ’s   on   a   s cale   of   1 -­‐10   (10   -­‐ highest   a nd   1 -­‐ lowest).

© 2013 e-Careers Limited

118

Process Discovery X-Y Diagram: Steps (cont.) For each X listed along the left, rank its effect on each corresponding metric based on a scale of 0, 1, 3 or 9. You can use any scale you choose however we recommend this on. If you use a scale of 1 to 10 this can cause uncertainty within the team…is it a 6 or a 7, what’s the difference, etc.?

The template we have provided automatically calculates and sorts the ranking shown here.

LSS Black Belt Manual XL v11

F or   e ac h   X   lis ted,   rank   its   e ffec t   o n   e ac h   m etric   b as ed   o n   a   s c ale   o f   1 ,   3   o r   9 . – 9   =   H ighest – 3   =   Marginal – 1   =   N one

“R anking ” multiplies   the   rank   o f   e ac h   X   b y   the   W eig ht   o f   e ac h   Metric .     The   p roduc t   o f   that   is   a dded   tog ether   to   b ec ome   the  “R anking ”.

© 2013 e-Careers Limited

119

Process Discovery Example

C lic k   the   D emo   b utton   to   s ee   a n   e xample.

Shown here is a basic example of a completed X-Y Diagram. You can click “Demo” on your template to view this anytime.

Example

C lick  the   S ummary  Works heet YX Diagram Summary Process: laminating Date: 5/2/2006

LSS Black Belt Manual XL v11

time

pressure

clean room cleanliness

temperature

Input Variables Description Ranking Rank % temperature 162 14.90% human handling 159 14.63% material properties 130 11.96% washer 126 11.59% pressure 120 11.04% robot handling 120 11.04% time 102 9.38% clean room practices 90 8.28% clean room cleanliness 78 7.18% 0.00%

100.00% 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% material properties

Output Variables Description Weight broken 10 unbonded area 9 smears 8 thickness 7 foreign material 6 0 0 0 0 0

Input Matrix Results

Output (Y's)

This is the summary worksheet. If you click on the “Summary” tab you will see this output. Take some time to review the worksheet.

Input Summary Input (X's)

© 2013 e-Careers Limited

120

Process Discovery Fishbone Diagram Exercise

Ex e rcis e   o b je ctiv e : C reate  an  X-­‐Y  diag ram   using  the  information  from  the  Fishbone   analysis. 1 . Using  the  Fishbone  Dia g ra m  crea ted  ea rlier,  crea te   a n  X-­‐Y  dia g ra m. 2 . Present  results  to  your  mentor.

Definition of FMEA Failure Modes Effect Analysis or FMEA [*usually pronounced as F-M-E-A (individual letters) or FEMA** (as a word)] is a structured approach to: read bullets. FMEA at this point is developed with tribal knowledge with a cross-functional team. Later using process data the FMEA can be updated and better estimates of detection and occurrence can be obtained. The FMEA is not a tool to eliminate X’s but rather control the X’s. It is only a tool to identify potential X’s and prioritize the order in which the X’s should be evaluated.

LSS Black Belt Manual XL v11

Failure Modes Effect Analysis (FMEA) is a structured approach to: •  Predict failures and prevent their occurrence in manufacturing and other functional areas which generate defects. •  Identify the ways in which a process can fail to meet critical customer requirements (Y). •  Estimate the Severity, Occurrence and Detection (SOD) of defects •  Evaluate the current Control Plan for preventing these failures from occurring and escaping to the customer. •  Prioritize the actions that should be taken to improve and control the process using a Risk Priority Number (RPN).

Give me an F , give me an M ……!

© 2013 e-Careers Limited

121

Process Discovery History of FMEA

H is to ry   o f   FM EA : • First  used  in  the  1 9 6 0 ’s  in  the  A erospace  industry  during  the   A pollo  missions • In  1 9 7 4  the  N avy  developed  MIL-­‐S TD-­‐1 6 2 9  reg arding  the  use  of   FMEA • In  the  late  1 9 7 0 ’s,  automotive  applications  driven  by  liability   costs,  beg an  to  incorporate  FMEA  into  the  manag ement  of  their   processes • A utomotive  Industry  A ction  G roup  (A IA G )  now  maintains  the   FMEA  standard  for  both  Desig n  and  Process  FMEA ’s

The “edge of your seat” info on the history of the FMEA! I’m sure you will all be sharing this with everyone tonight at the dinner table!

Types of FMEA’s There are many different types of FMEA’s. The basic premise is the same.

System FMEA: Performed on a product or service product at the early concept/design level when various modules all tie together. All the module level FMEA s tie together to form a system. As you go lower into a system more failure modes are considered. –  Example: Electrical system of a car, consists of the following modules: battery, wiring harness, lighting control module and alternator/regulator. –  System FMEA focuses on potential failure modes associated with the modules of a system caused by design Design DFMEA: Performed early in the design phase to analyze product fail modes before they are released to production. The purpose is to analyze how fail modes affect the system and minimize them. The severity rating of a fail mode MUST be carried into the Process PFMEA. Process PFMEA: Performed in the early quality planning phase of manufacturing to analyze fail modes in manufacturing and transactional processes that may escape to the customer. The failure modes and the potential sources of defects are rated and corrective action taken based on a Pareto analysis ranking. Equipment FMEA: used to analyze failure modes in the equipment used in a process to detect or make the part. –  Example: Test Equipment fail modes to detect open and short circuits.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

122

Process Discovery Purpose of FMEA

F ME A ’s : • Improve  the  quality,  reliability,  and  s afety  of  products . • Increas e  cus tomer  s atis faction. • R educe  product  development  time  and  cos t. • D ocument  and  track  actions  taken  to  reduce  ris k  and   improve  the  proces s . • F ocus  on  continuous  problem  prevention  not  problem   s olving.

Who Creates FMEAs and When? FMEA’s are a team tool like most in this phase of the methodology. They are applicable is most every project, manufacturing or service based. For all intensive purposes they will be used in conjunction with your problem solving project to characterize and measure process variables. In some cases the FMEA will manifest itself as a management tool when the project concludes and in some cases it will not be appropriate to be used in that nature.

LSS Black Belt Manual XL v11

Who

When

•

T he   focused   team   working   on   a   breakthrough   project.

•

•

ANY ONE   who   had   or   has   a   role   in   defining,   e xecuting,   or   c hanging   the   process.

•

•

T his   includes: •

Associates

•

Technical   E xperts

•

S upervisors

•

Managers

•

E tc.

•

•

P rocess   F ME As   s hould   be   s tarted:   • At   the   c onceptual   design   phase. P rocess   F ME As   s hould   be   updated: • When   a n   e xisting   design   or   p rocess   is   being   c hanged. • When   c arry-­‐over   designs   or   processes   will   be   used   in   new   applications   a nd   e nvironments. • When   a   p roblem   s olving   s tudy   is   completed   a nd   needs   to   be   documented. S ystem   F ME As   s hould   be   c reated   a fter   system   functions   a re   defined   but   before   specific   hardware   is   s elected.   Design   F ME As   s hould   be   c reated   when   new   s ystems,   products   a nd   processes   a re   being   designed.

© 2013 e-Careers Limited

123

Process Discovery Why Create an FMEA?

As   a   means   to   manage…

R IS K !!!

FMEA’s help you manage RISK by classifying your process inputs and monitoring their effects. This is extremely important during the course of your project work.

We   want   to   a void   c ausing   failures   in   the  P rocess as   well   a s   the   P rimary &   S econdary Metrics   .

The FMEA… This is an FMEA. We have provided a template for you to use.

# Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C Potential E l Causes of V a Failure s (X's) s

O Current D R Recommen Responsibl Taken S O D R C Process E P d Actions e Person & Action E C E P C Controls T N Target s V C T N Date

1 2 3 4 5 6 7 8 9

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

124

Process Discovery FMEA Components…# # Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C E l V a s s

Potential Causes of Failure (X's)

O Current C Process C Controls

D R Recommen E P d Actions T N

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

The first column highlighted here is the “Process Step Number”.

The   first   c olumn   is   the   P rocess   S tep   N umber. 1 2 3 4 5 E tc.    

FMEA Components…Process Step The second column is the Name of the Process Step. The FMEA should sequentially follow the steps documented in your Process Map. §  Phone §  Dial Number §  Listen for Ring §  Say Hello §  Introduce Yourself §  Etc. #

Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D R E P T N

Recommen d Actions

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

Enter the Name of the Process Step here. The FMEA should sequentially follow the steps documented in your Process Map. Phone Dial Number Listen for Ring Say Hello Introduce Yourself Etc.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

125

Process Discovery FMEA Components…Potential Failure Modes The third column to the mode in which the process could potentially fail. These are the defects caused by a C, P or N factor that could occur in the Process. # Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O Current C Process C Controls

D R Recommen E P d Actions T N

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

T his   refers   to   the   mode   in   which   the   process   c ould   potentially   fail.     T hese   a re   the   defects   c aused   by   a   C ,P   or   N   factor   that   c ould   occ ur   in   the   P rocess.     T his   information   is   obtained   from     Historical   D efect   D ata. F Y I..A   failure   mode   is   a   fancy   name   for   a   defect.

FMEA Components…Potential Failure Effects The fourth column highlighted here is simply the effect of realizing the potential failure mode on the overall process and is focused on the output of each step.

# Process Functio n (Step)

This information is usually obtained from your Process Map.

LSS Black Belt Manual XL v11

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C Potential E l Causes of V a Failure s (X's) s

O Current C Process C Controls

D R Recommen Responsibl E P d Actions e Person & T N Target Date

Taken S O D R Action E C E P s V C T N

This   is  s imply   the   e ffect   of   realizing   the  potential   failure   mode   on   the  overall   process.     It  focuses   on   the   outputs   of   e ach  s tep.     This   information   c an   be   obtained   in   the   P rocess   Map.

© 2013 e-Careers Limited

126

Process Discovery FMEA Components…Severity (SEV # Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O Current C Process C Controls

D R Recommen E P d Actions T N

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

T his   ranking   s hould   be   developed   based   on   the  teams   k nowledge of   the   process   in   c onjunction   with   the   predetermined  scale. T he   measure   of   S everity   is   a   financial   measure   of   the   impact   to  the   business   of   realizing   a   failure   in   the   output. The fifth column highlighted here is the ranking that is developed based on the team’s knowledge of the process in conjunction with the predetermined scale. Severity is a financial measure of the impact to the business of a failure in the output. Ranking Severity The Automotive Industry Action Group, a consortium of the “Big Three”: Ford, GM and Chrysler developed this criteria. If you don’t like it develop one that fits your organization; just make sure it’s standardized so everyone uses the same scale. Effect Hazardous: Without Warning Hazardous: With Warning Very High High Moderate Low Very Low Minor Very Minor None

Criteria: Severity of Effect Defined

Ranking

May endanger the operator. Failure mode affects safe vehicle operation and/or involves non-compliance with government regulation. Failure will occur WITHOUT warning. May endanger the operator. Failure mode affects safe vehicle operation and/or involves non-compliance with government regulation. Failure will occur WITH warning. Major disruption to the production line. 100% of the product may have to be scrapped. Vehicle/item inoperable, loss of primary function. Customers will be very dissatisfied.

10

Minor disruption to the production line. The product may have to be sorted and a portion (less than 100%) scrapped. Vehicle operable, but at a reduced level of performance. Customers will be dissatisfied. Minor disruption to the production line. A portion (less than 100%) may have to be scrapped (no sorting). Vehicle/item operable, but some comfort/convenience item(s) inoperable. Customers will experience discomfort. Minor disruption to the production line. 100% of product may have to be re-worked. Vehicle/item operable, but some comfort/convenience item(s) operable at a reduced level of performance. Customers will experience some dissatisfaction. Minor disruption to the production line. The product may have to be sorted and a portion (less than 100%) re-worked. Fit/finish/squeak/rattle item does not conform. Most customers will notice the defect. Minor disruption to the production line. A portion (less than 100%) of the product may have to be re-worked online but out-of-station. Fit/finish/squeak/rattle item does not conform. Average customers will notice the defect. Minor disruption to the production line. A portion (less than 100%) of the product may have to be re-worked online but in-station. Fit/finish/squeak/rattle item does not conform. Discriminating customers will notice the defect. No effect.

7

9 8

6 5 4 3 2 1

* Potential Failure Mode and Effects Analysis (FMEA), Reference Manual, 2002. Pgs 29-45. Chrysler Corporation, Ford Motor Company, General Motors Corporation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

127

Process Discovery Applying Severity Ratings to Your Process • • •

T he  g uidelines  pres ented  on  the  previous  s lide  were  developed  fo r   the  auto  indus try. T his  was  included  only  as  a  guideline....”ac tual  res ults  may  vary” for   your  project. Y our  s everity  may  be  linked  to  impact  on  the  bus ines s  or  impact   on   the  next  cus tomer,  etc. Y o u  will  n eed  to  defin e  yo u r  o wn  c riteria … an d  be  c o n s is tent  th ro u gh o u t  y o u r  F ME A L et’s  brains torm  how  we  might  define  the  following  S E V E R IT Y   levels  in  our  own  projec ts : 1, 5,    10

The actual definitions of the severity are not so important as the fact that the team remains consistent in its use of the definitions. The next slide shows a sample of transactional severities. Sample Transactional Severities

Effect

Criteria: Impact of Effect Defined

Ranking

Critical Business May endanger company’s ability to do business. Failure mode affects process Unit-wide operation and / or involves noncompliance with government regulation. Critical Loss Customer Specific High

Moderate

Low

Minor None

10

May endanger relationship with customer. Failure mode affects product delivered and/or customer relationship due to process failure and/or noncompliance with government regulation.

9

Major disruption to process/production down situation. Results in near 100% rework or an inability to process. Customer very dissatisfied.

7

Moderate disruption to process. Results in some rework or an inability to process. Process is operable, but some work arounds are required. Customers experience dissatisfaction. Minor disruption to process. Process can be completed with workarounds or rework at the back end. Results in reduced level of performance. Defect is noticed and commented upon by customers. Minor disruption to process. Process can be completed with workarounds or rework at the back end. Results in reduced level of performance. Defect noticed internally, but not externally. No effect.

5

3

2 1

Shown here is an example for severity guidelines developed for a financial services company.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

128

Process Discovery FMEA Components…Classification “Class” #

Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D E T

R P N

Recommen d Actions

Responsibl e Person & Target Date

Taken Action s

S E V

O C C

D E T

R P N

C las s  s hould  c ateg oriz e  eac h  s tep  as  a … § C ontrollable  (C )   § P rocedural  (P )   § Nois e  (N) T his  information  can  be  obtained  in  the   P roc es s  Map. C ontrollable – A  fac tor  that  c an  be  dialed  into  a  s pec ific  s etting/value.  F or   example  T emperature  or   F low. P roc edures – A  s tandardiz ed  s et  of  ac tivities  leading  to  readines s  of  a  s tep.  F or  example  S afety   C omplianc e,  “L oc k  -­‐O ut  T ag -­‐O ut.” Nois e -­‐ A  fac tor  that  can  not  be  dialed  in  to  a  s pec ific  s etting /value. F or  example  rain  in  a  mine.

Recall the classifications of Procedural, Controllable and Noise developed when constructing your Process Map and Fishbone Diagram? Use those classifications from the Fishbone in the “Class” column, highlighted here, in the FMEA.

Potential Causes of Failure (X’s)

# Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C Potential E l Causes of V a Failure s (X's) s

O Current C Process C Controls

D R Recommen Responsibl E P d Actions e Person & T N Target Date

Taken S O D R Action E C E P s V C T N

Potential  C auses  of  the  F ailure  refers  to  how  the  failure  c ould   occur. This  information  s hould  be  obtained  from  the  F ishbone  D iagram. The column “Potential Causes of the Failure”, highlighted here, refers to how the failure could occur. This should also be obtained from the Fishbone Diagram.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

129

Process Discovery FMEA Components…Occurrence “OCC”

#

Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D R E P T N

Recommen d Actions

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

The column “Occurrence” highlighted here, refers to how frequently the specified failure is projected to occur. This information should be obtained from Capability Studies or Historical Defect Data in conjunction with the predetermined scale.

Ranking Occurrence

Probability of Failure Very High: Failure is almost inevitable. High: Generally associated with processes similar to previous processes that have often failed. Moderate: Generally associated with processes similar to previous processes that have experienced occasional failures but not in major proportions. Low: Isolated failures associated with similar processes. Very Low: Only isolated failures associated with almost identical processes. Remote: Failure is unlikely. No failures ever associated with almost identical processes.

Possible Failure Rates

Cpk

Ranking

≥ 1 in 2

< 0.33

10

1 in 3

³

0.33

9

1 in 8

³

0.51

8

1 in 20

³

0.67

7

1 in 80

³

0.83

6

1 in 400

³

1.00

5

1 in 2,000

³

1.17

4

1 in 15,000

³

1.33

3

1 in 150,000

³

1.5

2

≤ 1 in 1,500,000

³

1.67

1

Potential Failure Mode and Effects Analysis (FMEA), Reference Manual, 2002. Pg. 35.. Chrysler Corporation, Ford Motor Company, General Motors Corporation.

The Automotive Industry Action Group, a consortium of the “Big Three”: Ford, GM and Chrysler developed these Occurrence rankings.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

130

Process Discovery FMEA Components…Current Process Controls #

Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D R E P T N

Recommen d Actions

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

C urrent  P roces s  C ontrols  refers  to  the  three  types  of  controls that  are   in  place  to  prevent  a  failure  in   with  the  X ’s .    T he  3  types  of  controls  are: •S P C  (S tatis tical  P roces s  C ontrol)   •P oke-­‐Y oke  – (Mis take  P roofing) •D etection  after  F ailure

A s k  yours elf  “how  do  we  c ontrol  this  defec t? ” The column “Current Process Controls” highlighted here refers to the three types of controls that are in place to prevent a failures.

FMEA Components…Detection (DET)

# Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C E l V a s s

Potential Causes of Failure (X's)

O Current C Process C Controls

D R Recommen E P d Actions T N

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

Detection   is   a n   a ssessment   of   the   probability   that   the   proposed  type   of   c ontrol  will   detect   a   s ubsequent   failure   mode. This   information   s hould   be   obtained   from   y our  Measurement   S ystem   Analysis S tudies   a nd   the   P rocess   Map.     A   rating   s hould   be   a ssign   in   conjunction  with   the   predetermined  scale.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

131

Process Discovery Ranking Detection Criteria: The likelihood that the existence of a defect will be detected by the test content before the product advances to the next or subsequent process

Detection

Ranking

Almost Impossible

Test content must detect < 80% of failures

10

Very Remote

Test content must detect 80% of failures

9

Remote

Test content must detect 82.5% of failures

8

Very Low

Test content must detect 85% of failures

7

Low

Test content must detect 87.5% of failures

6

Moderate

Test content must detect 90% of failures

5

Moderately High

Test content must detect 92.5% of failures

4

High

Test content must detect 95% of failures

3

Very High

Test content must detect 97.5% of failures

2

Almost Certain

Test content must detect 99.5% of failures

1

Potential Failure Mode and Effects Analysis (FMEA), AIAG Reference Manual, 2002 Pg. 35.. Chrysler Corporation, Ford Motor Company, General Motors Corporation.

The Automotive Industry Action Group, a consortium of the “Big Three”: Ford, GM and Chrysler developed these Detection criteria.

Risk Priority Number “RPN” The “The Risk Priority Number” highlighted here is a value that will be used to rank order the concerns from the process. We provided you with a template which will automatically calculate this for you based on your inputs for Severity, Occurrence and Detection.

# Process Functio n (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O Current C Process C Controls

D R E P T N

Recomme nd Actions

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

The   R isk   P riority   N umber   is   a   v alue   that   will   be   used   to   rank   order   the   c oncerns   from   the   process.   The   R P N   is   the   product   of,   S everity,   O ccurrence   a nd   D etect   a bility   as   represented   here… R P N   =   (S E V)*(OC C )*(DE T)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

132

Process Discovery FEMA Components…Actions #

Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S E V

C l a s s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D E T

R P N

Recommen d Actions

Responsibl e Person & Target Date

Taken Action s

S O E C V C

D E T

R P N

R ecommended  Actions refers  to  the  activity  for  the  prevention  of  a   defect. R es pons ible  P ers on  &  D ate refers  to  the  name  of  the  group  or  pers on   res pons ible  for  completing  the  activity  and  when  they  will  complete  it. T aken  Action refers  to  the  action  and  effective  date  after  it  has  been   completed. The columns highlighted here are a type of post FMEA. Remember to update the FMEA throughout your project, this is what we call a “Living Document” as it changes throughout your project. FMEA Components…Adjust RPN

# Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

S C Potential E l Causes of V a Failure s (X's) s

O Current C Process C Controls

D R Recommen E P d Actions T N

Responsibl e Person & Target Date

Taken Action s

S O D R E C E P V C T N

Once   the   R ecommended   A ctions,   R esponsible   P erson   &   D ate,   Taken   A ction  have   been  c ompleted  the  S everity,   O ccurrence   a nd   Detection  s hould   be   a djusted.     T his  will   result   in   a   new   R PN   rating. The columns highlighted here are the adjusted levels based on the actions you have taken within the process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

133

Process Discovery FMEA Exercise

E x erc is e  objec tive: As s emble  your  team  in  order   to  create  a  F ME A  us ing  the  information   generated  from  the  P roces s  Map,  F is hbone   D iagram  and  X -­‐Y  D iagram.   1. B e  prepared  to  pres ent  res ults  to  your  mentor.

OKTeam,  T eam,   l et’s   OK let’s g et  that   F ME A ! get that FMEA!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

134

Process Discovery At this point, you should be able to: §  Create a high-level Process Map §  Create a Fishbone Diagram §  Create an X-Y Diagram §  Create an FMEA §  Describe the purpose of each tool and when it should be used

You have now completed Measure Phase – Process Discovery.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

135

Lean Six Sigma Black Belt Training

Measure Phase Six Sigma Statistics

Now we will continue in the Measure Phase with “Six Sigma Statistics”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

136

Six Sigma Statistics Overview In this module you will learn how your processes speak to you in the form of data. If you are to understand the behaviors of your processes, then you must learn to communicate with the process in the language of data. The field of statistics provides the tools and techniques to act on data, to turn data into information and knowledge which you will then use to make decisions and to manage your processes. The statistical tools and methods that you will need to understand and optimize your processes are not difficult. Use of Excel spreadsheets or specific statistical analytical software has made this a relatively easy task. In this module you will learn basic, yet powerful analytical approaches and tools to increase your ability to solve problems and manage process behavior.

Purpose of Basic Statistics

Basic Statistics purpose: • 

Provide a numerical summary of the data being analyzed. – 

Data (n) • 

Factual information organized for analysis.

• 

Numerical or other information represented in a form suitable for processing by computer

• 

Values from scientific experiments.

• 

Provide the basis for making inferences about the future.

• 

Provide the foundation for assessing process capability.

• 

Provide a common language to be used throughout an organization to describe processes.

Relax….it won t be that bad!! Statistics is the basic language of Six Sigma. A solid understanding of Basic Statistics is the foundation upon which many of the subsequent tools will be based. Having an understanding of Basic Statistics can be quite valuable. Statistics however, like anything, can be taken to the extreme. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

137

Six Sigma Statistics Purpose of Basic Statistics (Cont.) But it is not the need or the intent of this course to do that, nor is it the intent of Six Sigma. It can be stated that Six Sigma does not make people into statisticians, rather it makes people into excellent problem solvers by using appropriate statistical techniques. Data is like crude oil that comes out of the ground. Crude oil is not of much good use. However if the crude oil is refined many useful products occur; such as medicines, fuel, food products, lubricants, etc. In a similar sense statistics can refine data into usable “products” to aid in decision making, to be able to see and understand what is happening, etc Statistics is broadly used by just about everyone today. Sometimes we just don’t realize it. Things as simple as using graphs to better understand something is a form of statistics, as are the many opinion and political polls used today. With easy to use software tools to reduce the difficulty and time to do statistical analyses, knowledge of statistics is becoming a common capability amongst people. An understanding of Basic Statistics is also one of the differentiating features of Six Sigma and it would not be possible without the use of computers and programs like MINITAB™. It has been observed that the laptop is one of the primary reasons that Six Sigma has become both popular and effective.

Statistical Notation – Cheat Sheet

Summation

An individual value, an observation

The standard deviation of sample data

A particular (1st) individual value

The standard deviation of population data

For each, all, individual values

The variance of sample data

The mean, average of sample data

The variance of population data

The grand mean, grand average

The range of data The mean of population data The average range of data Multi-purpose notation, i.e. # of subgroups, # of classes

A proportion of sample data A proportion of population data

The absolute value of some term Greater than, less than Greater than or equal to, less than or equal to

Sample size Population size

Use this as a cheat sheet, don’t bother memorizing all of this. Actually most of the notation in Greek is for population data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

138

Six Sigma Statistics Parameters vs. Statistics P opulation:    A ll  the  items  that  have  the   “property  of  interes t” under  s tudy. F rame:    A n  identifiable  s ubs et  of  the  population. S ample:    A  s ignificantly  s maller  s ubs et  of  the  population  us ed  to  make an  inference.

Population Sample Sample Sample

P opulation  P arameters : – –

S ample  S tatis tic s :

A rithmetic  des criptions  of  a  population µ,  σ ,  P ,  σ2 ,  N

– –

A rithmetic  des criptions  of  a s ample X -­‐bar  ,  s ,  p,  s 2 ,  n

The purpose of sampling is: To get a “sufficiently accurate” inference for considerably less time, money, and other resources, and also to provide a basis for statistical inference; if sampling is done well, and sufficiently, then the inference is that “what we see in the sample is representative of the population” A population parameter is a numerical value that summarizes the data for an entire population, a sample has a corresponding numerical value called a statistic. The population is a collection of all the individual data of interest. It must be defined carefully, such as all the trades completed in 2001. If for some reason there are unique subsets of trades it may be appropriate to define those as a unique population, such as, “all sub custodial market trades completed in 2001” or “emerging market trades”. Sampling frames are complete lists and should be identical to a population with every element listed only once. It sounds very similar to population… and it is. The difference is how it is used. A sampling frame, such as the list of registered voters, could be used to represent the population of adult general public. Maybe there are reasons why this wouldn’t be a good sampling frame. Perhaps a sampling frame of licensed drivers would be a better frame to represent the general public. The sampling frame is the source for a sample to be drawn. It is important to recognize the difference between a sample and a population because we typically are dealing with a sample of the what the potential population could be in order to make an inference. The formulas for describing samples and populations are slightly different. In most cases we will be dealing with the formulas for samples.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

139

Six Sigma Statistics Types of Data A ttrib u te  D ata  (Q u alitative) –

Is  always  binary,  there  are  only  two  pos s ible  values  (0,  1) • Y es ,  No • G o,  No  go • P as s /F ail

Variab le  D ata  (Q u an titative) –

D is crete  (C ount)  D ata • C an  be  categ oriz ed  in  a  clas s ification  and  is  bas ed  on  counts . – Number  of  defects – Number  of  defective  units – Number  of  cus tomer  returns

–

C ontinuous  D ata • C an  be  meas ured  on  a  continuum,  it  has  d ecimal  s ubdivis ions  that  are   meaningful – T ime,  P res s ure,  C onveyor  S peed,  Material  feed  rate – Money – P res s ure – C onveyor  S peed – Material  feed  rate

The nature of data is important to understand. Based on the type of data you will have the option to utilize different analyses. Data, or numbers, are usually abundant and available to virtually everyone in the organization. Using data to measure, analyze, improve and control processes forms the foundation of the Six Sigma methodology. Data turned into information, then transformed into knowledge, lowers the risks of decision. Your goal is to make more decisions based on data versus the typical practices of “I think”, “I feel” and “In my opinion”. One of your first steps in refining data into information is to recognize what the type of data it is that you are using. There are two primary types of data, they are Attribute and Variable Data. Attribute Data is also called qualitative data. Attribute Data is the lowest level of data. It is purely binary in nature. Good or bad, yes or no type data. No analysis can be performed on Attribute Data. Attribute Data must be converted to a form of Variable Data called Discrete Data in order to be counted or be useful. Discrete Data is information that can be categorized into a classification. Discrete Data is based on counts. It is typically things counted in whole numbers. Discrete Data is data that can't be broken down into a smaller unit to add additional meaning. Only a finite number of values is possible and the values cannot be subdivided meaningfully. For example, there is no such thing as a half of defect or a half of a system lockup. Continuous Data is information that can be measured on a continuum or scale. Continuous Data, also called quantitative data can have almost any numeric value and can be meaningfully subdivided into finer and finer increments, depending upon the precision of the measurement system. Decimal sub-divisions are meaningful with Continuous Data. As opposed to Attribute Data like good or bad, off or on, etc., Continuous Data can be recorded at many different points (length, size, width, time, temperature, cost, etc.). For example 2.543 inches is a meaningful number, whereas 2.543 defects does not make sense. Later in the course we will study many different statistical tests but it is first important to understand what kind of data you have. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

140

Six Sigma Statistics Discrete Variables

Shown here are additional Discrete Variables. Can you think of others within your business? Continuous Variables C ontinuous  Variable

P os s ible  Values  for  the  Variable

T he  length  of  pris on  time  s erved  for  individuals   convicted  of  firs t  degree  murder

A ll  the  real  numbers  between  a and  b,  where  a is   the  s malles t  amount  of  time  s erved  and  b is  the   larges t.

T he  hous ehold  income  for  hous eholds  with   incomes  les s  than  or  equal  to  $30,000

A ll  the  real  numbers  between  a and  $30,000,   where  a is  the  s malles t  hous ehold  income  in  the   population

T he  blood  glucos e  reading  for  thos e  individuals   having  glucos e  readings  equal  to  or  greater  than   200

A ll  real  numbers  between  200  and  b,  where  b is   the  larges t  glucos e  reading  in  all  s uch  individuals

Shown here are additional Continuous Variables. Can you think of others within your business?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

141

Six Sigma Statistics Definitions of Scaled Data

Understanding the nature of data and how to represent it can affect the types of statistical tests possible. • 

Nominal Scale – data consists of names, labels, or categories. Cannot be arranged in an ordering scheme. No arithmetic operations are performed for nominal data.

• 

Ordinal Scale – data is arranged in some order, but differences between data values either cannot be determined or are meaningless.

• 

Interval Scale – data can be arranged in some order and for which differences in data values are meaningful. The data can be arranged in an ordering scheme and differences can be interpreted.

• 

Ratio Scale – data that can be ranked and for which all arithmetic operations including division can be performed. (division by zero is of course excluded) Ratio level data has an absolute zero and a value of zero indicates a complete absence of the characteristic of interest.

Shown here are the four types of scales. It is important to understand these scales as they will dictate the type of statistical analysis that can be performed on your data.

Nominal Scale Listed are some examples of Nominal Data. The only analysis is whether they are different or not.

Qualitative Variable

Possible nominal level data values for the variable

Blood Types

A, B, AB, O

State of Residence

Alabama, …, Wyoming

Country of Birth

United States, China, other

Time to weigh in!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

142

Six Sigma Statistics Ordinal Scale These are examples of Ordinal Data.

Qualitative  Variable

P os s ible  O rdinal  level  data   values

Automobile  S iz es

S ubcompact,  compact,   intermediate,  full  s iz e,  luxury

P roduct  rating

P oor,  good,  excellent

B as eball  team  clas s ification

C las s  A,  C las s  AA,  C las s  AAA,   Major  L eague

Interval Scale

Interval  Variable

IQ  s cores  of  s tudents  in   B lackB elt  T raining

P os s ible  S c ores

100… (the  difference  between  s cores   is  meas urable  and  has   meaning  but  a  difference  of  20   points  between  100  and  120   does  not  indicate  that  one   s tudent  is  1.2  times  more   intelligent    )

These are examples of Interval Data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

143

Six Sigma Statistics Ratio Scale

R atio   V ariable

P os s ible   S c ores

G rams   of   fat   c onsumed   per   a dult   in   the   United   S tates

Shown here is an example of Ratio Data.

0   … (If   person   A   c onsumes   2 5   g rams   of   fat   a nd   person   B   c onsumes   5 0   g rams,   we   c an   s ay   that   person   B   c onsumes   twice   a s   much   fat   as   person   A .     If   a   person   C   c onsumes   z ero   grams   of   fat   per   day,   we   c an   s ay   there   is   a   complete   a bsence   of   fat   c onsumed   on   that   day.   N ote   that   a   ratio   is   interpretable   a nd   an   a bsolute   z ero   e xists.)  

Converting Attribute Data to Continuous Data Continuous Data provides us more opportunity for statistical analyses. Attribute Data can often be converted to Continuous by converting it to a rate.

LSS Black Belt Manual XL v11

•  Continuous Data is always more desirable •  In many cases Attribute Data can be converted to Continuous •  Which is more useful? –  15 scratches or Total scratch length of 9.25 –  22 foreign materials or 2.5 fm/square inch –  200 defects or 25 defects/hour

© 2013 e-Careers Limited

144

Six Sigma Statistics Descriptive Statistics We will review the Descriptive Statistics shown here which are the most commonly used. 1) For each of the measures of location, how alike or different are they? 2) For each measure of variation, how alike or different are they?

Meas ures  of  L oc ation  (c entral  tendenc y) – Mean – Median   – Mode

Meas ures  of  Variation  (dis pers ion) – – – –

R ange   Interquartile  R ange S tandard  deviation V ariance

3) What do these similarities or differences tell us?

Descriptive Statistics We are going to use the worksheet shown here to create graphs and statistics. Open the workbook “Measure Data Sets.xls” and select the “Basic Statistics” worksheet. Change the Start Point and the Bin Width as shown and click Update Chart. Typically one would use the default values but these changes produce a cleaner histogram.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

145

Six Sigma Statistics Measures of Location Mean are the most common measure of location. A “Mean”, implies that you are talking about the population or inferring something about the population. Conversely, average, implies something about sample data. Although the symbol is different, there is no mathematical difference between the Mean of a sample and Mean of a population.

To produce chart, SigmaXL>Graphical Tools>Basic Histogram, Select Data, as “Numeric Data Variable (Y)”. Set Start Point to 4.97 and Bin width to 0.01 then click update chart. Please select Descriptive Statistics. After clicking OK, the X axis should be modified to show 2 decimal places. Note, that Descriptive Statistics are also available in SigmaXL>Statistical Tools>Descriptive Statistics, and SigmaXL>Graphical Tools>Histograms & Descriptive Statistics. The physical center of a data set is the Median and unaffected by large data values. This is why people use Median when discussing average salary for an American worker, people like Bill Gates and Warren Buffet skew the average number.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

146

Six Sigma Statistics Measures of Location (cont.)

The Trimmed Mean (highlighted above) is less susceptible to the effects of extreme scores. SigmaXL® does not include Trimmed Mean, but Excel’s native function can be used as shown above. We will explain each part of this formula next.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

147

Six Sigma Statistics Measures of Location (cont.)

It is possible to have multiple Modes. When this happens it’s called Bi-modal Distributions. Here we only have one; Mode = 5.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

148

Six Sigma Statistics Measures of Variation

A range is typically used for small data sets which is completely efficient in estimating variation for a sample of 2. As your data increases the Standard Deviation is a more appropriate measure of variation.

The Standard Deviation for a sample and population can be equated with short and long-term variation. Usually a sample is taken over a short period of time making it free from the types of variation that can accumulate over time so be aware. We will explore this further at a later point in the methodology. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

149

Six Sigma Statistics Measures of Variation (cont.)

The Variance is the square of the Standard Deviation. It is common in statistical tests where it is necessary to add up sources of variation to estimate the total. Standard Deviations cannot be added, variances can. Normal Distribution The Normal Distribution is the most recognized distribution in statistics.

What are the characteristics of a Normal Distribution? –  Only random error is present –  Process free of assignable cause –  Process free of drifts and shifts

So what is present when the data is Non-normal?

We can begin to discuss the Normal Curve and its properties once we understand the basic concepts of central tendency and dispersion. As we begin to assess our distributions know that sometimes it’s actually more difficult to determine what is effecting a process if it is Normally Distributed. When we have a Non-normal Distribution there is usually special or more obvious causes of variation that can be readily apparent upon process investigation. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

150

Six Sigma Statistics The Normal Curve The Normal Distribution is the most commonly used and abused distribution in statistics and serves as the foundation of many statistical tools which will be taught later in the methodology.

Normal Distribution The shape of the Normal Distribution is a function of 2 parameters, (the Mean and the Standard Deviation). We will convert the Normal Distribution to the standard Normal in order to compare various Normal Distributions and to estimate tail area proportions. By normalizing the Normal Distribution this converts the raw scores into standard Z-scores with a Mean of 0 and Standard Deviation of 1, this practice allows us to use the Z-table.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

151

Six Sigma Statistics Normal Distribution (cont.)

The area under the curve between any two points represents the proportion of the distribution. The concept of determining the proportion between 2 points under the standard Normal curve is a critical component to estimating Process Capability and will be covered in detail in that module. Empirical Rule The Empirical rule allows us to predict or more appropriately make an estimate of how our process is performing. You will gain a great deal of understanding within the Process Capability module. Notice the difference between +/- 1 SD and +/- 6 SD.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

152

Six Sigma Statistics The Empirical Rule (cont.)

No  matter   what  the  s hape   of  your  dis tribution  is ,   a s  you  travel   3  S tandard   D eviations  from  the  Mean,  the  probability  of  occurrence  beyond  that  point   begins  to   c onverge  to  a  very  low  number.

Why Assess Normality? There is no good and bad. It is not always better to have “Normal” data, look at it in respect to the intent of your project. Again, there is much informational content in nonNormal Distributions, for this reason it is useful to know how Normal our data are. Go back to your project, what do you want to do with your distribution, Normal or Non-normal. Many distributions simply by nature can NOT be Normal. Assume that your dealing with a time metric, how do you get negative time, without having a flux capacitor as in the movie “Back to the Future.” If your metric is, by nature bound to some setting.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

153

Six Sigma Statistics Tools for Assessing Normality The Anderson Darling test yields a statistical assessment (called a goodness-of-fit test) of Normality and the SigmaXL® version of the Normal Probability test produces a graph to visually demonstrate just how good that fit is.

Watch that curve!!

Goodness-of-Fit

Anderson-Darling test assesses how closely actual frequency at a given value corresponds to the theoretical frequency for a Normal Distribution with the same Mean and Standard Deviation. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

154

Six Sigma Statistics The Normal Probability Plot Open the worksheet tab “Amount”. The graph shows the probability density of your data plotted against the expected density of a Normal curve. Notice that the y-axis (probability) does not increase linearly. Normal data will lie on a straight line (the black line) in this analysis. The graph shows you which values tend to deviate from the Normal Curve. Descriptive Statistics

Open the worksheet tab “Descriptive Statistics”. Using SigmaXL®’s Histograms and Descriptive Statistics tool, select Anderson Darling and click OK. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

155

Six Sigma Statistics Anderson-Darling Caveat

If the Data Are Not Normal, Don’t Panic! Once again, Nonnormal Data is NOT a bad thing, depending on the type of process / metrics you are working with. Sometimes it can even be exciting to have Non-normal Data because in some ways it represents opportunities for improvements.

Don’t touch that button!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

156

Six Sigma Statistics Normality Exercise

Answers: 1) Is Distribution A Normal? Answer > No 2) Is Distribution B Normal? Answer > No Isolating Special Causes from Common Causes Don’t get too worried about killing all variation, get the biggest bang for your buck and start making improvements by following the methodology. Many companies today can realize BIG gains and reductions in variation by simply measuring, describing the performance and then making common sense adjustments within the process…recall the “ground fruit”?

S pec ial  C aus e: Variation  is  caus ed  by  known  factors  that  res ult  in   a  non-­‐random  dis tribution  of  output.    Als o  referred  to  as  “As s ignable   C aus e”. C ommon  C aus e: Variation  caus ed  by  unknown  factors  res ulting  in   a  s teady  but  random  dis tribution  of  output  around  the  average  of the  data.  It  is  the  variation  left  over  after  s pecial  caus e  variation  has   been  removed  and  typically  (not  always )  follows  a  normal   dis tribution. If   we  know  that  the  bas ic  s tructure  of  the  data  s hould  follow  a   normal  dis tribution,  but  plots  from  our  data  s hows  otherwis e;   we know  the  data  contain  s pecial  caus es .

S pec ial  C aus es  =  O pportunity

Think about your data in terms of what it should look like, then compare it to what it does look like. See some deviation, maybe some Special Causes at work?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

157

Six Sigma Statistics Introduction to Graphing Passive data collection means don’t mess with the process! We are gathering data and looking for patterns in a graphical tool. If the data is questionable, so is the graph we create from it. For now utilize the data available, we will learn a tool called Measurement System Analysis later in this phase.

The purpose of Graphing is to: •  • 

Identify potential relationships between variables. Identify risk in meeting the critical needs of the Customer, Business and People. Provide insight into the nature of the X s which may or may not control Y. Show the results of passive data collection.

•  • 

In this section we will cover… 1.  2.  3.  4.  5. 

Box Plots Scatter Plots Dot Plots Time Series Plots Histograms

Data Sources Data demographics will come out of the basic Measure Phase tools such as Process Maps, X-Y Diagrams, FMEAs and Fishbones. Put your focus on the top X’s from X-Y Diagram to focus your activities.

Data sources are suggested by many of the tools that have been covered so far: –  –  –  – 

Process Map X-Y Matrix Fishbone Diagrams FMEA

Examples are:

LSS Black Belt Manual XL v11

1.

Time Shift Day of the week Week of the month Season of the year

3.

Operator Training Experience Skill Adherence to procedures

2.

Location/position Facility Region Office

4.

Any other sources?

© 2013 e-Careers Limited

158

Six Sigma Statistics Graphical Concepts The characteristics of a graph are critical to the graphing process. The validity of data allows us to understand the extent of error in the data. The selection of variables impacts how we can control a specific output of a process. The type of graph will depend on the data demographics while the range will be related to the needs of the customer. The visual analysis of the graph will qualify further investigation of the quantitative relationship between the variables.

T he  c harac teris tic s  of  a  g ood  g raph  inc lude: • Variety  of  data • S elec tion  of   – Variables – G raph – R ang e

Information  to  interpret  relations hips E xplore  quantitative  relations hips

The Histogram A Histogram is a basic graphing tool that displays the relative frequency or the number of times a measured items falls within a certain cell size. The values for the measurements are shown on the horizontal axis (in cells) and the frequency of each size is shown on the vertical axis as a bar graph. The graph illustrates the distribution of the data by showing which values occur most and least frequently. A Histogram illustrates the shape, centering and spread of the data you have. It is very easy to construct and an easy to use tool that you will find useful in many situations. This graph represents the data for the 20 days of arrival times at work from the previous lesson page. In many situations the data will form specific shaped distributions. One very common distribution you will encounter is called the Normal Distribution, also called the bell shaped curve for its appearance. You will learn more about distributions and what they mean throughout this course.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

159

Six Sigma Statistics Histogram Caveat As you can see in the SigmaXL® file the columns used to generate the Histograms above only have 20 data points. It is easy to generate your own samples to create Histogram simply by using the SigmaXL® menu path: “Data Manipulation>Ran dom Subset”

Variation on a Histogram The Histogram shown here looks to be very Normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

160

Six Sigma Statistics Dot Plot Using the “Graphing Data ” tab, create a Dot Plot. Histogram for the granular distribution obscures the granularity, whereas the Dot Plot reveals it. Points could have Special Causes associated with them. These occurrences should also be identified in the Logbook in order to assess the potential for a Special Cause related to them. You should look for potential Special Cause situations by examining the Dot Plot for both high frequencies and location. If in fact there are Special Causes (Uncontrollable Noise or Procedural non-compliance) then they should be addressed separately and then excluded from this analysis. Take a few minutes and create other Dot Plots using the columns in this worksheet.

Box Plot A Box Plot (sometimes called a Whisker Plot) is made up of a box representing the central mass of the variation and thin lines, called whiskers, extending out on either side representing the thinning tails of the distribution. Box Plots summarize information about the shape, dispersion and center of your data. Because of their concise nature, it easy to compare multiple distributions side by side. These may be “before” and “after” views of a process or a variable. Or they may be several alternative ways of conducting an operation. Essentially, when you want to quickly find out if two or more distributions are different (or the same) then you create a Box Plot. They can also help you spot outliers quickly which show up as asterisks on the chart. LSS Black Belt Manual XL v11

B ox  P lots  s ummarize  data  about  the  s hape,  dis pers ion  and  center   of  the   data  and  als o  help  s pot  outliers . B ox  P lots  require  that  one  of  the  variables ,  X  or   Y ,  be  categorical  or   dis crete  and  the  other  be  continuous .   A  minimum  of  10  obs ervations  s hould  be  included  in  generating  the  box   plot. Maximum Value

75th Percentile Middle 50% of Data

50th Percentile (Median) Mean 25th Percentile

min(1.5 x Interquartile Range or minimum value) Outliers

© 2013 e-Careers Limited

161

Six Sigma Statistics Box Plot Anatomy

Box

A Box Plot is based on quartiles and Outlier represents a distribution as shown * on the left of the graphic. The lines Upper Limit: Q3+1.5(Q3-Q1) extending from the box are called Upper Whisker whiskers. The whiskers extend outward to indicate the lowest and highest values in the data set Q3: 75th Percentile (excluding outliers). The lower Median Q2: Median 50th Percentile whisker represents the first 25% of the data in the Histogram (the light Q1: 25th Percentile grey area). The second and third quartiles form the box, which Lower Whisker represents fifty percent of the data and finally the whisker on the right Lower Limit: Q1+1.5(Q3-Q1) represents the fourth quartile. The line drawn through the box represents the median of the data. Extreme values, or outliers, are represented by asterisks. A value is considered an outlier if it is outside of the box (greater than Q3 or less than Q1) by more than 1.5 times (Q3-Q1). You can use the Box Plot to assess the symmetry of the data: If the data are fairly symmetric, the Median line will be roughly in the middle of the box and the whiskers will be similar in length. If the data are skewed, the Median may not fall in the middle of the box and one whisker will likely be noticeably longer than the other. Box Plot Examples The first Box Plot shows the differences in glucose level for nine different people. The second Box Plot shows the effects of cholesterol medication over time for a group of patients.

LSS Black Belt Manual XL v11

What can you tell about the data expressed in a Box Plots?

Eat this – then check the Box Plot!!

© 2013 e-Careers Limited

162

Six Sigma Statistics Box Plot Examples Use the “Graphing Data” worksheet tab.

The data shows the setup cycle time to complete “Lockout – Tagout” for three people in the department. Looking only at the Box Plots, it appears that Brian should be the benchmark for the department since he has the lowest median setup cycle time with the smallest variation. On the other hand, Shree’s data has 3 outlier points that are well beyond what would be expected for the rest of the data and his variation is larger. Be cautious drawing conclusions solely from a Box Plot. Shree may be the expert who is brought in for special setups because no one else can complete the job.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

163

Six Sigma Statistics Multi-Vari Chart Enhancement The Multi-Vari Chart shows the individual data points that are represented in the Box Plot. Open the workbook “Measure Data Sets” and select the “Graphing Data” tab.

The individual value plot shown here was created using SigmaXL®’s MultiVari Chart tool.

Attribute Y Box Plot Open the “Graphing Data” tab. To create this Box Plot follow the SigmaXL® menu path “SigmaXL>Graphical Tools>Boxplots” If the output is pass/fail, it must be plotted on the y axis. Use the data shown to create the transposed Box Plot. The reason we do this is for consistency and accuracy. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

164

Six Sigma Statistics Attribute Y Box Plot SigmaXL® does not permit transposed value and category scales so the above Box Plot shows pass/fail on the xaxis and Hydrogen Content on the Yaxis.

Individual Value Plot Open the “Graphing Data” worksheet, select “Graphical Tools > Boxplots”. Select Data as the Numeric Data Variable (Y), and Distribution Type as the Group Category (X). The Multi-Vari Chart was created and modified using “Graphical Tools > Multi-Vari Options” using the same variables as the Box Plot. Note, if these options are saved they will be used in “Graphical Tools > Multi-Vari Charts”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

165

Six Sigma Statistics Multi-Vari Individuals Go to the MultiVari Individuals worksheet. Note, SigmaXL® does not support Jitter, a feature used to spread the individual data points.

Time Series Plot Using the “Graphing Data” worksheet. A Run Chart is created by following the SigmaXL® menu path “SigmaXL>Graphic al Tools>Run Chart”. Run charts, also known as Time Series Plots are very useful in most projects. Every project should provide Run Chart data to look for frequency, magnitude and patterns. What X would cause these issues?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

166

Six Sigma Statistics Time Series Example Looking at the Time Series Plot, the response appears to be very dynamic. What other characteristic is present? The benefit of this approach to charting is you can see every data point as it is gathered over time. Some interesting occurrences can be revealed. Now, using the “Graphing Data” worksheet….. Now let’s lay 2 Time Series on top of each other. This can be done by following the SigmaXL® menu path “Graphical Tools > Overlay Run Chart” (use variables Time 2 and Time 3). What is happening within each plot? What’s the difference between the two plots? Time 3 appears to have wave pattern.

Note: SigmaXL® does not include Lowess Smoothing, however an advanced user could utilize exponential smoothing in Excel’s Data Analysis Toolpak.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

167

Six Sigma Statistics At this point, you should be able to: §  Explain the various statistics used to express location and spread of data §  Describe characteristics of a Normal Distribution §  Explain Special Cause variation §  Use data to generate various graphs and make interpretations based on their output

You have now completed Measure Phase – Six Sigma Statistics.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

168

Lean Six Sigma Black Belt Training

Measure Phase Measurement System Analysis

Now we will continue in the Measure Phase with “Measurements System Analysis”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

169

Measurement System Analysis Overview Measurement System Analysis is one of those non-negotiable items! MSA is applicable in 98% of projects and it alone can have a massive effect on the success of your project and improvements within the company.

Welc Welcome  to  Meas ome  to  Meas ure ure P Proc roces es ss  D  Dis is cco overy very SS ix ix  S  S ig igma  S ma  S tatis tatis tic ticss Meas Meas urement  S urement  S ys ys tem tem  A  Analys nalys is is B B as as ic icss  o  of  MS f  MS A A

In other words, LEARN IT & DO IT. It is very important.

V Variables ariables  MS  MS A A A Attribu ttribute  MS te  MS A A P Proc roces es ss  C  C apability apability Wrap  Up  &  A Wrap  Up  &  Acction  Items tion  Items

Introduction to MSA So far we have learned that the heart and soul of Six Sigma is that it is a data driven - methodology. – –

How do you know that the data you have used is accurate and precise? How do know if a measurement is a repeatable and reproducible?

How good are these?

Measurement System Analysis Measurement System Analysis or

MSA MSA In order to improve your processes, it is necessary to collect data on the "critical to" characteristics. When there is variation in this data, it can either be attributed to the characteristic that is being measured and to the way that measurements are being taken; which is known as measurement error. When there is a large measurement error, it affects the data and may lead to inaccurate decisionmaking. Measurement error is defined as the effect of all sources of measurement variability that cause an observed value (measured value) to deviate from the true value. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

170

Measurement System Analysis Introduction to MSA (Cont.) The measurement system is the complete process used to obtain measurements, such as the procedures, gages and personnel that are employed to obtain measurements. Each component of this system represents a potential source of error. It is important to identify the amount of error and, if necessary, the sources of error. This can only be done by evaluating the measurement system with statistical tools. There are several types of measurement error which affect the location and the spread of the distribution. Accuracy, linearity and stability affect location (the average). Measurement accuracy describes the difference between the observed average and the true average based on a master reference value for the measurements. A linearity problem describes a change in accuracy through the expected operating range of the measuring instrument. A stability problem suggests that there is a lack of consistency in the measurement over time. Precision is the variability in the measured value and is quantified like all variation by using the standard deviation of the distribution of measurements. For estimating accuracy and precision, multiple measurements of one single characteristic must be taken. The primary contributors to measurement system error are repeatability and reproducibility. Repeatability is the variation in measurements obtained by one individual measuring the same characteristic on the same item with the same measuring instrument. Reproducibility refers to the variation in the average of measurements of an identical characteristic taken by different individuals using the same instrument. Given that Reproducibility and Repeatability are important types of error, they are the object of a specific study called a Gage Repeatability & Reproducibility study (Gage R&R). This study can be performed on either attribute-based or variable-based measurement systems. It enables an evaluation of the consistency in measurements among individuals after having at least two individuals measure several parts at random on a few trials. If there are inconsistencies, then the measurement system must be improved. Measurement System Analysis Measurement System Analysis is the entire system, NOT just calibration or how good the measurement instrument is. We must evaluate the entire environment and Measurement System Analysis gives us a way to evaluate the measurement environment mathematically. All these sources of variation combine to yield a measurement that is different than the true value. It is also referred to as “Gage R&R” studies where R&R is: Repeatability & Reproducibility.

LSS Black Belt Manual XL v11

MS A   is   a   mathematical   procedure   to   quantify   v ariation   introduced to   a   process   or   product   by   the   a ct   of   measuring.

R eference

Item   to   b e   Meas ured

Meas urement Operator

E nvironment

Measurement E quipment P rocess P rocedure

The   item   to   be   m easured   c an   be   a   physical   part,   document   or   a   s c enario   for   c ustomer   s ervice.     Operator   c an   refer   to   a   person   or   c an   be   different   instruments   measuring  the   s ame   products.   R eference is   a   s tandard   that   is   used   to   c alibrate   the   e quipment.     P rocedure is   the   method   used   to   perform   the   test.     E quipment is   the   device   used   to   measure   the   product.     E nvironment is   the   s urroundings   where   the   measures   a re   performed.

© 2013 e-Careers Limited

171

Measurement System Analysis Measurement Purpose Measurement is a process within itself. In order to measure something you must go through a series of tasks and activities in sequence. Usually there is some from of set-up, there is an instrument that makes the measurement, there is a way of recording the value and it may be done by multiple people. Even when you are making a judgment call about something, there is some form of setup. You become the instrument and the result of a decision is recorded someway; even if it is verbal or it is a set of actions that you take.

Measurement Systems must provide value…

Value = Accurate Information = Usable Knowledge Key Question…

What do I need to know? Too often, organizations build complex data collection and information management systems without truly understanding how the data collected and metrics calculated can actually benefit the organization.

The types and sophistication of measurement vary almost infinitely. It is becoming increasingly popular or cost effective to have computerized measurement systems. The quality of measurements also varies significantly - with those taken by computer tending to be the best. In some cases the quality of measurement is so bad that you would be just as well off to guess at what the outcome should be. You will be primarily concerned with the accuracy, precision and reproducibility of measurements to determine the usability of the data.

Purpose The purpose of conducting an MSA is to mathematically partition sources of variation within the measurement system itself. This allows us to create an action plan to reduce the biggest contributors of measurement error.

LSS Black Belt Manual XL v11

MSA Objective

Reduce Error

The error can be partitioned into specific sources: –  Precision •  Repeatability - within an operator or piece of equipment •  Reproducibility - operator to operator or attribute gage to attribute gage –  Accuracy •  Stability - accuracy over time •  Linearity- accuracy throughout the measurement range •  Resolution •  Bias – Off-set from true value –  Constant Bias –  Variable Bias – typically seen with electronic equipment, amount of Bias changes with setting levels

© 2013 e-Careers Limited

172

Measurement System Analysis Accuracy and Precision Measurement systems, like all things, generate some amount of variation in the results/data they output. In measuring, we are primarily concerned with 3 characteristics:

Ac Acccurate  but  not  prec urate  but  not  precisise  -­‐ e  -­‐OOn  n   average,  the  s average,  the  shots hots  are  in  the    are  in  the   center  of  the  target  but  there  is center  of  the  target  but  there  is  a    a   lot  of  variability lot  of  variability

PPrec recisise  but  not  ac e  but  not  acccurate  -­‐ urate  -­‐TThe   he   average  is average  is  not  on  the  center,  but    not  on  the  center,  but   the  variability  is the  variability  is  s  small mall

1. How accurate is the measurement? For a repeated measurement, where is the average compared to some known standard?. Think of the target as the measurement system, the known standard is the bulls eye in the center of the target. In the first example you can see the “measurements” are very dispersed, there is a lot of variability as indicated by the Histogram curve at the bottom. But on average, the “measurements” are on target. When the average is on target, we say the measurement is accurate. However, in this example they are not very precise. 2. How precise is the measurement? For a repeated measurement, how much variability exists? As seen in the first target example, the “measurements” are not very precise, but on the second target they have much less dispersion. There is less variability as seen in the Histogram curve. However, we notice that the tight cluster of “measurements” are off target, they are not very accurate. 3. The third characteristic is how reproducible is the measurement from individual to another? What is the accuracy and precision from person to person. Here you would expect each person that performs the measurement to be able to reproduce the same amount of accuracy and precision as that of other person performing the same measurement. Ultimately, we make decisions based on data collected from measurement systems. If the measurement system does not generate accurate or precise enough data, we will make the decisions that generate errors, waste and cost. When solving a problem or optimizing a process, we must know how good our data are and the only way to do this is to perform a Measurement System Analysis.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

173

Measurement System Analysis MSA Uses

M S A   ca n   b e   u s e d   to : C ompa re  interna l  inspection  standa rds  with  the  standards  of  your customer. Hig hlig ht  a rea s  where  ca libra tion  tra ining  is  required. Provide  a  method  to  evaluate  inspector  tra ining  effectiveness  as well   a s  serves  a s  an  excellent  training  tool. Provide  a  g rea t  wa y  to: –C ompa re  existing  mea surement  equipment. –Q ua lify  new  inspection  equipment.

The measurement system always has some amount of variation and that variation is additive to the actual amount of true variation that exists in what we are measuring. The only exception is when the discrimination of the measurement system is so poor that it virtually sees everything the same. This means that you may actually be producing a better product or service than you think you are, providing that the measurement system is accurate; meaning it does not have a bias, linearity or stability problem. It may also mean that your customer may be making the wrong interpretations about your product or service. The components of variation are statistically additive. The primary contributors to measurement system error are Repeatability and Reproducibility. Repeatability is the variation in measurements obtained by one individual measuring the same characteristic on the same item with the same measuring instrument. Reproducibility refers to the variation in the average of measurements of an identical characteristic taken by different individuals using the same instrument. Why MSA? Why is MSA so important? MSA is was allows us to trust the data generated from our processes. When you charter a project you are taking on a significant burden which will require Statistical Analysis. What happens if you have a great project, with lots of data from measurement systems that produce data with no integrity?

LSS Black Belt Manual XL v11

M e a s u r e m e n t   S y s te m   A n a ly s is is  important  to: • Study  the  %  of  variation  in  our  process  that  is  caused  by  our   measurement  system. • C ompare  measurements  between  operators. • C ompare  measurements  between  two  (or  more)  measurement   devices. • Provide  criteria  to  accept  new  measurement  systems  (consider  new equipment). • Evaluate  a  suspect  g ag e. • Evaluate  a  g ag e  before  and  after  repair. • Determine  true  process  variation. • Evaluate  effectiveness  of  training  prog ram.

© 2013 e-Careers Limited

174

Measurement System Analysis Appropriate Measures Sufficient, means that are measures are available to be measured regularly, if not it would take too long to gather data. Relevant, means that they will help to understand and isolate the problems. Representative measures mean that we can detect variation across shifts and people.

A p p r o p r ia te   M e a s u r e s are: • Sufficient – available  to  be  measured  reg ularly • Relevant –help  to  understand/ isolate  the  problems • Representative -­‐ of  the  process  across  shifts  and  people • C ontextual – collected  with  other  relevant  information  that   mig ht  explain  process  variability.

Contextual means they are necessary to gather information on other relevant information that actually would help to explain sources of variation.

Poor Measures It is very common while working projects P o o r   M e a s u r e s can  result  from: to discover that the • Poor  or  non-­‐existent  operational  definitions current measurement systems are poor. • Difficult  measures Have you ever come • Poor  sampling across a situation where the data from • Lack  of  understanding  of  the  definitions your customer or • Inaccurate,  insufficient  or  non-­‐c alibrated  measurement   supplier doesn’t match yours? It devices happens often. It is likely a problem with M e a s u r e m e n t   Er r o r compromises  decisions  that  affect:   one of the – C ustomers   measurement systems. We have – Producers   worked MSA projects – Suppliers across critical measurement points in various companies, it’s not uncommon for more than 80% of the measurements to fail in one way or another.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

175

Measurement System Analysis Examples of What to Measure At this point you should have a fairly good idea of what to measure, listed here are some ideas to get you thinking…

Ex a m p le s   o f   w h a t   a n d   w h e n   to   m e a s u re : • Primary  and  secondary  metrics • Decision  points  in  Process  Maps • A ny  and  all  g aug es,  measurement  devices,  instruments,  etc • “X’s” in  the  process • Prior  to  Hypothesis  Testing • Prior  to  modeling • Prior  to  planning  desig ned  experiments • Before  and  after  process  chang es • To  qualify  operators

M S A   is   a   S h o w   S to p p e r!!!

Components of Variation

W h e n e v e r   y o u   m e a s u re   a n y th in g ,   th e   v a ria tio n   th a t   y o u   o b s e rv e   ca n   b e   s e g m e n te d   in to   th e   fo llo w in g   co m p o n e n ts …

O b s e rv e d   V a ria tio n Measurement  System  Error

Unit-­‐to-­‐unit  (true)  Variation Precision

Repeatability

Reproducibility

A ccuracy

Stability

Bias

Linearity

A ll  measurement  systems  ha ve  error.    If  you  don’t  know  how  much  of  the   variation  you  observe  is  contributed  by  your  measurement  system, you   cannot  make  confident  decisions. If   y o u   w e re   o n e   s p e e d in g   tick e t   a w a y   fro m   lo s in g   y o u r   lice n s e ,   h o w   fa s t   w o u ld   y o u   b e   w illin g   to   d riv e   in   a   s ch o o l   z o n e ? We are going to strive to have the measured variation be as close as possible to the true variation. In any case we want the variation from the measurement system to be a small as possible. We are now going to investigate the various components of variation of measurements. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

176

Measurement System Analysis Precision

A  precise  metric  is  one  that  returns  the  same  value  of  a  g iven   attribute  every  time  an  estimate  is  made. Precise  data  are  independent  of  who  estimates  them  or  when   the  estimate  is  made.

The spread of the data is measured by Precision. This tells us how well a measure can be repeated and reproduced.

Precision  ca n  be  partitioned  into  two  components: – Repeatability – Reproducibility R e p e a ta b ility   a n d   R e p ro d u cib ility   =   G a g e   R + R

Repeatability Measurements will be different…expect it! If measurement are always exactly the same this is a flag, sometimes it is because the gauge does not have the proper resolution, meaning the scale doesn’t go down far enough to get any variation in the measurement. For example, would you use a football field to measure the gap in a spark plug?

LSS Black Belt Manual XL v11

R e p e a ta b ility is  the  variation  in  measurements  obtained  with   o n e   m e a s u re m e n t   in s tru m e n t   used  several  times  by  one  appraiser   while  measuring  the  identical  characteristic  on  the   s a m e   p a rt. Y

Repeatability For  example: – Manufacturing :    O ne  person  measures  the  purity  of  multiple  samples   of  the  same  via l  and  g ets  different  purity  measures. – Transactiona l:    O ne  person  evaluates  a  contract  multiple  times  (over  a   period  of  time)  and  makes  different  determina tions  of  errors.

© 2013 e-Careers Limited

177

Measurement System Analysis Reproducibility Reproducibility will be present when it is possible to have more than one operator or more than one instrument measure the same part.

R e p r o d u cib ility is  the  variation  in  the  averag e  of  the   measurements  made  by  d iffe re n t   appraisers  using  the  s a m e   m e a s u rin g   in s tru m e n t   when  measuring  the  identical   characteristic  on  the  s a m e   p a rt. R e p ro d u cib ility Y

O perator  A O perator  B

For  example: – Manufacturing :    Different  people  perform  purity  test  on  samples   from   the  same  vial  and  g et  different  results. – Transactional:    Different  people  evaluate  the  same  contract  and   make  different  determinations.

Time Estimate Exercise

Ex e rcis e   o b je ctiv e : Demonstrate  how  well  you  can   estimate  a  1 0  second  time  interval. 1 . Pair  up  with  an  associate. 2 . O ne  person  will  say  start  and  stop  to  indicate  how   long  they  think  the  1 0  seconds  last.    Do  this  6  times. 3 . The  other  person  will  have  a  watch  with  a  second   hand  to  actually  measure  the  duration  of  the  estimate.     Record  the  value  where  your  partner  can’t  see  it.     4 . Switch  tasks  with  partner  and  do  it  6  times  also. 5 . Record  all  estimates,  what  do  you  notice?  

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

178

Measurement System Analysis Accuracy Accuracy and the average are related. Recall in the Basic Statistics module we talked about the Mean and the variance of a distribution. Think of it this way….If the Measurement System is the distribution then accuracy is the Mean and the precision is the variance.

A n  accurate  measurement  is  the  difference  between  the  observed  a verag e  of   the  measurement  and  a  reference  value.     – W hen  a  metric  or  measurement  system  consistently  over  or  under  estimates  the   value  of  an  attribute,  it  is  said  to  be   “inaccurate”

A ccuracy  can  be  assessed  in  several  ways: – Measurement  of  a  known  sta ndard – C omparison  with  another  known  measurement  method – Prediction  of  a  theoretical  value

W hat  happens  if  we  don’t  have  standards,  comparisons  or  theories? Tru e A v e ra g e

W a rn in g ,   d o   n o t   a s s u m e   y o u r   m e tro lo g y   re fe re n ce   is   g o s p e l.

A ccu ra cy

M e a s u re m e n t

Accuracy Against a Known Standard

In Transactional Processes the measurement system can consist of a database query. !  For example, you may be interested in measuring product returns where you will want to analyze the details of the returns over some time period. !  The query will provide you all the transaction details.

However, before you invest a lot of time analyzing the data, you must ensure the data has integrity. !  The analysis should include a comparison with known reference points. !  For the example of product returns, the transaction details should add up to the same number that appears on financial reports, such as the income statement.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

179

Measurement System Analysis Accuracy vs. Precision

A C C U R A TE

B O TH

P R EC IS E

+

= A ccuracy  relates  to  how  close  the   averag e  of  the  shots  are  to  the   Master  or  bull's-­‐eye. Precision relates  to  the  spread  of   the  shots  or  Variance.    

N EITH ER

Most Measurement Systems are accurate but not at all precise.

Bias

B ia s is  defined  as  the  deviation  of  the  measured  value  from  the   actual  value.   C alibration  procedures  can  minimiz e  and  control    bias  within   acceptable  limits.    Ideally,  Bias  can  never  be  eliminated  due  to material  wear  and  tear! Bias

Bias

Bias is a component of Accuracy. Constant Bias is when the measurement is off by a constant value. A scale is a prefect example, if the scale reads 3 lbs when there is no weight on it then there is a 3lb Bias. Make sense? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

180

Measurement System Analysis Stability Stability just looks for changes in the accuracy or Bias over time.

S ta b ility of  a  g aug e  is  defined  as  error  (measured  in  terms  of   standard  deviation)  as  a  function  of  time.    Environmental  conditions   such  as  cleanliness,  noise,  vibration,  lig hting ,  chemical,  wear   and   tear  or  other  factors  usually  influence  g aug e  instability.    Idea lly,   g aug es  can  be  maintained  to  g ive  a  hig h  deg ree  of  stability  but   can   never  be  eliminated  unlike  reproducibility.    G aug e  stability  studies   would  be  the  first  exercise  past  calibration  procedures.     C ontrol  C harts  are  commonly  used  to  track  the  stability  of  a   measurement  system  over  time.     Drift S ta b ility   is   B ia s   ch a ra cte riz e d   a s   a   fu n ctio n   o f   tim e !

Linearity Lin e a rity is  defined  as  the  difference  in  Bias  values  throug hout  the   measurement  rang e  in  which  the  g aug e  is  intended  to  be  used.  This  tells  you   how  accurate  your  measurements  are  throug h  the  expected  rang e  of the   measurements.  It  answers  the  question,  "Does  my  g ag e  have  the  sa me   accura cy  for  all  siz es  of  objects  being  measured?" Linearity  =  | Slope|  *  Process  Variation Low

High

+e B i a s (y)

%  Linearity  =  | Slope|  *  1 0 0

Nominal

-e

0.00

*

*

*

Reference Value (x) y = a + b.x y: Bias, x: Ref. Value a: Slope, b: Intercept

Linearity just evaluates if any Bias is consistent throughout the measurement range of the instrument. Many times Linearity indicates a need to replace or maintenance measurement equipment. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

181

Measurement System Analysis Types of MSA’s Variable Data is always preferred over Attribute because it give us more to work with. Now we are gong to review Variable MSA testing.

M S A ’ s   fa ll   in to   tw o   ca te g o rie s : – A ttrib u te – V a ria b le A ttrib u te

V a ria b le

– – – – –

– – – – –

P a s s / Fa il G o / N o   G o D o cu m e n t   P r e p a ra tio n S u rfa ce   im p e rfe ctio n s C u s to m e r   S e rv ice   Resp onse

C o n tin u o u s   s ca le   D is cre te   s ca le C ritica l   d im e n s io n s P u ll   s tre n g th W a rp

Tra n s a ctio n a l   p ro je cts   ty p ica lly   h a v e   a ttrib u te   b a s e d   m e a s u re m e n t   s y s te m s .     M a n u fa ctu rin g   p ro je cts   g e n e ra lly   u s e   v a ria b le   s tu d ie s   m o re   o fte n ,   b u t   d o   u s e   a ttrib u te   s tu d ie s   to   a   le s s e r   d e g re e .

Variable MSA’s MSA’s use a random effects model meaning that the levels for the variance components are not fixed or assigned, they are assumed to be random.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

182

Measurement System Analysis Cheat Sheet SigmaXL®’s default is 6 * StDev. Select “5.15 * StDev” in the dialog box. SigmaXL® uses this default to be consistent with 6 * StDev used in process capability . The 5.15 multiplier is common in the automotive industry (AIAG MSA Handbook). The worksheet used for this example is “Gage AIAG 2 -SigmaXL Template” . The above slide is for demonstration purposes, this dataset will be used in a later exercise. Notice the calculation method explained here for Distinct Categories.

Traditionally NDC is truncated to an integer value, but SigmaXL® reports a more informative one decimal place. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

183

Measurement System Analysis Number of Distinct Categories

Th e   n u m b e r   o f   d is tin ct   ca te g o rie s   te lls   y o u   h o w   m a n y   s e p a ra te   g ro u p s   o f   p a rts   th e   s y s te m   is   a b le   to   d is tin g u is h . U n a ccep ta b le   fo r   e s tim a tin g   p ro ces s   p a ra m e te rs   a n d   in d ice s O n ly   in d ica te s   w h e th e r   th e   p ro ces s   is   p ro d u cin g   co n fo rm in g   o r   n o n co n fo rm in g   p a rts

1 Data Category

G e n e ra lly   u n a cce p ta b le   fo r   e s tim a tin g   p ro ce s s   p a ra m e te rs   a n d   in d ice s O n ly   p ro v id es   co a rs e   e s tim a tes

2 - 4 Categories

R eco m m e n d e d 5 or more Categories

Here is a rule of thumb for distinct categories.

AIAG Standards for Gage Acceptance

Here  are  the  A utomotive  Industry  A ction  G roup’s  definitions  for   G ag e  acceptance. %   To le ra n ce   or %   S tu d y   V a ria n ce

%   C o n trib u tio n

S y s tem   is …

1 0 %   o r   le s s

1 %   o r   le s s

Id e a l

1 0 %   -­‐ 2 0 %

1 %   -­‐ 4 %

A ccep ta b le

2 0 %   -­‐ 3 0 %

5 %   -­‐ 9 %

M a rg in a l

3 0 %   o r   g re a te r

LSS Black Belt Manual XL v11

1 0 %   o r   g re a te r

Poor

© 2013 e-Careers Limited

184

Measurement System Analysis SigmaXL® Graphic Output Cheat Sheet

This chart may be recreated by taking the following steps: 1. Copy the “% Total Variation (TV)” column. 2. Paste the column to the right of the “% Contribution of Variance Component” column. 3. Highlight the entire table which the “% Total Variation (TV)” was added. 4. From Excel, Insert> (Chart) Column>2-D Clustered Column. 5. Delete the “Variance Component “ column from this chart.

This chart may be found in the “Gage R&R - X-Bar & R (1)” worksheet. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

185

Measurement System Analysis SigmaXL® Graphic Output Cheat Sheet (cont.)

SigmaXL® produces these Multi-Vari Charts as part of the Gage R&R report. Select the “Gage R&R - X-Bar & R (1)” worksheet. Currently the Gage R&R report in SigmaXL® does not include an Interaction Plot. The following steps show how to create the Interaction Plot using Two-Way ANOVA: 1. Select the data which will be used for the chart. 2. Select “SigmaXL>Statistical Tools>Two-Way ANOVA” 3. This chart was generated from the “Gage AIAG2 SigmaXL Format” worksheet. Select “Response” as “Numerical Data Variable (Y)”, “Part” as “Group Category Factor (X1)”, and “Operator” as “Group Category Factor (X2)”. The operator by part interaction plot is given in the Two-Way ANOVA output worksheet.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

186

Measurement System Analysis SigmaXL® Graphic Output Cheat Sheet (cont.) Currently the Gage R&R report in SigmaXL® does not include a Multi-Vari Chart showing all parts. To create the above chart, use SigmaXL®’s Multi-Vari tool: 1.  Select the data which will be used for the chart. 2.  Select “SigmaXL>Graphical Tools>Multi-Vari Chart” 3. This chart was generated from the “Gage AIAG2 SigmaXL Format” worksheet. Select “Response” as “Numerical Data Variable (Y)”, “Part” as “Group Category Factor (X1)”, and “Operator” as “Group Category Factor (X2)”.

This Multi-Vari Chart was created with SigmaXL®’s Multi-Vari tool: 1.  Select the data which will be used for the chart. 2.  Select “SigmaXL>Graphical Tools>Multi-Vari Chart” 3. This chart was generated from the “Gage AIAG2 SigmaXL Format” worksheet. Select “Response” as “Numerical Data Variable (Y)”, “Operator” as “Group Category Factor (X1)”, and “Part” as “Group Category Factor (X2)”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

187

Measurement System Analysis Practical Conclusions

Repeatability and Reproducibility Problems For Repeatability Problems: If all operators have the same Repeatability and it is too big, the gage needs to be repaired or replaced. If only one operator or in the case where there are no operators, but several gages and only one gage is showing Repeatability problems, retrain the one operator or replace the one gage.

R e p e a ta b ility   P r o b le m s : • •

C alibrate  or  replace  g ag e. If  only  occurring  with  one  operator,  re-­‐train.

R e p r o d u cib ility   P r o b le m s : •

•

Measurement  ma chines – Similar  machines   • Ensure  all  have  been  calibrated  a nd  that  the  sta ndard  measurement   method  is  being  utiliz ed.   – Dissimilar  ma chines   • O ne  machine  is  superior. O perators – Training  and  skill  level  of  the  operators  must  be  assessed. – O perators  should  be  observed  to  ensure  that  sta nda rd  procedures   are   followed. O perator/ machine  by  part  intera ctions – Understand  why  the  operator/ machine  had  problems  measuring  some   parts   and  not  others. • Re-­‐measure  the  problem  parts     • Problem  could  be  a  result  of  g ag e  linearity • Problem  could  be  fixture  problem • Problem  could  be  poor  g ag e  design

• For Reproducibility Problems: In the case where only machines are used and the multiple machines are all similar in design, check the calibration and ensure that the standard measurement method is being used. One of the gages maybe performing differently than the rest, the graphs will show which one is performing differently. It may need to go in for repair or it may simply be a setup or calibration issue. If dissimilar machines are used it typically means that one machine is superior. In the case where multiple operator are the graphs will show who will need additional training to perform at the same level as the rest. The most common operator/machine interactions are either someone misread a value, recorded the value incorrectly or that the fixture holding the part is poor.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

188

Measurement System Analysis Design Types Crossed Designs are the workhorse of MSA. They are the most commonly used design in industries where it is possible to measure something more than once. Chemical and biological systems can use Crossed Designs also as long as you can assume that the samples used come from a homogeneous solution and there is no reason they can be different.

C ro s s e d   D e s ig n • A  crossed  desig n  is  used  only  in  non-­‐d estructive  testing  and  assumes  that  all   the  parts  can  be  measured  multiple  times  by  either  operators  or   multiple   machines.     – G ives  the  ability  to  separate  part-­‐to-­‐p art  varia tion  from  measurement   system  variation. – A ssesses  repeatability  and  reproducibility. – A ssesses  the  interaction  between  the  operator  and  the  part. N e s te d   D e s ig n • A  nested  desig n  is  used  for  destructive  testing  (we  will  learn  a bout  this  in   MBB  tra ining )  and  also  situations  where  it  is  not  possible  to  ha ve  all   operators  or  machines  measure  all  the  parts  multiple  times. – Destructive  testing  assumes  that  all  the  parts  within  a  sing le  b atch  are   identical  enoug h  to  claim  they  are  the  same. – N ested  desig ns  are  used  to  test  measurement  systems  where  it  is   not   possible  (or  desirable)  to  send  operators  with  parts  to  different  locations. – Do  not  include  all  possible  combinations  of  factors. – Uses  slig htly  different  mathematical  model  than  the  crossed  desig n.

Nested Designs must be used for destructive testing. In a Nested Design, each part is measured by only one operator. This is due to the fact that after destructive testing, the measured characteristic is different after the measurement process than it was at the beginning. Crash testing is an example of destructive testing. If you need to use destructive testing, you must be able to assume that all parts within a single batch are identical enough to claim that they are the same part. If you are unable to make that assumption then part-to-part variation within a batch will mask the measurement system variation. If you can make that assumption, then choosing between a Crossed or Nested Gage R&R Study for destructive testing depends on how your measurement process is set up. If all operators measure parts from each batch, then use Gage R&R Study (Crossed). If each batch is only measured by a single operator, then you must use Gage R&R Study (Nested). In fact, whenever operators measure unique parts, you have a Nested Design. Your Master Black Belt can assist you with the set-up of your design.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

189

Measurement System Analysis Gage R & R Study A Gage R&R, like any study, Gage R&R Study requires careful planning. The •  Is a set of trials conducted to assess the Repeatability and common way of doing an Reproducibility of the measurement system. Attribute Gage R&R consists •  Multiple people measure the same characteristic of the same set of of having at least two people multiple units multiple times (a crossed study) measure 20 parts at random, •  Example: 10 units are measured by 3 people. These units are then twice each. This will enable randomized and a second measure on each unit is taken. you to determine how consistently these people A Blind Study is extremely desirable. evaluate a set of samples •  Best scenario: operator does not know the measurement is a part of a against a known standard. If test there is no consistency •  At minimum: operators should not know which of the test parts they are among the people, then the currently measuring. measurement system must be improved, either by defining a measurement NO, not that kind of R&R!! method, training, etc. You use an Excel spreadsheet template to record your study and then to perform the calculations for the result of the study. Variable Gage R & R Steps The parts selected for S te p   1 : C all  a  team  meeting  a nd  introduce  the  concepts  of  the  G ag e  R&R the MSA are not S te p   2 : Select  parts  for  the  study  across  the  rang e  of  interest random samples. We – If  the  intent  is  to  evaluate  the  measurement  system  throug hout  the  process  rang e,   want to be sure the select  parts  throug hout  the  rang e     parts selected – If  only  a  small  improvement  is  being  made  to  the  process,  the  ra ng e  of  interest  is   now  the  improvement  rang e represent the overall S te p   3 : Identify  the  inspectors  or  equipment  you  plan  to  use  for  the  ana lysis spread of parts that – In  the  case  of  inspectors,  explain  the  purpose  of  the  analysis  a nd  that  the   would normally be seen inspection  system  is  being  evaluated  not  the  people in manufacturing. Do S te p   4 : C alibrate  the  g ag e  or  g ag es  for  the  study not include parts that – Remember  linearity,  stability  and  bias are obviously grossly S te p   5 : Have  the  first  inspector  measure  all  the  sa mples  once  in  random order defective, they could S te p   6 :   Have  the  second  inspector  measure  all  the  samples  in  random  order     actually skew your – C ontinue  this  process  until  all  the  operators  have  measured  all   the  parts  one  time     mathematical results – This  completes  the  first  replicate and conclude that the S te p   7 : Repeat  steps  5  and  6  for  the  required  number  of  replicates     MSA is just fine. For – Ensure  there  is  always  a  delay  between  the  first  and  second  insp ection example, an engine S te p   8 : Enter  the  data  into  MIN ITA B TM and    analyz e  your  results     manufacturer was using S te p   9 : Draw  conclusions  and  ma ke  chang es  if  necessary a pressure tester to check for leaks in engine blocks. All the usual ports were sealed with plugs and the tester was attached and pressure was applied. Obviously, they were looking for pin hole leaks that would cause problems later down the line. The team performing the MSA decided to include an engine block that had a hole in the casting so large you could insert your entire fist. That was an obvious gross defect and should never been included in the MSA. Don’t be silly saying that once in a while you get a part like that and it should be tested. NO IT SHOULDN’T - you should never have received it in the first place and you have got much bigger problems to take care of before you do an MSA.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

190

Measurement System Analysis Gage R & R Study This is the most commonly used Crossed Design. 10 parts are each measure by 3 different operators 2 different times. To get the total number of data points in the study simply multiply these numbers together. In this study we have 60 measurements.

P a rt   A llo ca tio n   Fro m   A n y   P o p u la tio n 1 0   x   3   x   2   C ro s s e d   D e s ig n   is   s h o w n A   m in im u m   o f   tw o   m e a s u re m e n ts / p a rt/ o p e ra to r   is   re q u ire d Th re e   is   b e tte r! Tria l   1

O p e ra to r   1

P a r t s

Tria l   2 1

2

3

4

5

6

7

8

9 10

Tria l   1

O p e ra to r   2

Tria l   2 Tria l   1

O p e ra to r   3

Tria l   2

Data Collection Sheet

This and the next few slides show how to create a data collection table in SigmaXL®.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

191

Measurement System Analysis Data Collection Sheet

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

192

Measurement System Analysis Gage R & R We will now repeat the analysis of the previous Gage R&R data with a Standard Deviation Multiplier of 6 and a Tolerance value of 1. Recall that the previous analysis used a Standard Deviation Multiplier of 5.15. Change Alpha to remove interaction to 0.25. This will prevent SigmaXL® from removing the part by operator interaction term. Select “SigmaXL>Measurement Systems Analysis > Analyze Gage R&R (Crossed)” and enter the values as shown above. Graphical Output This chart may be recreated by taking the following steps: 1. Copy the “% Total Variation (TV)” column. 2. Paste the column to the right of the “% Contribution of Variance Component” column. 3. Copy the “% Tolerence” column. 4. Paste the column to the right of the “% Total Variation (TV)” column. 5. Highlight the entire table which the “% Total Variation (TV)” was added. 6. From Excel, Insert> (Chart) Column>2-D Clustered Column. 7. Delete the “Variance Component “ column from this chart.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

193

Measurement System Analysis Graphical Output (cont.) This Multi-Vari Chart was created with SigmaXL®’s Multi-Vari tool: 1. Select the data which will be used for the chart. 2. Select “SigmaXL>Graphical Tools>MultiVari Chart” 3. This chart was generated from the “Gage AIAG2 - SigmaXL Format” worksheet. Select “Response” as “Numerical Data Variable (Y)”, “Operator” as “Group Category Factor (X1)”, and “Part” as “Group Category Factor (X2)”. The ANOVA table values are utilized to calculate % Contribution and Standard Deviation. To calculate % study variation and % tolerance, you will need to know values for the Standard Deviation and tolerance ranges. SigmaXL® defaults to a value of 6 (the number of Standard Deviations within which about 99.7 % of your values should fall). Tolerance ranges are based on process tolerance and are business values specific to each process.

I can see clearly now!!

This output tells us the Tolerance is 19.40, the output is 17.05. Therefore, this gage is acceptable. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

194

Measurement System Analysis Signal Averaging

Signal Averaging Example

Suppose  SV/ Tolerance  is  3 5 %. SV/ Tolerance  must  be  1 5 %  or  less  to  use  g ag e. Suppose  the  Standard  Deviation  for  one  part  measured  by  one  person   many  times  is  9 .5 . Determine  what  the  new  reduced  Standard  Deviation  should  be.

Here we have a problem with Repeatability, not Reproducibility so we calculate what the Standard Deviation should be in order to meet our desire of a 15% gage. The 35% represents the biggest problem, Repeatability. We are assuming that 15% will be acceptable for the short term until an appropriate fix can be implemented. The 9.5 represents our estimate for Standard Deviation of population of Repeatability. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

195

Measurement System Analysis Signal Averaging Example (cont.) We now use it in the Central Limit Theorem equation to estimate the needed number of repeated measures to do this we will use the Standard Deviation estimated previously.

Determine sample size:

Using the average of 6 repeated measures will reduce the Repeatability component of measurement error to the desired 15% level.

This method should be considered temporary!

Paper Cutting Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

196

Measurement System Analysis Attribute MSA The Discrete Measurement Study is a set of trials conducted to assess the ability of operators to use an operational definition or categorize samples, an Attribute MSA has: 1 . Multiple operators measure (categorize) multiple samples a multiple number of times. For example: 3 operators each categorize the same 50 samples, then repeat the measures at least once.

A  methodolog y  used  to  assess  A ttribute  Measurement  Systems.

AAttribute  G ttribute  Gag age  Error e  Error

Repeata Repeatability bility

Reproducibility Reproducibility

CCaalibration libration

– They  a re  used  in  situa tions  where  a  continuous  mea sure  ca nnot   be  obta ined. – It  requires  a  minimum  of  5 x  a s  ma ny  sa mples  a s  a  continuous   study.   – Disa g reements  should  be  used  to  cla rify  opera tiona l  definitions   for  the  ca teg ories.   • A ttribute  data  are  usua lly  the  result  of  huma n  judg ment  (which   categ ory  does  this  item  belong  in). • W hen  ca teg oriz ing  items  (g ood/ bad;  type  of  call;  reason  for   leaving )  you  need  a  hig h  deg ree  of  ag reement  on  which  way  a n   item  should  be  ca teg oriz ed.

2. The test should be blind. It is difficult to run this without the operator knowing it is a calibration test, but the samples should be randomized and their true categorization unknown to each operator.

The test is analyzed based on correct (vs. incorrect) answers to determine the goodness of the measuring system.

Attribute MSA Purpose

The  purpose  of  an  A ttr ib u te   M S A is: – – – –

To  determine  if  all  inspectors  use  the  same  criteria  to  determine  “pass” from  “fail”. To  assess  your  inspection  sta ndards  ag ainst  your  customer’s  requirements. To  determine  how  well  inspectors  are  conforming  to  themselves.   To  identify  how  inspectors  are  conforming  to  a   “known  master,” which  includes: • How  often  operators  ship  defective  product. • How  often  operators  dispose  of  acceptable  product. – Discover  areas  where: • Training  is  required. • Procedures  must  be  developed. • Sta ndards  are  not  available. A n  A ttribute  MSA  is  similar  in  many  ways  to  the  continuous  MSA ,   including  the   purposes.    Do  you  ha ve  any  visual  inspections  in  your  processes? In  your  experience   how  effective  ha ve  they  been?

When a Continuous MSA is not possible an Attribute MSA can be performed to evaluate the quality of the data being reported from the process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

197

Measurement System Analysis Visual Inspection Test Take 60 Seconds and count the number of times “F” appears in this paragraph?

The  N ecessity  of  Training  Farm  Hands  for  First  C lass  Farms   in  the  Fatherly  Handling  of  Farm  Live  Stock  is  Foremost  in   the  Eyes  of  Farm  O wners.  Since  the  Forefathers  of  the  Farm   O wners  Trained  the  Farm  Hands  for  First  C lass  Farms  in   the  Fatherly  Handling  of  Farm  Live  Stock,  the  Farm  O wners   Feel  they  should  carry  on  with  the  Family  Tradition  of   Training  Farm  Hands  of  First  C lass  Farmers  in  the  Fatherly   Handling  of  Farm  Live  Stock  Because  they  Believe  it  is  the   Basis  of  G ood  Fundamental  Farm  Manag ement. Tally the answers? Did everyone get the same answer? Did anyone get 36? That’s the right answer! Why not? Does everyone know what an “F” (defect) looks like? Was the lighting good in the room? Was it quite so you could concentrate? Was the writing clear? Was 60 seconds long enough? This is the nature of visual inspections! How many places in your process do you have visual inspection? How good do you expect them to be? How can we Improve Visual Inspection?

V is u a l   In s p e ctio n ca n   b e   im p ro v e d   b y : • O p e ra to r   Tra in in g   &   C e rtifica tio n • D e v e lo p   V is u a l   A id s / B o u n d a ry   S a m p le s • Es ta b lis h   S ta n d a rd s • Es ta b lis h   S e t-­‐U p   P ro ce d u re s • Es ta b lis h   Ev a lu a tio n   P ro ce d u re s – Ev a lu a tio n   o f   th e   s a m e   lo ca tio n   o n   e a ch   p a rt. – Ea ch   e v a lu a tio n   p e rfo rm e d   u n d e r   th e   s a m e   lig h tin g . – En s u re   a ll   e v a lu a tio n s   a re   m a d e   w ith   th e   s a m e   s ta n d a rd .

ook  closely  n ow! Look Lclosely now!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

198

Measurement System Analysis Attribute Agreement Analysis

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

199

Measurement System Analysis Attribute Agreement Analysis (cont.) Fleiss’ Kappa statistic is a “correlation coefficient” for discrete data. Kappa ranges from -1 to +1. A Kappa value of +1 indicates perfect agreement. If Kappa = 0, then agreement is the same as would be expected by chance. If Kappa = -1, then there is perfect disagreement. Kappa values > 0.9 indicate a very good measurement system; Kappa values > 0.7 indicate an acceptable measurement system. The Between Appraiser Agreement and All Appraisers vs. Standard Agreement are also known as “System Effectiveness Scores”, with > 95% considered very good, 90-95% acceptable, 80 to < 90 % marginal, and < 80 % unacceptable. Clearly this measurement system needs to be improved, but we should not be quick to judge Appraiser C. The confidence intervals are quite wide and overlap. It is a good practice to “blame the process not the people”. Look for unclear or confusing operational definitions, inadequate training, operator distractions or poor lighting. Consider the use of pictures to clearly define a defect. Use Attribute MSA as a way to “put your stake in the ground” and track the effectiveness of improvements to the measurement system.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

200

Measurement System Analysis M&M Exercise

Exercise objective: Perform and Analyze an Attribute MSA Study. • 

•  Number

Part

Attribute

1

M&M

Pass

2

M&M

Fail

3

M&M

Pass

You will need the following to complete the study: – 

A bag of M&Ms containing 50 or more pieces

– 

The attribute value for each piece.

– 

Three or more inspectors.

Judge each M&M as pass or fail. – 

The customer has indicated that they want a bright and shiny M&M and that they like M s.

• 

Pick 50 M&Ms out of a package.

• 

Enter results into SigmaXL® s Attribute MSA Template and draw conclusions.

• 

The instructor will represent the customer for the Attribute score.

To complete this study you will need, a bag of M&Ms containing 50 or more “pieces”. The Attribute Value for each piece, which means the “True” value for each piece, in addition to being the facilitator of this study you will also serve as the customer, so you will have the say as to if the piece is actually a Pass or Fail piece. Determine this before the inspectors review the pieces. You will need to construct a sheet as shown here to keep track of the “pieces” or “parts” in our case M&Ms it is important to be well organized during these activities. Then the inspectors will individually judge each piece based on the customer specifications of bright and shiny M&M with nice M’s.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

201

Measurement System Analysis At this point, you should be able to: §  Understand Precision & Accuracy §  Understand Bias, Linearity and Stability §  Understand Repeatability & Reproducibility §  Understand the impact of poor gage capability on product quality. §  Identify the various components of variation §  Perform the step by step methodology in variable, and attribute MSA’s You have now completed Measure Phase – Measurement System Analysis.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

202

Lean Six Sigma Black Belt Training

Measure Phase Process Capability

Now we will continue in the Measure Phase with “Process Capability”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

203

Process Capability Overview Within this module we are going to go through Stability and its affect on a process as well as how to measure the Capability of a process.

W W eelco lcom m ee    to to    M Meeaa ssuure re

We will examine the meaning of each of these and show you how to apply them.

M Meeaa ssuure rem m eennt  t  SSyy sste tem m     AA nnaa ly ly ssis is

PPro roce cessss    D Dis isco covv eery ry SSix ix    SSig ig m m aa    SSta ta tis tistics tics

PPro roce cessss    CCaa ppaa bbility ility CC ontinuous  C ontinuous  C apa apability bility CC oncept  of  Stability oncept  of  Stability AAttribute  C ttribute  C apability apability W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Understanding Process Capability

Process Capability: • 

The inherent ability of a process to meet the expectations of the customer without any additional efforts.

• 

Provides insight as to whether the process has a : –  –  –  – 

• 

Centering Issue (relative to specification limits) Variation Issue A combination of Centering and Variation Inappropriate specification limits

Allows for a baseline metric for improvement.

Are you capable?! *Efforts: Time, Money, Manpower, Technology, and Manipulation

This is the Definition of Process Capability. We will now begin to learn how to assess it.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

204

Process Capability Capability as a Statistical Problem Simply put Six Sigma always starts with a practical problem, translates it into a statistical problem, corrects the statistical problem and then validates the practical problem.

O u r   S ta tis tica l   P ro b le m : W hat  is  the  probability  of  our   process  producing  a  defect  ? Define  a  Practical Problem C reate  a   Sta tistical  Problem C orrect  the Sta tistical  Problem

We will re-visit this concept over and over, especially in the Analyze Phase when determining sample size.

A pply  the  C orrection to  the  Practical   Problem

Capability Analysis

Op i

Verified ?

Op i + 1

Analysis

Scrap

Frequency

Capability Analysis provides The X’s The Y’s you with a quantitative Y = f(X) (Process Function) Variation – “Voice of (Inputs) (Outputs) the Process” assessment of your processes ability to meet the Data for requirements placed on it. Y1…Yn Y1 Capability Analysis is Y2 traditionally used for Y3 assessing the outputs of a process, in other words comparing the Voice of the Requirements – “Voice Critical X(s): Process to the Voice of the of the Customer” Any variable(s) USL = 10.44 LSL = 9.96 which exerts an Customer. However, you can undue influence on the important use the same technique to outputs (CTQ’s) of a process assess the capability of the inputs going into the C a p a b ility   A n a ly s is   N u m erica lly   process. they are after all, C o m p a re s   th e   V O P   to   th e   V O C outputs from some previous Percent Composition process, and you have expectations, specifications or requirements for their performance. Capability Analysis will give you a metric that you can use to describe how well it performs and you can convert this metric to a sigma score if you so desire. X1

X2

Off-Line Correction

X3

X4

Yes

X5

No

10.16 10.11 10.16 10.05 10.11 10.33 10.05 10.44 10.33 9.86 10.44 10.07 9.86 10.29 10.07 10.36 10.29 10.36

9.87 10.16 9.99 9.87 10.11 10.12 9.99 10.05 10.43 10.12 10.33 10.21 10.43 10.44 10.01 10.21 9.86 10.15 10.01 10.07 10.44 10.15 10.29 10.03 10.44 10.36 10.33 10.03 10.15 10.33 10.15

9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5

Correctable

?

Data - VOP

10.16 10.11 10.05 10.33 10.44 9.86 10.07 10.29 10.36

9.87 9.99 10.12 10.43 10.21 10.01 10.15 10.44 10.03 10.33 10.15

10.16 10.11 10.05 10.33 10.44 9.86 10.07 10.29 10.36

Defects

-6

-5

Defects

-4

-3

-2

-1

+1

+2

+3

+4

+5

+6

9.70 9.80 9.90 10.0 10.1 10.2 10.3 10.4 10.5 10.6

You will learn in the lesson how the output variation width of a given process output compares with the specification width established for that out put. This ratio, the output variation width divided by the specification width is what is know as capability. Since the specification is an essential part of this assessment, a rigorous understanding of the validity of the specification is vitally important, it also has to be accurate. This is why it is important to perform a RUMBA type analysis on process inputs and outputs. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

205

Process Capability Process Output Categories

e uc

d Re

Two output behaviors determine how well we meet Incapable Off target our customer or process Average LSL USL Average LSL USL output expectations. The first is the amount of variation present in the output and the second is how well the output is centered relative to the Target Target requirements. If the amount of s es variation is larger than the Capable and oc r on target p difference between the upper er Average nt e LSL USL spec limit minus the lower C spec limit, our product or service output will always produce defects, it will not be capable of meeting the Target customer or process output requirements. As you have learned, variation exists in everything. There will always be variability in every process output. You can’t eliminate it completely, but you can minimize it and control it. You can tolerate variability if the variability is relatively small compared to the requirements and the process demonstrates long-term stability, in other words the variability is predictable and the process performance is on target meaning the average value is near the middle value of the requirements. ad

re

sp

The output from a process is either: capable or not capable, centered or not centered. The degree of capability and/or centering determines the number of defects generated. If the process is not capable, you must find a way to reduce the variation. And if it is not centered, it is obvious that you must find a way to shift the performance. But what do you do if it is both incapable and not centered? It depends, but most of the time you must minimize and get control of the variation first, this is because high variation creates high uncertainty, you can’t be sure if your efforts to move the average are valid or not. Of course, if is just a simple adjustment to shift the average to where you want it, you would do that before addressing the variation. Problem Solving Options – Shift the Mean Our efforts in a Six Sigma project that is examining a process that is performing at a level less than desired is to Shift the Mean of performance such that all outputs are within an acceptable range.

This  involves  finding  the  variables  that  will  shift  the  process   over  to  the   targ et.    This  is  usually  the  easiest  option. LS L

S hift

US L

Our ability to Shift the Mean involves finding the variables that will shift the process over to the target. This is the easiest option.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

206

Process Capability Problem Solving Options – Reduce Variation Reducing the variation means fewer of our outputs fail further away from the target. Our objective then is to reduce variation of the inputs to stabilize the output.

This  is  typically  not  so  easy  to  accomplish  and  occurs  often  in   Six   Sig ma  projects. LS L

US L

Problem Solving Options – Shift Mean & Reduce Variation Combination of shifting the Mean and reducing variation – This is the primary objective of Six Sigma projects.

This  occurs  often  in  Six  Sig ma  projects.

LS L

S hift  &  Reduce

US L

Problem Solving Options Move the specification limits – Obviously this implies making them wider, not narrower. Customers usually do not go for this option.

LSS Black Belt Manual XL v11

O bviously  this  implies  making  them  wider,  not  narrower.    C ustomers   usually  do  not  g o  for  this  option  but  if  they  do… it’s  the  easiest! LS L

US L

US L Move  S pec

© 2013 e-Careers Limited

207

Process Capability Capability Studies A stable process is one that is consistent with time. Time Series Plots are one way to check for stability, Control Charts are another. Your process may not be stable at this time. One of the purposes of the Measure Phase is to identify the many X’s possible for the defects seen, gather data and plot it to see if there are any patterns to identify what to work on first.

C a p a b ility   S tu d ie s : • A re  intended  to  be  reg ular,  periodic,  estimations  of  a  process’s  ability   to  meet  its  requirements.       • C an  be  conducted  on  both  discrete  and  continuous  data. • A re  most  meaning ful  when  conducted  on  stable,  predictable   processes. • A re  commonly  reported  as  Sig ma  Level  which  is  optimal  (short  term)   performance.   • Require  a  thoroug h  understanding  of  the  following : – – – – –

C ustomer’s  or  business’s  specifica tion  limits N a ture  of  long  term  vs.  short  term  da ta Mea n  a nd  S ta nda rd  Devia tion  of  the  process A ssessment  of  the  norma lity  of  the  da ta  (continuous  da ta  only) Procedure  for  determining  S ig ma  level

When performing Capability Analysis, try to get as much data as are possible, back as far in time as possible, over a reference frame that is generally representative of your process.

Steps to Capability

Select Output for Improvement

#1

Verify Customer Requirements

#2

Validate Specification Limits

#3

Collect Sample Data

#4

Determine Data Type (LT or ST)

#5

Check data for normality

#6

Calculate Z-Score, PPM, Yield, Capability Cp, Cpk, Pp, Ppk

#7

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

208

Process Capability Verifying the Specifications

Q u e s tio n s   to   co n s id e r:

Specifications must be verified before completing the Capability Analysis. It doesn’t mean that you will be able to change them, but on occasion some internal specifications have been made much tighter than the customer wants.

• W hat  is  the  source  of  the  specifications? – – – –

C ustomer  requirements  (VO C ) Business  requirements  (targ et,  benchmark) C ompliance  requirements  (reg ulations) Desig n  requirements  (blueprint,  system)

• A re  they  current?  Likely  to  chang e? • A re  they  understood  and  ag reed  upon? – O perationa l  definitions – Deployed  to  the  work  force

Data Collection Capability Studies should include all observations (100% sampling) for a specified period.

Long-term data: • Is collected across a broader inference space. • Monthly, quarterly; across multiple shifts, machines, operators, etc • Subject to both common and special causes of variation. • More representative of process performance over a period of time. • Typically consists of at least 100 – 200 data points.

Short-term data: • Collected across a narrow inference space. • Daily, weekly; for one shift, machine, operator, etc. • Is potentially free of special cause variation. • Often reflects the optimal performance level. • Typically consists of 30 – 50 data points. Lot 1

Fill Quantity

You must know if the data collected from process outputs is a short-term or a long-term representation of how well the process performs. There are several reasons for this, but for now we will focus on it from the perspective of assessing the capability of the process.

Lot 5 Lot 3

To help you understand Lot 2 short-term vs. long-term Lot 4 data, we will start by Short-term studies looking at a manufacturing Long-term study example first. In this scenario the manufacturer is filling bottles with a certain amount of fluid. Assume that the product is built in lots. Each lot is built using a particular vendor of the bottle, by a particular shift and set of employees and by one of many manufacturing lines. The next lot could be from a different vendor, employees, line, shift, etc. Each lot is sampled as it leaves the manufacturing facility on its way to the warehouse. The results are represented by the graphic where you see the performance data on a lot by lot basis for the amount of fill based on the samples that were taken. Each lot has its own variability and average as shown. The variability actually looks reasonable and we notice that the average from lot to lot is varying as well. What the customer eventually experiences in the amount of fluid in each bottle is the value across the full variability of all the lots. It can now be seen and stated that the long-term variability will always be greater than the short-term variability. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

209

Process Capability Baseline Performance Here is another way to look at long-term and short-term performance. The “road” appearing graphic actually represents the target (center line) and the upper and lower spec limits. Here again you see the representative performance in short-term snapshots, which result in the larger long-term performance.

PPro roce cessss    BBaasseelin linee:  :  The   The  

averag average,  long e,  long-­‐t-­‐erm  performance   term  performance   level  of  a  process  when  all  input   level  of  a  process  when  all  input   variables  are  unconstrained. variables  are  unconstrained.

Lo Lonngg-­‐te -­‐term rm     bbaasseelin linee

4

SShhoort   rt  Te Term rm     PPeerfo rforrmmaannce ce

`

3

Process Baseline is a term 2 that you will use frequently 1 as a way to describe the output performance of a LSL TARGET USL process. Whenever you hear the word “Baseline” it automatically implies long-term performance. To not use long-term data to describe the Baseline Performance would be dangerous. As an example, imagine you reported that the process performance Baseline was based on distribution 3 in the graphic, you would mislead yourself and others that the process had excellent on target performance. If you used distribution 2, you would be led to believe that the average performance was near the USL and that most of the output of the process was above the spec limit. To resolve these potential problems, it is important to always use long-term data to report the Baseline. How do you know if the data you have is short or long-term data? Here are some guidelines. A somewhat technical interpretation of long-term data is the process has had the opportunity to experience most of the sources of variation that can impact it. Remembering the outputs are a function of the inputs, what we are saying is that most of the combinations of the inputs, each with their full range of variation has been experienced by the process. You may use these situations as guidelines. Short-term data is a “snapshot” of process performance and is characterized by these types of conditions: One shift One line One batch One employee One type of service One or only a few suppliers Long-term data is a “video” of process performance and is characterized by these types of conditions: Many shifts Many batches Many employees Many services and lines Many suppliers Long-term variation is larger than short-term variation because of : material differences, fluctuations in temperature and humidity, different people performing the work, multiple suppliers providing materials, equipment wear, etc. As a general rule, short-term data consist of 20 to 30 data points over a relatively short period of time and long-term data consist of 100 to 200 data points over an extended period of time. Do not be LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

210

Process Capability Baseline Performance (cont.) misled by the volume of product or service produced as an indicator of long and short-term performance. Data that represents the performance of a process that produces 100,000 widgets a day for that day will be short-term performance. Data the represents the performance of a process that produces 20 widgets a day over a 3 month period will be long-term performance. While we have used a manufacturing example to explain all this, it is exactly the same for a service or administrative type of process. In these types of processes, there are still different people, different shifts, different workloads, differences in the way inputs come into the process, different software, computers, temperatures, etc. The same exact concepts and rules apply. You should now appreciate why, when we report process performance, we need to know what the data is representative of. Using such data we will now demonstrate how to calculate process capability and then we will show how it is used.

Components of Variation There are many ways to look at the difference between short-term and longterm data. First keep on mind that you never have purely short-term or purely long-term data. It is always something in between. Short-term data basically represent your “entitlement” situation: you are controlling all the controllable sources of variation.

Even  stable  processes  will  drift  and  shift  over  time  by  as  much   as  1 .5   Standard  Deviations  on  the  averag e. Lo n g   Te rm O v e ra ll   V a ria tio n

S h o rt   Te rm B e tw e e n   G ro u p   V a ria tio n

S h o rt   Te rm   W ith in   G ro u p   V a ria tio n

Long-term data includes (in theory) all the variation that one can expect to see in the process. Usually what we have is something in between. It is a judgment call to decide which type of data you have: it varies depending on what you are trying to do with it and what you want to learn from it. In general one or more months of data are probably more long-term than short-term; two weeks or less is probably more like short-term data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

211

Process Capability Sum of the Squares Formulas These are the equations describing the sum of squares which are the basis for the calculations used in capability.

=

to ta l

SS

+

b e tw e e n

x x x x

x x

x

SS

x

x

x

x x

x x

x x

w ith in

P rec is ion (s hort-­‐term  c apability)

S hift Output Y

No, you do not need to memorize them or even really understand them. They are built into SigmaXL® for the processing of data.

SS

x

x

x

x

x x

x

x

T ime

x

Stability Stability is established by plotting data in a Time Series Plot or in a Control Chart. If the data used in the Control Chart goes out of control, the data is not stable. At this point in the Measure Phase there is no reason to assume the process is stable. Performing a Capability Study at this point effectively draws a line in the sand.

A Stable Process is consistent over time. Time Series Plots and Control Charts are the typical graphs used to determine stability.

Tic toc… tic toc…!

If however, the process is stable, short-term data provides a more reliable estimate of true Process Capability. Looking at the Time Series Plot shown here, where would you look to determine the entitlement of this process? As you can see the circled region has a much tighter variation. We would consider this the process entitlement; meaning, that if we could find the X’s that are causing the instability this is the best the process can perform in the short term. The idea is that we’ve done it for some time, we should be able to do it again. This does not mean that this is the best this process will ever be able to do. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

212

Process Capability Measures of Capability

Hope!

Cp and Pp: •  What is Possible if your process is perfectly Centered •  The Best your process can be •  Process Potential (Entitlement)

Reality!

Cpk and Ppk: •  The Reality of your process performance •  How the process is actually running •  Process Capability relative to specification limits

Capability Formulas

S ix   tim e s   th e   s a m p le   S ta n d a rd   D e v ia tio n

S a m p le   M e a n

Th re e   tim e s   th e   s a m p le   S ta n d a rd   D e v ia tio n Note: Consider the “K” value the penalty for being off center

LSL – Lower specification limit USL – Upper specification limit

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

213

Process Capability SigmaXL® Example There are two columns of data that show the length of camshafts from two different suppliers. Check the Normality of each supplier. In order to use Process Capability as a predictive statistic, the data must be Normal for the tool we are using in SigmaXL®. SigmaXL® also includes advanced capabilities for Nonnormal data. At this point in time we are only attempting to get a baseline number that we can compare to at the end of problem solving. We are not using it to predict a quality, we want to get a snapshot. DO NOT try and make your process STABLE BEFORE working on it! Your process is a project because there is something wrong with it so go figure it out, don’t bother playing around with stability. Ensure that X-Bar & S Charts are selected. SigmaXL® will compute the short term StDev using the within subgroup variation calculated for the X-Bar & S Charts. Note that SigmaXL® defaults to using a pooled StDev to calculate short term StDev.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

214

Process Capability SigmaXL® Example (cont.) 599.548 is the process Mean which falls short of the target (600) for Supplier 1, and the left tail of the distribution falls outside the lower specification limits. From a practical standpoint what does this mean? You will have camshafts that do not meet the lower specification of 598 mm. Next we look at the Cp index. This tells us if we will produce units within the tolerance limits. Supplier 1 Cp index is .66 which tells us they need reduce the process variation and work on centering. Look at the PMM levels? What does this tell us? Looking below, 600.06 is the process Mean for Supplier 2 and is very close to the target although both tails of the distribution fall outside of the specification limits. The Cpk index is very similar to Supplier 1 but this infers that we need to work on reducing variation. When making a comparison between Supplier 1 and 2 elative to Cpk vs Ppk we see that Supplier 2 process is more prone to shifting over time. That could be a risk to be concerned about. Again, Compare the PPM levels? What does this tell us? Hint look at PPM < LSL. So what do we do. In looking only at the means you may claim that Supplier 2 is the best. Although Supplier 1 has greater potential as depicted by the Cp measure and it will likely be easier to move their Mean than deal with the variation issues of Supplier 2. Therefore we will work with Supplier 1. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

215

Process Capability SigmaXL® Example (cont.) SigmaXL® does not include Benchmark Z’s (sigma level) in Process Capability. To compute sigma level, use the Process Sigma Level Calculator as shown above.

This slide shows Sigma Shift as 0, resulting in sigma levels that match Benchmark Z’s. This is optional. If the Sigma Shift is kept at 1.5 this will be added to the Sigma Level Values. The overall long term sigma level is 1.86 for Supplier 1. If you enter the short term StDev of .556 the potential Process Sigma Level will be 2.16.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

216

Process Capability SigmaXL® Example (cont.) The overall Long Term sigma level is 1.4. for Supplier 2. If you enter the short term StDev of 1.0 the potential Process Sigma Level will be 1.72.

Continuous Variable Caveats Well this is one way to lie with Statistics…When used as a predictive model, Capability makes assumptions about the shape to the data. When data is Non-normal, the model’s assumptions don’t work and would be inappropriate to predict. It’s actually good news to have data that looks like this because your project work will be easy!!! Why? Clearly there is something occurring in the process that should be fairly obvious and is causing these very two distinct distribution to occur. Take a look at each of the distributions individually and determine what is causing this. DON’T fuss or worry about Normality at this point, hop out to the process and see what is going on. Here in the Measure Phase stick with observed performance unless your data are Normal. There are ways to deal with Non-normal data for predictive capability but we’ll look at that once you have removed some of the Special Causes from the process. Remember here in the Measure Phase we get a snapshot of what we’re dealing with, at this point don’t worry about predictability, we’ll eventually get there. Please note, the Normal Distribution shown in blue has been added manually to illustrate the short term variation. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

217

Process Capability Capability Steps When we follow the steps in performing a capability study on Attribute Data we hit a wall at step 6. Attribute Data is not considered Normal so we will use a different mathematical method to estimate capability.

We can follow the steps for calculating capability for Continuous Data until we reach the question about data Normality…

Select Output for Improvement

#1

Verify Customer Requirements

#2

Validate Specification Limits

#3

Collect Sample Data

#4

Determine Data Type

(LT or ST)

#5

Check data for Normality

#6

Calculate Z-Score, PPM, Yield, Capability Cp, Cpk, Pp, Ppk

#7

Select Output for Improvement

#1

Notice the difference when we come to step 5…

Verify Customer Requirements

#2

Validate Specification Limits

#3

Collect Sample Data

#4

Calculate DPU

#5

Find Z-Score

#6

Convert Z-Score to Cp & Cpk

#7

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

218

Process Capability Z Scores

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

219

Process Capability Z Table In our case we have to lookup the proportion for the Z score of 1.33. This means that approximately 9.1% of our data falls beyond the upper spec limit of 54. If we are interested in determining parts per million defective we would simply multiply the proportion .09176 by one million. In this case there are 91,760 parts per million defective.

Attribute Capability A ttribute  data  is  a lw a y s long  term  in  the  shifted  condition  since  it  requires  so   many  samples  to  g et  a  g ood  estimate  with  reasonable  confidence. Short  term  capability  is  typically  reported,  so  a  shifting  method  will  be  employed   to  estimate  short  term  capability.

You Want to Estimate : Your Data Is :

ZST

Short Term Capability

ZLT

Long Term Capability

ZST Short Term Capability

ZLT Long Term Capability Subtract 1.5

Add 1.5

Sigma Level

Short-Term DPMO

Long-Term DPMO

1

158655.3

691462.5

2

22750.1

308537.5

3

1350.0

66807.2

4

31.7

6209.7

5

0.3

232.7

6

0.0

3.4

Stable process can shift and drift by as much as 1.5 Standard Deviations. Want the theory behind the 1.5…Google it! It doesn’t matter.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

220

Process Capability Attribute Capability (cont.) Some people like to use sigma level (SigmaXL® reports this as “Z-bench”), other like to use Cpk, Ppk. If you are using Cpk and Ppk you can easily translate that into a Z score or sigma level by dividing by 3.

By  viewing  these  formula s  you  ca n  see  there  is  a  rela tionship  between  them. If  we  divide  our  Z  short-­‐term  by  3  we  ca n  determine  our  C pk  a nd  if  we  divide   our  Z  long -­‐term  by  3  we  ca n  determine  our  Ppk.

Attribute Capability Example

A customer service group is interested in estimating the Capability of their call center. A total of 20,000 calls came in during the month but 2,500 of them dropped before they were answered (the caller hung up). Results of the call center data set: Samples = 20,000 Defects = 2,666

They hung up….!! We will use this example to demonstrate the capability of a customer service call group.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

221

Process Capability Attribute Capability Example (cont.) Follow these steps to determine your process capability. Remember that, DPU is Defects per unit, the total number of possible errors or defects that could be counted in a process or service. DPU is calculated by dividing the total number of defects by the number of units or products.

"Cpk” is an index (a simple number) which measures how close a process is running to its specification limits, relative to the natural variability of the process. A Cpk of at least 1.33 is desired and is about 4 sigma + with a yield of 99.3790% . The above Cpk of . 87 is about 2.61 sigma or a 87% Yield. If you want to know how that variation will affect the ability of your process to meet customer requirements (CTQ's), you should use Cpk. If you just want to know how much variation the process exhibits, a Ppk measurement is fine. Remember Cpk represents the short-term capability of the process and Ppk represents the longterm capability of the process. With the 1.5 shift, the above Ppk process capability will be worse than the Cpk short-term capability.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

222

Process Capability At this point, you should be able to: §  Estimate capability for Continuous Data §  Estimate capability for Attribute Data §  Describe the impact of Non-normal Data on the analysis presented in this module for continuous capability

You have now completed Measure Phase – Process Capability.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

223

Lean Six Sigma Black Belt Training

Measure Phase Wrap Up and Action Items

The Measure Phase is now complete. Get ready to apply it. This module will help you create a plan to implement the Measure Phase for your project.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

224

Wrap Up and Action Items Measure Phase Overview - The Goal

Th e   g o a l   o f   th e   M e a s u re   P h a s e   is   to : • Define,  explore  and  classify   “X” variables  using  a  variety  of  tools. – – – –

Detailed  Process  Mapping Fishbone  Diag rams X-­‐Y  Diag rams FMEA

• Demonstrate  a  working  knowledg e  of  Basic  Statistics  to  use  as  a   communication  tool  and  a  basis  for  inference. • Perform  Measurement  C apability  studies  on  output  variables. • Evaluate  stability  of  process  and  estimate  starting  point  capability.

Six Sigma Behaviors

•  Being tenacious, courageous •  Being rigorous, disciplined •  Making data-based decisions •  Embracing change & continuous learning •  Sharing best practices

Walk the Walk!!

Each player in the Six Sigma process must be A ROLE MODEL for the Six Sigma culture

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

225

Wrap Up and Action Items Measure Phase Deliverables

Listed here are the Measure Deliverables that each candidate should present in a Power Point presentation to their mentor and project champion. At this point you should understand what is necessary to provide these deliverables in your presentation. –  –  –  –  –  –  –  –  –  –  –  – 

Team Members (Team Meeting Attendance) Primary Metric Secondary Metric(s) Process Map – detailed FMEA X-Y Matrix Basic Statistics on Y MSA Stability graphs Capability Analysis Project Plan Issues and Barriers

Measure Phase - The Roadblocks

Look for the potential roadblocks and plan to address them before they become problems: –  Team members do not have the time to collect data. –  Data presented is the best guess by functional managers. –  Process participants do not participate in the creation of the X-Y Matrix, FMEA and Process Map.

It won t all be smooth sailing…..! You will run into roadblocks throughout your project. Listed here are some common ones that Belts have to deal with in the Measure Phase.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

226

Wrap Up and Action Items

Champion/ Process Owner

DMAIC Roadmap

Identify Problem Area

Define

Determine Appropriate Project Focus Estimate COPQ

Improve

Analyze

Measure

Establish Team Assess Stability, Capability, and Measurement Systems

Identify and Prioritize All X’s

Prove/Disprove Impact X’s Have On Problem

Identify, Prioritize, Select Solutions Control or Eliminate X’s Causing Problems

Control

Implement Solutions to Control or Eliminate X’s Causing Problems

Implement Control Plan to Ensure Problem Doesn’t Return

Verify Financial Impact

The DMAIC Phases Roadmap is a flow chart of what goals should be reached during each phase of DMAIC. Please take a moment to review. Measure Phase This map of the Measure Phase rollout is more of a guideline than a rule. The way that you apply the Six Sigma problem-solving methods to a project depends on the type of project your working with and the environment that you are working in. For example in some cases it may make sense to jump directly into Measurement System Analysis studies while you collect data to characterize other aspects of the process in parallel. In other cases it may be necessary to get a better understanding of the process first. Let common sense and data dictate your path.

Detailed  Problem  Statement  Determined Detailed  Process  Mapping Identify  A ll  Process  X’s  C ausing  Problems  (Fishbone,  Process  Map)

S elect  the  Vital  Few  X’s  C ausing  Problems  (X-­‐Y  Matrix,  FMEA ) A ssess  Mea surement  S ystem

N

Repeatable  & Reproducible?

Y

Implement  C hang es  to  Make  S ystem  A cceptable A ssess  S tability  (S tatistical  C ontrol) A ssess  C a pa bility  (Problem  with  C entering / S pread) Estimate  Process  Sig ma  Level Review  Prog ress  with  C hampion

Ready  for  A nalyz e

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

227

Wrap Up and Action Items Measure Phase Checklist These are questions that you should be able to answer in clear, understandable language at the end of this phase.

M e a s u re   Q u e s tio n s

Id e n tify   critica l   X ’ s   a n d   p o te n tia l   fa ilu re   m o d es • Is  the  “a s  is” Process  Ma p  crea ted? • A re  the  decision  points  identified? • W here  a re  the  da ta  collection  points? • Is  there  a n  analysis  of  the  mea surement  system? • W here  did  you  g et  the  da ta ? Id e n tify   critica l   X ’ s   a n d   p o te n tia l   fa ilu re   m o d es • Is  there  a  completed  X-­‐Y  Ma trix? • W ho  pa rticipa ted  in  these  a ctivities? • Is  there  a  completed  FMEA ? • Ha s  the  Problem  Sta tement  chang ed? • Ha ve  you  identified  more  C O PQ ? S ta b ility   A s s es s m e n t • is  the  “Voice  of  the  Process” sta ble? • If  not,  ha ve  the  special  causes  been  acknowledg ed? • C an  the  g ood  sig na ls  be  incorpora ted  into  the  process? • C an  the  bad  sig nals  be  removed  from  the  process? • How  sta ble  can  you  ma ke  the  process? C a p a b ility   A s s e s s m e n t • W ha t  is  the  short-­‐term  and  long -­‐term  ca pa bility  of  the  process? • W ha t  is  the  problem,  one  of  centering ,  spread  or  some  combina tion? G e n e ra l   Q u es tio n s • A re  there  any  issues  or  ba rriers  tha t  prevent  you  from  completing  this  phase? • Do  you  ha ve  adequa te  resources  to  complete  the  project?

Planning for Action WHAT

WHO

W H EN

WHY

W H Y   N O T

HOW

Id e n tify   th e   co m p le x ity   o f   th e   p ro ce s s Fo cu s   o n   th e   p r o b le m   s o lv in g   p ro ce s s D e fin e   C h a ra cte ris tics   o f   D a ta V a lid a te   Fin a n cia l   B e n e fits B a la n ce   a n d   Fo cu s   R e s o u rce s Es ta b lis h   p o te n tia l   re la tio n s h ip s   b e tw e e n   v a ria b le s Q u a n tify   ris k   o f   m e e tin g   critica l   n e e d s   o f   C u s to m e r ,   B u s in e s s   a n d   P e o p le P re d ict   th e   R is k   o f   s u s ta in a b ility   C h a rt   a   p la n   to   a cco m p lis h   th e   d e s ire d   s ta te   o f   th e   cu ltu re W h a t   is   y o u r   d e fe ct? W h e n   d o e s   y o u r   d e fe ct   o ccu r?   H o w   is   y o u r   d e fe ct   m e a s u re d ?   W h a t   is   y o u r   p ro je ct   fin a n cia l   g o a l   (ta rg e t   &   tim e )   to   re a ch   it?   W h a t   is   y o u r   P rim a ry   m e tric? W h a t   a re   y o u r   S e co n d a ry   m e trics ? D e fin e   th e   a p p ro p ria te   e le m e n ts   o f   w a s te

Over the last decade of deploying Six Sigma it has been found that the parallel application of the tools and techniques in a real project yields the maximum success for the rapid transfer of knowledge. For maximum benefit you should apply what has been learned in the Measure Phase to a Six Sigma project. Use this checklist to assist. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

228

Wrap Up and Action Items At this point, you should: §  Have a clear understanding of the specific action items §  Have started to develop a Project Plan to complete the action items §  Have identified ways to deal with potential roadblocks §  Be ready to apply the Six Sigma method within your business

You have now completed the Measure Phase. Congratulations!

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

229

Lean Six Sigma Black Belt Training

Analyze Phase Welcome to Analyze

Now that we have completed the Measure Phase we are going to jump into the Analyze Phase. Welcome to Analyze will give you a brief look at the topics we are going to cover.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

230

Welcome to Analyze Overview These are the deliverables for the Analyze Phase.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infe fere renntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    H H yy ppooth theessis is    Te Tesstin tingg H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP11 H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP22 H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP11 H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP22 W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

C hampion/ Process  O wner

Analyze Phase Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

231

Understanding Six Sigma Analyze Phase Process Map

Vital  Few  X’s  Identified State  Practical  Theories  of  Vital  Few  x’s  Impact  on  Problem Translate  Practical  Theories  into  Scientific  Hypothesis Select  A nalysis  Tools  to  Prove/ Disprove  Hypothesis C ollect  Data Perform  Statistical  Tests State  Practical  C onclusion

Statistically Sig nificant?

N

Y

Update  FMEA

N

Practically Sig nificant? Y Root C ause Y

N Identify  Root  C ause

Ready  for  Improve  and  C ontrol

This provides a process look at putting “Analyze” to work. By the time we complete this phase you will have a thorough understanding of the various Analyze Phase concepts. We will build upon the foundational work of the Define and Measure Phases by introducing techniques to find root causes, then using experimentation and Lean Principles to find solutions to process problems. Next you will learn techniques for sustaining and maintaining process performance using control tools and finally placing your process knowledge into a high level process management tool for controlling and monitoring process performance.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

232

Lean Six Sigma Black Belt Training

Analyze Phase “X” Sifting

Now we will continue in the Analyze Phase with “X Sifting” – determining what the impact of the inputs to our process are.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

233

“X” Sifting Overview The core fundamentals of this phase are Multi-Vari Analysis and Classes and Causes. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee

M Muulti-­‐V lti-­‐Vaa ri   ri  AAnnaa ly lyssis is

““ XX ”” SSiftin iftingg CCla la sssseess    aa nndd    CCaa uusseess

In Infe fere renntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    H H yy ppooth theessis is    Te Tesstin tingg H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP11 H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP22 H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP11 H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP22 W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Multi-Vari Studies

Define Phase Measure Phase

Process Map

Possible X s

X-Y Matrix, FMEA, Process Map

The Themany manyXXss when whenwe wefirst firststart start (The (Thetrivial trivialmany) many)

XXXXXXXXXX XXXXXXXXXX X XX XXXXX X X X XX XXXXX X X

XX XX XX X

The Thequantity quantityofofXXs s when remaining we apply after leverage DMAIC (The vital few)

Probable X s

The Thequantity quantityof ofXXss keep after we reducing think as you about workY= the f(Xproject )+e

XXX

In the Define Phase you use tools like Process Mapping to identify all possible “X’s”. In the Measure Phase you use tools to help refine all possible “X’s” like the X-Y Diagram and FMEA. In the Analyze Phase we start to “dis-assemble” the data to determine what it tells us. This is the fun part.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

234

“X” Sifting Multi-Vari Definition Multi-Vari Studies – is a tool that graphically displays patterns of variation. Multi-Vari Studies are used to identify possible X’s or families of variation. These families of variation can hide within a subgroup, between subgroups, or over time. The Multi-Vari Chart helps in screening factors by using graphical techniques to logically subgroup discrete X’s (Independent Variables) plotted against a continuous Y (Dependent). By looking at the pattern of the graphed points, conclusions are drawn from about the largest family of variation. Multi-Vari Chart can also be used to assess capability, stability and graphical relationships between X’s and Y’s. The use of a Multi-Vari Chart is to illustrate analysis of variance data graphically. A picture can be worth a thousand words, or numbers. - Multi-Vari Charts are useful in visualizing two-way interactions. Multi-Vari Charts reveal information such as: -  Effect of work shift on Y’s. -  Impact of specific machinery, or material on Y’s. - Effect of noise factors on Y’s, etc.

Shift Changes Machinery Variance Noise

At this point in DMAIC, Multi-Vari Charts are intended to be used as a passive study, but later in the process they can be used as a graphical representation where factors were intentionally changed. The only caveat with using SigmaXL® to graph the data is that the data must be balanced. Each source of variation must have the same number of data points across time. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

235

“X” Sifting Multi-Vari Example

To put Multi-Vari studies in practice follow an example of an injection molding process. You are probably asking yourself what is Injection Molding? Well basically an injection molding machine takes hard plastic pellets and melts them into a fluid. This fluid is then injected into a mold or die, under pressure, to create products, such as piping and computer cases.

Method Typically, we start with a data collection sheet that makes sense based on our knowledge of the process. Then follow the steps.

Sampling Plans steps: 1. Create Sampling Plan 2. Gather Passive Date 3. Graph Data

4. Check to see if Variation is Exposed If we only see minor 5. Interpret Results variation in the sample, it is time to go back and collect No additional data. When Is Gather Create Graph Variation your data collection Passive Sampling Data Exposed Data represents at least Plan 80% of the variation within the process then you should have enough information to evaluate the graph.

Yes Interpret Results

Remember for a Multi-Vari Analysis to work the output must be continuous and the sources of variation discrete.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

236

“X” Sifting Sources of Variation Within unit, between unit and temporal are the classic causes of variation. A unit can be a single piece or a grouping of pieces depending on whether they were created at unique times. Multi-Vari Analysis can be performed on other processes, simply identify the categorical sources of variation you are interested in.

W ithin  unit  or  P o s itio n a l – – –

W ithin  piece  variation  related  to  the  geometry  of  the  part. Variation  across  a  single  unit  containing  many  individual  parts   such  as  a  wafer  containing  many  computer  processors. Location  in  a  batch  process  such  as  plating.

Between  unit  or  C y clica l – – –

Variation  among  consecutive  pieces. Variation  among  groups  of  pieces. Variation  among  consecutive  batches.

Te m p o r a l or  O ver  time  S hift-­‐to-­‐S hift – –

Day-­‐to-­‐D ay W eek-­‐to-­‐W eek

Machine Layout & Variables In this example there are 4 widgets created with each die cycle. Therefore, a unit is 4 widgets that were created at that unique time. M a s te r   In je ctio n   P re s s u re D is ta n ce   to   ta n k

%   O x y g e n

In je ctio n   P re s s u re   P e r   C a v ity Flu id   Le v e l

#1 D ie Te m p

#2 A m b ie n t Te m p

#3 #4

D ie R e le a s e

An example of Within Unit Variation is measured by differences in the 4 widgets from a single die cycle. For example, we could measure the wall thickness for each of the 4 widgets. Between Unit Variation is measured by differences from sequential die cycles. An example of Between Unit Variation is, comparing the average of wall thickness from die cycle to die cycle. Temporal Variation is measured over some meaningful time period. For example, we would compare the average of all the data collected in a time period say the 8 o’clock hour to the 10 o’clock hour. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

237

“X” Sifting Sampling Plan To continue with this example, the Multi-Vari sampling plan will be to gather data for 3 die cycles on 3 different days for 4 widgets inside the mold. If you find this initial sampling plan does not show the variation of interest, it will be necessary to continue sampling, or make changes to the sampling plan.

Monday

W ednesday Die   C ycle   #3

Die   C ycle   #2

Die   C ycle   #3

Friday Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

C a vity  # 2

C a vity  # 3 C a vity  # 4

Monday Die   C ycle   #1

Die   C ycle   #2

W ednesday Die   C ycle   #3

Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

Friday Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

C a vity  # 1 C a vity  # 2

C a vity  # 3 C a vity  # 4

Monday

Between-Unit Encoding Comparing the averages from each die cycle is called Between Unit Variation.

Die   C ycle   #1

C a vity  # 1

Within-Unit Encoding Comparing individual data points within a die cycle is Within Unit Variation. Examples of measurement could be wall thickness, diameter or uniformity of thickness to name a few

Die   C ycle   #2

Die   C ycle   #1

Die   C ycle   #1

Die   C ycle   #2

W ednesday Die   C ycle   #3

Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

Friday Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

C a vity  # 1 C a vity  # 2

C a vity  # 3 C a vity  # 4

Monday

Temporal Encoding Comparing the average of all the data within a day and plot 3 time periods is known as Temporal Variation.

Die   C ycle   #1

Die   C ycle   #2

W ednesday Die   C ycle   #3

Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

Friday Die   C ycle   #1

Die   C ycle   #2

Die   C ycle   #3

C a vity  # 1 C a vity  # 2

C a vity  # 3 C a vity  # 4

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

238

“X” Sifting Using Multi-Vari to Narrow X’s

G ather  the  list  of  potential  X’s  and  assig n  to  one  of  the  families  of   variation. – This  information  can  be  pulled  from  the  X-­‐Y  Diag ram  from  the   Measure  Phase. If  an  X  spans  one  or  more  families,  assig n  % ’s  to  the  supposed  split.

Now let’s use the same information from the X-Y Diagram that was created in the Measure Phase. The following exercise will help you assign one of the variables to the family of variation. If you find yourself with a variable or (X) then assign percentages to split. Use your best judgment for the splits. Don’t assume that the true X’s causing variation has to come from one in the list.

Step  1  -­‐ G raph  the  data  from  the  process  in  Multi-­‐V ari  form. Step  2  -­‐ Identify  the  larg est  family  of  variation. Step  3  -­‐ Establish  statistical  sig nificance  throug h  the  appropriate   statistical  testing . Step  4  -­‐ Focus  further  effort  on  the  X’s  associated  with  the  family  of   larg est  variation.

R e m e m b er   th e   g o a l   is   n o t   to   o n ly   fig u re   o u t   w h a t   it   is ,   b u t   w h a t   it   is   n o t! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

239

“X” Sifting Data Worksheet Open the workbook “Analyze Datasets.xls” and select the worksheet “MVInjectionMold”. Now create the Multi-Vari Chart in SigmaXL®. 1. Select SigmaXL>Graphical Tools>Multi-Vari Options. Uncheck Standard Deviation Chart. 2. Click Finish. SigmaXL will then open the Multi-Vari Charts dialog box. 3. If the Multi-Vari Options have been previously saved, select SigmaXL>Graphical Tools>MultiVari Charts. 4. Select “Diameter” as Numeric Response (Y), “Unit to Unit” as Group Category (X1), and “Temporal” as Group Category (X2). “Within Unit” should not be added as a group category. SigmaXL® will display the “Within Unit” variation automatically as a vertical bar. After you create the graph as indicated, take a few minutes to create graphs using a different order. Always use the graph that shows the variation in the easiest manner to interpret. Run Multi-Vari

Here is the graph that should have been generated.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

240

“X” Sifting Identify The Largest Family of Variation To find an example of within unit variation, look at Unit 1 in the second time period. Notice the spread of data is 0.07. Now let’s try and find between unit variation, compare the averages of the units within a time period. All three time periods appear similar so looking at the first time period it appears the spread of the data is 0.18 units. To determine temporal variation, compare the averages between time periods. It appears time period 3 and 2 have a difference of 0.06. To determine within unit variation, find the unit with the greatest variation like Unit 1 in the second time period. Notice the spread of data is 0.07. It appears the second unit in the third. Notice that the shifting from unit to unit is not consistent, but it certainly jumps up and down. The question at this point should be: Does this graph represent the problem I’m working on? Do I see at least 80% of the variation? Read the units off the Y axis or look in the worksheet. Notice the spread of the data is 0.22 units. If the usual spread of the data is 0.25 units, then this data set represents 88% of the usual variation which tells us our sampling plan was sufficient to detect the problem. Root Cause Analysis After the analysis we now know the largest source of variation is occurring die cycle to die cycle we can focus our effort on those X’s that we suspect have the greatest impact. In this case, the pattern of variation is not consistent within the small scope of data we gave gathered. Additional data may be required or this process may be ready for experimentation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

241

“X” Sifting Call Center Example Let’s try another example, open the worksheet “CallCenter”. This example is a transactional application of the tool. In this particular case, a company with two call centers wants to compare two methods of handling calls at each location at different times of the day. One method involves a team to resolve customer issues, and the other method requires a single subject-matter expert to handle the call alone.

What is the largest source of variation… §  Method? §  Location? §  Time?

Method

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

242

“X” Sifting Call Center Example (cont.) Is the largest source of variation more or less obvious? Notice the Multi-Vari graph plotted is dependent on the order in which the variable column names are entered into SigmaXL®.

Location

This example is not as easy to draw conclusions because of the source of the data. With the injection molding process we know we are making the same parts over and over. However, in this example of a call center, there is no control over the nature of calls coming in, so a single outlier could affect your judgment. It is not necessary to force fit any one tool to your project. For transactional projects Multi-Vari may be difficult to interpret purely graphically. We will re-visit this data set later when working through Hypothesis Testing.

Time

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

243

“X” Sifting Multi-Vari Exercise

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

244

“X” Sifting MVA Solution Do you recall the reason why Normality is an issue? Normality is required if you intend to use the information as a predictive tool. Early in the Six Sigma process there is no reason to assume that your data will be Normal. Remember, if it is not Normal it usually makes finding potential causes easier. Let’s work the problem now.

Check for Normality…

First check the data for Is that Normality. Use normal?! SigmaXL>Process Capability>Capability Combination Report (Individuals). Select Volume as Numeric Data Variable (Y), Set USL to 500. From the generated report we can see that the P-value is greater than 0.05, therefore the data is considered Normal.

Having a graphical summary is quite nice since it provides a picture of the data as well as the summary statistics. Histograms and Descriptive Statistics is a powerful tool which allows you to chick for Normality. Notice that the Pvalue in this window is the same as the previous. Notice that even though the data are Normal, the distribution is quite wide. If you had a process where you were filling bottles wouldn’t you expect the process to be Normal?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

245

“X” Sifting MVA Solution (cont.) Now it is time to perform the process capability. For subgroup size is enter 12 since all 12 bottles are filled at the same time. Also, use 500 milliliters as the upper spec limit in order to see how bad the capability was from a manufacturers prospective.

SigmaXL® has a template that will allow us to determine the Sigma Level for this process. “Select Process Capability>Basic Process Capability Templates>Process Sigma Level – Continuous” to open the template. Using the data from the Process Capability Report, we can find the Sigma Level. Is this process is in trouble? The answer is yes, since the Z bench value is negative! That is very bad. To correct this problem the process has to be set in such a manner that none of the bottles are ever under filled, while trying to minimize the amount of overfill.

To answer step three of this exercise, it is a combination of reducing variation and shifting the Mean. The Mean cannot be shifted however, until the variation is reduced dramatically.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

246

“X” Sifting MVA Solution (cont.) The order in which you enter the factors will produce different graphs. The “classical” method is to use Within, Between and over-time (Temporal) order. SigmaXL®’s Multi-Vari Charts do not require the lowest level “Within” category. This will appear automatically as vertical bars.

The graph shows the variation within a unit (vertical bars) is fairly consistent across all the data. The variation between units (red lines connecting means) also looks consistent across all the data. What seems to stand out is the machine may be set up differently from first shift (top row) to second (bottom row). That should be easy to fix! What is the largest source of variation? Within Unit Variation is the largest, Temporal is the next largest (and probably easiest to fix) and Between Unit Variation comes in last. So to fix this process your game plan should be based on the information in the Excel file and involve additional information you have about the process. This example was based on a real process where the nasty culprit was actually the location of the in-line scale. No one wanted to believe that a high price scale could be generating significant variation. The in-line scale weighed the bottles and either sent them forward to ship or rejected them to be topped off. The wind generated by the positive pressure in the room blew across the scale making the weights recorded fluctuate unacceptably. The filling machine was actually quite good, there were a few adjustments made once the variation from the scale was fixed. Once the variation in the data was reduced, they were able to shift the Mean closer to the specification of 500 ml. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

247

“X” Sifting Data Collection Sheet The injection molding data collection sheet was created to include: 3 time periods 4 widgets per die cycle 3 units per time period for a total of 36 rows of data. (3 times 4 times 3)

The data sheet is now balanced meaning that there is an equal number of data points for each condition in the data table and ready for data to be entered.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

248

“X” Sifting Classes of Distributions By now you are convinced that Multi-Vari is a tool that helps screen X’s by visualizing three primary sources of variation. At this point we will review classes and causes of distributions that can also help us screen X’s to perform Hypothesis Tests.

M u lti-­‐V a ri   is   a   to o l   th a t   h e lp s   s cre e n   X ’ s   b y   v is u a liz in g   th re e   p rim a ry   s o u rce s   o f   v a ria tio n .   La te r   w e   w ill   p e rfo rm   H y p o th e s is   Te s ts   b a s e d   o n   o u r   fin d in g s . A t  this  point  we  will  review  classes  and  causes  of  distributions that   can  also  help  us  screen  X’s  to  perform  Hypothesis  Tests. – N ormal  Distribution – N on-­‐normality  – 4  Primary  C lassifications 1 . Skewness 2 . Multiple  Modes 3 . Kurtosis 4 . G ranularity

The Normal (Z) Distribution Please review the characteristics of the Gaussian curve shown here…

Characteristics of Normal Distribution (Gaussian curve) are: –  It is considered to be the most important distribution in statistics. –  The total area under the curve is equal to 1. –  The distribution is mounded and symmetric; it extends indefinitely in both directions, approaching but never touching the horizontal axis. –  All processes will exhibit a normal curve shape if you have pure random variation (white noise). –  The Z distribution has a Mean of 0 and a Standard Deviation of 1. –  The Mean divides the area in half, 50% on one side and 50% on the other side. –  The Mean, Median and Mode are at the same data point.

-6

LSS Black Belt Manual XL v11

-5

-4

-3

-2

-1

+1

+2

+3

+4

+5

+6

© 2013 e-Careers Limited

249

“X” Sifting Normal Distribution This Normal Curve is NOT a plot of our observed data!!! This theoretical curve is estimated based on our data’s Mean and Standard Deviation. Many Hypothesis Tests that are available assume a Normal Distribution. If the assumption is not satisfied we cannot use them to infer anything about the future. However, just because a distribution of sample data looks Normal does not mean that the variation cannot be reduced and a new Normal Distribution created.

Non-Normal Distributions Data may follow Non-normal Distributions for a variety of reason, or there may be multiple sources of variation causing data that would otherwise be normal to appear not Normal. 1 Skewed

3 Multi-Modal

LSS Black Belt Manual XL v11

2 Kurtosis

4 Granularity







Copyright OpenSourceSixSigma.com

© 2013 e-Careers Limited

250

“X” Sifting Skewness Classification

P o te n tia l   C a u s e s   o f   S k e w n e s s Le ft   S k e w

R ig h t   S k e w 60

Frequency

40

Frequency

When a distribution is not symmetrical, then it’s Skewed. Generally a Skewed distribution longest tail points in the direction of the Skew.

30 20 10

50 40 30 20 10

0

0 10

15

20

4

5

6

7

8

9

10

11

1 -­‐1 N a tura l  Limits 1 -­‐2 A rtificia l  Limits  (S orting ) 1 -­‐3 Mixtures 1 -­‐4 N on-­‐Linea r  Rela tionships 1 -­‐5 Intera ctions 1 -­‐6 N on-­‐Random  Pa tterns  A cross  Time

Mixed Distributions 1-3

M ix e d   D is trib u tio n s occur  when  data  comes  from  multiple  sources   that  are  supposed  to  be  the  same  yet  are  not.

M a ch in e   A O p e ra to r   A P a y m e n t   M e th o d   A In te rv ie w e r   A

S a m p le   A

M a ch in e   B O p e ra to r   B P a y m e n t   M e th o d   B In te rv ie w e r   B

+

S a m p le   B

C o m b in e d

=

What causes Mixed Distributions? Mixed Distributions occur when data comes from several sources that are supposed to be the same but are not. Note that both distributions that formed the combined Skewed Distribution started out as Normal Distributions. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

251

“X” Sifting 1-4 Non-Linear Relationships

N o n -­‐Lin e a r   R e la tio n s h ip s o ccu r   w h e n   th e   X   a n d   Y   s ca le s   a re   d ifferen t.

Y

10

M a rg in a l   D is tr ib u tio n o f   Y

Just because your Input (X) is Normally Distributed about a Mean, the Output (Y) may not be Normally Distributed.

5

0 0

50

100

X

M a rg in a l   D is tr ib u tio n o f   X

1-5 Interactions

In te r a ctio n s occur  when  two  inputs  interact  with  each  other  to   have  a  larg er  impact  on  Y  than  either  would  by  themselves.

Room Temperature

Interaction Plot for Process Output

Aerosol Hairspray

On

35

Spray

Off

30

25

No Spray No Fire

With Fire

If you find that two inputs have a large impact on Y but would not effect Y by themselves, this is called a Interaction. For instance, if you spray an aerosol can in the direction of a flame what would happen to room temperature? What do you see regarding these distributions? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

252

“X” Sifting 1-6 Time Relationships / Patterns

Th e   d is trib u tio n   is   d e p e n d e n t   o n   tim e .

Time relationships occur when the distribution is dependent on time, some examples are tool wear, chemical bath depletion, stock prices, etc.

M a rg in a l   D is tr ib u tio n o f   Y

30

25

20

10

20

30

40

50

Tim e

O O fte ftenn    sseeeenn    w w hheenn    to tooolin lingg    rreeqquuire iress    ““ w w aa rm rm in ingg    uupp”” ,  ,  to toool  l  w w eeaa r,   r,   ch e m ica l   b a th   d e p le tio n s ,   a m b ie n t   te m p e r a tu re   e ffe ct   o n   to o lin ch e m ica l   b a th   d e p le tio n s ,   a m b ie n t   te m p e r a tu re   e ffe ct   o n   to o lingg ..

Non-Normal Right (Positive) Skewed Open the worksheet “Distrib 1”, select Pos Skew.

To measure Skewness we use Descriptive Statistics. When looking at a symmetrical distribution, Skewness will be close to zero. If the distribution is skewed to the left it will have a negative number, if skewed to the right, it should be positive. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

253

“X” Sifting Kurtosis 2

K u rto s is re fers   to   th e   s h a p e   o f   th e   ta ils .

Platykurtic are flat with shorttails.

– Leptokurtic – Platykurtic • Different  combinations  of  distributions  causes  the  resulting  overall   shapes.

Le p to k u rtic P e a k e d   w ith   Lo n g -­‐Ta ils

P la ty k u rtic Fla t   w ith   S h o rt-­‐Ta ils

Platykurtic

Multiple Means shifting over time produces a plateau of the data as the shift exhibits this shift. Causes: 2-1. Mixtures: (Combined Data from Multiple Processes) Multiple Set-Ups Multiple Batches Multiple Machines Tool Wear (over time) 2-2 Sorting or Selecting: Scrapping product that falls outside the spec limits 2-3 Trends or Patterns: Lack of Independence in the data (example: tool wear, chemical bath) 2-4 Non Linear Relationships Chemical Systems

Open the worksheet “Distrib 1”, select Flat. Negative coefficient of Kurtosis indicates Platykurtic distribution. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

254

“X” Sifting Leptokurtic Open the worksheet “Distrib 1”, select Long Tail. Positive Kurtosis value indicates Leptokurtic distribution.

Distributions overlaying each other that have very different variance can cause a Leptokurtic distribution. Causes: 2-1. Mixtures: (Combined Data from Multiple Processes) Multiple Set-Ups Multiple Batches Multiple Machines Tool Wear (over time) 2-2 Sorting or Selecting: Scrapping product that falls outside the spec limits 2-3 Trends or Patterns: Lack of Independence in the data (example: tool wear, chemical bath) 2-4 Non Linear Relationships Chemical Systems

Multiple Modes 3

Reasons for Multiple Modes: 3-1 Mixtures of distributions (most likely) 3-2 Lack of independence – trends or patterns 3-3 Catastrophic failures (example: testing voltage on a motor and the motor shorts out so we get a zero reading etc.)

I ll have mine Ala Mode!! Multiple Modes have such dramatic combinations of underlying sources that they show distinct modes. They may have shown as Platykurtic, but were far enough apart to see separation. Celebrate! These are usually the easiest to identify causes. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

255

“X” Sifting Bimodal Distributions This is an example of a Bi-Modal Distribution. Interestingly each peak is actually a Normal Distribution, but when the data is viewed as a group it is obviously not Normal. Open the worksheet “Distrib 1”, select BiModal.

Extreme Bi-Modal (Outliers) If you see an extreme outlier, it usually has its on cause or own source of variation. It’s relatively easy to isolate the cause by looking on the X Axis of the Histogram. Open the worksheet “Distrib 1”, select Extreme BiModal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

256

“X” Sifting Bi-Modal – Multiple Outliers Open the worksheet “Distrib 1”, select Multiple Outliers. Having multiple outliers is more difficult to correct. This action typically means multiple inputs.

Granular 4

Open the worksheet “Distrib 1”, select Granular and let’s take a moment and notice the P-value in the Normal Probability Plot, it is definitely smaller than 0.05! There simply is not enough resolution in the data. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

257

“X” Sifting Normal Example

Open the worksheet “Distrib 1”, select Normal Dotplot.

Conclusions Regarding Distributions

Hey Honey, I found the key….! Here is what to conclude regarding distributions. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

258

“X” Sifting At this point, you should be able to: §  Perform a Multi-Vari Analysis §  Interpret and a Multi-Vari Graph §  Identify when a Multi-Vari Analysis is applicable §  Interpret what Skewed Data looks like §  Explain how data distributions become Non-normal when they are really Normal

You have now completed Analyze Phase – ”X” Sifting.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

259

Lean Six Sigma Black Belt Training

Analyze Phase Inferential Statistics

Now we will continue in the Analyze Phase with Inferential Statistics.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

260

Inferential Statistics Overview The core fundamentals of this phase are Inferential Statistics, Nature of Sampling and Central Limit Theorem. We will examine the meaning of each of these and show you how to apply them.

W W elco elcom m e   e  to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg

Inferential  Statistics Inferential  Statistics

In Infere ferenntia tia l  l  SSta ta tis tistics tics

NN ature  of  Sampling ature  of  Sampling

In Intro tro    to to    HH yy ppooth theessis is    Te Tesstin tingg

CC entral  Limit  Theorem entral  Limit  Theorem

HH yy ppooth thes esis is    Te Tesstin tingg    NN DD    PP11 HH yy ppooth thes esis is    Te Tesstin tingg    NN DD    PP22 HH yy ppooth thes esis is    Te Tesstin tingg    NN NN DD    PP11 HH yy ppooth thes esis is    Te Tesstin tingg    NN NN DD    PP22 W W ra ra pp    UUpp    & &    AA ctio ctionn    Item Item ss

Nature of Inference

in ·∙fe r ·∙e n ce (n.)  “The  act  or  process  of  deriving  log ical  conclusions   from  premises  known  or  assumed  to  be  true.  The  act  of  reasoning   from  factual  knowledg e  or  evidence.” 1 1 .  Dictionary.com

In fe re n tia l   S ta tis tics – To  draw  inferences  about  the  process  or   population  being  studied  by  modeling  patterns  of  data  in  a  way  that   account  for  randomness  and  uncertainty  in  the  observations.   2 2 .  W ikipedia.com

Putting  tthe he  pieces   of   Putting pieces of the  the puz zpuzzle le   together….! tog ether…. One objective of Six Sigma is to move from only describing the nature of the data or descriptive statistics to that of inferring what will happen in the future with our data or Inferential Statistics. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

261

Inferential Statistics 5 Step Approach to Inferential Statistics

1 .   W h a t   d o   y o u   w a n t   to   k n o w ? 2 .   W h a t   to o l   w ill   g iv e   y o u   th a t   in fo rm a tio n ? 3 .   W h a t   k in d   o f   d a ta   d o e s   th a t   to o l   re q u ire ? 4 .   H o w   w ill   y o u   co lle ct   th e   d a ta ? 5 .   H o w   co n fid e n t   a re   y o u   o f   y o u r   d a ta   s u m m a rie s ?

S o  many m any   So questions….? questions.….! As with most things you have learned associated with Six Sigma – there are defined steps to be taken. Types of Error

1 . Erro r   in   s a m p lin g – Error  due  to  differences  among  samples  drawn  at  random  from  the   population  (luck  of  the  draw). – This  is  the  only  source  of  error  that  statistics  ca n  accommodate.

2 . B ia s   in   s a m p lin g – Error  due  to  lack  of  independence  among  random  samples  or  due  to systematic  sampling  procedures  (heig ht  of  horse  jockeys  only).

3 . Erro r   in   m e a s u re m e n t – Error  in  the  measurement  of  the  samples  (MSA / G R&R)

4 . La ck   o f   m e a s u re m e n t   v a lid ity – Error  in  the  measurement  does  not  actually  measure  what  it  intends  to   measure  (placing  a  probe  in  the  wrong  slot  measuring  temperature with  a  thermometer  that  is  just  next  to  a  furnace). Types of error contribute to uncertainty when trying to infer with data. There are four types of error that are explained above. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

262

Inferential Statistics Population, Sample, Observation

P o p u la tio n – EVERY  data  point  tha t  ha s  ever  been  or  ever  will  be  g enerated  from  a  g iven   cha racteristic.

S a m p le – A  portion  (or  subset)  of  the  population,  either  at  one  time  or  over  time.

X X

O b s e rv a tio n

X X X

– A n  individual  measurement.

X

Let’s just review a few definitions: A population is EVERY data point that has ever been or ever will be generated from a given characteristic. A sample is a portion (or subset) of the population, either at one time or over time. An observation is an individual measurement. Significance

Significance – Practical difference and significance is: –  The amount of difference, change or improvement that will be of practical, economic or technical value to you. –  The amount of improvement required to pay for the cost of making the improvement.

Statistical difference and significance is: The magnitude of difference or change required to distinguish between a true difference, change or improvement and one that could have occurred by chance.

Six Sigma decisions will ultimately have a return on resource investment (RORI)* element associated with them. * RORI includes not only dollars and assets but the time and participation of your teams.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

263

Inferential Statistics The Mission

Mean Shift

Variation Reduction

Both

Your mission, which you have chosen to accept, is to reduce cycle time, reduce the error rate, reduce costs, reduce investment, improve service level, improve throughput, reduce lead time, increase productivity… change the output metric of some process, etc… In statistical terms, this translates to the need to move the process Mean and/or reduce the process Standard Deviation You’ll be making decisions about how to adjust key process input variables based on sample data, not population data - that means you are taking some risks. How will you know your key process output variable really changed, and is not just an unlikely sample? The Central Limit Theorem helps us understand the risk we are taking and is the basis for using sampling to estimate population parameters.

A Distribution of Sample Means The Central Limit Theorem says that as the sample size becomes large, this new distribution (the sample Mean distribution) will form a Normal Distribution, no matter what the shape of the population distribution of individuals.

Central Limit Theorem 1.  Individual values of a population form some distribution. 2.  A sample will yield a Mean. 3.  Another sample will shift the Mean. 4.  At some point the distribution will become Normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

264

Inferential Statistics Sampling Distributions—The Foundation of Statistics

P o p u la tio n 3 5 2 12 10 1 6 12 5 6 12 14 3 6 11 9 10 10 12

•

S a mples  from  the  popula tion,  ea ch  with  five  observa tions: S a m p le   1 1   12 9 7 8 7 .4

• • •

S a m p le   2 9 8 5 14 10 9 .2

S a m p le   3 2 3 6 11 10 6 .4

In  this  exa mple,  we  ha ve  ta ken  three  sa mples  out  of  the   popula tion,  ea ch  with  five  observa tions  in  it.  W e  computed  a   Mea n  for  ea ch  sa mple.  N ote  tha t  the  Mea ns  a re  not  the  sa me! W hy  not? W ha t  would  happen  if  we  kept  ta king  more  samples?

Every statistic derives from a sampling distribution. For instance, if you were to keep taking samples from the population over and over, a distribution could be formed for calculating Means, Medians, Mode, Standard Deviations, etc. As you will see the above sample distributions each have a different statistic. The goal here is to successfully make inferences regarding the statistical data. Constructing Sampling Distributions To demonstrate how sampling distributions work we will create some random data for die rolls. Create a sample of 1,000 individual rolls of a die that we will store in a variable named “Population”. From the population, we will draw five random samples.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

265

Inferential Statistics Sampling Distributions Select the “Die Example” worksheet. This sheet has been created using a sample size of 5, 10 and 30 from the Population column.

Let s do something with the data -

Select the Die Example worksheet.

Sampling Error Now compare the Mean and Standard Deviation of the samples of 5 observations to the population. What do you see?

Calculate the Mean and Standard Deviation for Population and Samples 1-5 and compare the sample statistics to the population.

Select Column Format for easer viewing

Range in Mean 1.2

Range in Stdev 0.59

SigmaXL>Statistical Tools>Descriptive Statistics: Numeric Data Variables (Y): Population, Sample1, Sample 2, Sample 3, Sample 4, Sample 5

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

266

Inferential Statistics Sampling Error - Reduced Calculate the Mean and Standard Deviation for Samples 6-10 and compare the sample statistics to the population.

Calculate the Mean and Standard Deviation for Samples 6-10 and compare the sample statistics to the population.

Range in Mean 0.9

Range in Stdev 0.667

With 10 observations, the differences between samples are now much smaller. SigmaXL>Statistical Tools>Descriptive Statistics: Numeric Data Variables (Y):, Sample 6, Sample 7, Sample 8, Sample 9, Sample 10

Can you tell what is happening to the Mean and Standard Deviation? When the sample size increases, the values of the Mean and Standard Deviation decrease. What do you think would happen if the sample increased? Let’s try 30 for a sample size.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

267

Inferential Statistics Sampling Error - Reduced Do you notice anything different? Look how much smaller the range of the Mean and Standard deviations. Did the sampling error get reduced?

Sampling Distributions

Feeling lucky…?! Now instead of looking at the effect of sample size on error, we will create a sampling distribution of averages. Follow along to generate your own random data. Rename the column headings to Roll 1, Roll 2, …, Roll 10. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

268

Inferential Statistics Sampling Distributions

The commands shown above will create new columns that are now averages from the columns of random population data. We have 1000 averages of sample size 5 and 1000 averages of sample size 10.

In SigmaXL® follow the above commands. The Histogram being generated makes it easy to see what happened when the sample size was increased.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

269

Inferential Statistics Different Distributions

Observations

Answers 1.  The Center remains the same. 2.  The variation decreases. 3.  The shape of the distribution changes - it tending to Normal.

The Mean of the sample Mean distribution:

The Standard Deviation of the sample Mean distribution, also known as the Standard Error.

Good news: the Mean of the sample Mean distribution is the Mean of the population.

Better news: I can reduce my uncertainty about the population Mean by increasing my sample size n.

Central Limit Theorem If all possible random samples, each of size n, are taken from any population with a Mean µ and Standard Deviation σ, the distribution of sample Means will: have a Mean

Everything we have gone through with sampling error and sampling distributions was leading up to the Central Limit Theorem.

have a Std Dev and be Normally Distributed when the parent population is Normally Distributed or will be approximately Normal for samples of size 30 or more when the parent population is not Normally Distributed. This improves with samples of larger size.

Bigger is Better! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

270

Inferential Statistics So What? Recall that 95% of Normally Distributed data is within ± 2 Standard Deviations from the Mean. Therefore, the probability is 95% that my sample Mean is within 2 standard errors of the true population Mean.

So how does this theorem help me understand the risk I am taking when I use sample data, instead of population data?

A Practical Example

Le t’ s   s a y   y o u r   p ro je ct   is   to   re d u ce   th e   s e tu p   tim e   fo r   a   la rg e   ca s tin g : – Based  on  a  sample  of  2 0  setups,  you  learn  that  your  baseline   averag e  is  4 5  minutes,  with  a  Standard  Deviation  of  1 0   minutes. – Because  this  is  just  a  sample,  the  4 5  minute  averag e  is  just  an   estimate  of  the  true  averag e. – Using  the  central  limit  theorem,  there  is  9 5 %  probability  that   the  true  averag e  is  somewhere  between  4 0 .5  and  4 9 .5   minutes. – Therefore,  don’t  g et  too  excited  if  you  made  a  process  chang e   that  resulted  in  a  reduction  of  only  2  minutes.

What is the likelihood of getting a sample with a 2 second difference? This could be caused either by implementing changes or could be a result of random sampling variation, sampling error. The 95% confidence interval exceeds the 2 second difference (delta) seen as a result. What is the delta caused from? This could be a true difference in performance or random sampling error. This is why you look further than only relying on point estimators. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

271

Inferential Statistics Sample Size and the Mean

W h e n   ta k in g   a   s a m p le   w e   h a v e   o n ly   e s tim a te d   th e   tru e   M e a n :   – A ll  we  know  is  tha t  the  true  Mean  lies  somewhere  within  the   theoretical  distribution  of  sample  Means  or  the  t-­‐d istribution  which  are   ana lyz ed  using  t-­‐tests. – T-­‐tests  measure  the  sig nificance  of  differences  between  Means.

Th e o re tica l   d is trib u tio n   o f   s a m p le   M e a n s   fo r   n   =   2

Th e o re tica l   d is trib u tio n   o f   s a m p le   M e a n s   fo r   n   =   1 0

D is trib u tio n   o f   in d iv id u a ls   in   th e   p o p u la tio n

Standard Error of the Mean

Th e   S ta n d a r d   D e v ia tio n fo r   th e   d is trib u tio n   o f   M e a n s   is   ca lle d   th e   s ta n d a rd   e rro r   o f   th e   M e a n   a n d   is   d e fin e d   a s : – This  formula  shows  tha t  the  Mea n  is  more  sta ble  tha n  a  sing le   observa tion  by  a  fa ctor  of  the  squa re  root  of  the  sa mple  siz e.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

272

Inferential Statistics Standard Error

Standard Error

Standard Error approaches zero at about 30 samples.

0

5

10

20

30

Sample Size

When comparing standard error with sample size, the rate of change in the standard error approaches zero at about 30 samples. This is why a sample size of 30 comes up often in discussions on sample size. This is the point at which the t and the Z distributions become nearly equivalent. If you look at a Z table and a t table to compare Z=1.96 to t at 0.975 as sample approaches infinite degrees of freedom they are equal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

273

Inferential Statistics At this point, you should be able to: §  Explain the term “Inferential Statistics” §  Explain the Central Limit Theorem §  Describe what impact sample size has on your estimates of population parameters §  Explain Standard Error

You have now completed Analyze Phase – Inferential Statistics.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

274

Lean Six Sigma Black Belt Training

Analyze Phase Introduction to Hypothesis Testing

Now we will continue in the Analyze Phase with “Introduction to Hypothesis Testing”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

275

Introduction to Hypothesis Testing Overview The core fundamentals of this phase are Hypothesis Testing, Tests for Central Tendency, Tests for Variance and ANOVA. We will examine the meaning of each of these and show you how to apply them.

W W elco elcom m e   e  to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infere ferenntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    HH yy ppooth theessis is    Te Tesstin tingg HH yy ppooth thes esis is    Te Tesstin tingg    NN DD    PP11

HHyyppooth thes esis   is  Tes Testin tingg    PPuurp rpoossee Tes Tests   ts  fo for   r  CCen entra tra l  Ten l  Tendden ency cy Tes Tests   ts  fo for  V r  Vaa ria ria nnce ce AANN OO VVAA

HH yy ppooth thes esis is    Te Tesstin tingg    NN DD    PP22 HH yy ppooth thes esis is    Te Tesstin tingg    NN NN DD    PP11 HH yy ppooth thes esis is    Te Tesstin tingg    NN NN DD    PP22 W W ra ra pp    UUpp    & &    AA ctio ctionn    Item Item ss

Six Sigma Goals and Hypothesis Testing Our goal is to improve our Process Capability, this translates to the need to move the process Mean (or proportion) and reduce the Standard Deviation. §  Because it is too expensive or too impractical (not to mention theoretically impossible) to collect population data, we will make decisions based on sample data. §  Because we are dealing with sample data, there is some uncertainty about the true population parameters. Hypothesis Testing helps us make fact-based decisions about whether there are different population parameters or that the differences are just due to expected sample variation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

276

Introduction to Hypothesis Testing Purpose of Hypothesis Testing The purpose of appropriate Hypothesis Testing is to integrate the Voice of the Process with the Voice of the Business to make data-based decisions to resolve problems. Hypothesis Testing can help avoid high costs of experimental efforts by using existing data. This can be likened to: Local store costs versus mini bar expenses. There may be a need to eventually use experimentation, but careful data analysis can indicate a direction for experimentation if necessary. The probability of occurrence is based on a pre-determined statistical confidence. §  Decisions are based on: §  Beliefs (past experience) §  Preferences (current needs) §  Evidence (statistical data) §  Risk (acceptable level of failure)

Relax, it’s just a hypothesis test!!

The Basic Concept for Hypothesis Tests

Recall from the discussion on classes and cause of distributions that a data set may seem Normal, yet still be made up of multiple distributions. Hypothesis Testing can help establish a statistical difference between factors from different distributions.

0.8 0.7 0.6

freq

0.5 0.4 0.3 0.2 0.1 0.0 -3

-2

-1

0

1

2

3

x

Did my sample come from this population? Or this? Or this? Because of not having the capability to test an entire population, having to use a sample is the closest we can get to the population. Since we are using sample data and not the entire population we need to have methods what will allow us to infer the sample if a fair representation of then population. When we use a proper sample size, Hypothesis Testing gives us a way to detect the likelihood that a sample came from a particular distribution. Sometimes the questions can be: Did our sample come from a population with a mean of 100? Is our sample variance significantly different than the variance of the population? Is it different from a target? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

277

Introduction to Hypothesis Testing Significant Difference

A re  the  two  distributions   “sig nifica ntly” different  from  ea ch   other?  How  sure  a re  we  of  our  decision?   How  do  the  number  of  observa tions  a ffect  our  confidence  in   detecting  population  Mea n?

µ1 S a m p le   1

µ2 S a m p le   2

Do you see a difference between Sample 1 and Sample 2? There may be a real difference between the samples shown; however, we may not be able to determine a statistical difference. Our confidence is established statistically which has an effect on the necessary sample size. Our ability to detect a difference is directly linked to sample size and in turn whether we practically care about such a small difference. Detecting Significance

S ta tis tics   p ro v id e   a   m e th o d o lo g y   to   d e te ct   d iffe re n ce s . – Examples  mig ht  include  differences  in  suppliers,  shifts  or   equipment. – Two  types  of  sig nificant  differences  occur  and  must  be  well   understood,  p r a ctica l and  s ta tis tica l. – Failure  to  tie  these  two  differences  tog ether  is  one  of  the  most common  errors  in  statistics. H O :   Th e   s k y   is   n o t   fa llin g . H A :   Th e   s k y   is   fa llin g .

We will discuss the difference between practical and statistical throughout this session. We can affect the outcome of a statistical test simply by changing the sample size. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

278

Introduction to Hypothesis Testing Practical vs. Statistical

P r a ctica l   D iffe r e n ce : The  difference  which  results  in  an   improvement  of  practical  or  economic  value  to  the  company. – Example,  an  improvement  in  yield  from  9 6  to  9 9  percent.

S ta tis tica l   D iffe r e n ce : A  difference  or  chang e  to  the  process  that   probably  (with  some  defined  deg ree  of  confidence)  did  not  happen by  chance. – Examples  mig ht  include  differences  in  suppliers,  markets  or  servers.

W e   w ill   s e e   th a t   it   is   p o s s ib le   to   re a liz e   a   s ta tis tica lly   s ig n ifica n t   d iffere n ce   w ith o u t   re a liz in g   a   p ra ctica lly   s ig n ifica n t   d iffere n ce . Lets take a moment to explore the concept of Practical Differences versus Statistical Differences.

Detecting Significance During the Measure Phase, it is important that the nature of the problem be well understood.

M e a n   S h ift

In understanding the problem, the practical difference to be achieved must match the statistical difference. The difference d can be either a change in the Mean or in the variance. Detection of a difference is then accomplished using statistical Hypothesis Testing. An important concept to understand is the process of detecting a significant change. How much of a shift in the Mean will offset the cost in making a change to the process?

V a ria tio n   R e d u ctio n

This is not necessarily the full shift from the Business Case of your project. Realistically, how small or how large a delta is required? The larger the delta, the smaller the necessary sample will be because there will be a very small overlap of the distributions. The smaller the delta is, the larger the sample size has to be to be able to detect a statistical difference.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

279

Introduction to Hypothesis Testing Hypothesis Testing A Hypothesis Test is an a priori theory relating to differences between variables. That means we begin by saying either this will happen or that will happen. Then we proceed with a statistical test or Hypothesis Test to prove or disprove on or the other. A Hypothesis Test converts the practical problem into a statistical problem. Since relatively small sample sizes are used to estimate population parameters, there is always a chance of collecting a non-representative sample. Therefore we use Inferential statistics to help us estimate the probability of getting a non-representative sample.

DICE Example You have rolled dice before haven’t you? You know dice that you would find in a board game or in Las Vegas. Well assume that we suspect a single die is “Fixed.” Meaning it has been altered in some form or fashion to make a certain number appear more often that it rightfully should. Consider the example on how we would go about determining if in fact a die was loaded. If we threw the die five times and got five one’s, what would you conclude? How sure can you be? The probability of getting just a single one. The probability of getting five ones.

W e  could  throw  it  a  number  of  times  and  track  how  many  each  face occurred.    W ith  a  standard  die,  we  would  expect  each  face  to  occ ur  1 / 6  or   1 6 .6 7 %  of  the  time.

If  we  threw  the  die  5  times  and  g ot  5  one’s,  what  would  you  conclude?    How   sure  can  you  be?     – Pr  (1  one)  =  0 .1 6 6 7

Pr  (5  ones)  =  (0 .1 6 6 7 )5 =  0 .0 0 0 1 3

There  are  approximately  1 .3  chances  out  of  1 0 0 0  that  we  could  ha ve  g otten   5  ones  with  a  standard  die. Therefore,  we  would  sa y  we  are  willing  to  take  a  0 .1 %  chance  of   being   wrong  about  our  hypothesis  that  the  die  was   “loaded” since  the  results  do  not   come  close  to  our  predicted  outcome. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

280

Introduction to Hypothesis Testing Hypothesis Testing When it comes to Hypothesis Testing, you must look at three focus points to help validate your claim. These points are Type I, Type II and Sample Size.

α

DECISIONS

β

n

Statistical Hypotheses A hypothesis is a predetermined theory about the nature of, or relationships between variables. Statistical tests can prove (with a certain degree of confidence) that a relationship exists. With Hypothesis Testing the primary assumption is that the null hypothesis is true. Therefore statistically you can only reject or fail to reject the null hypothesis. The Null Hypothesis is always the “default” assumption. If the null is rejected, this means that you have data that supports the alternative hypothesis. Shortly we’ll look at how P-values help us understand the relationships.

Two alternatives – Ho

the null hypothesis

Ha

the alternative hypothesis

P-value > 0.05 P-value < 0.05

Ho = no difference or relationship Ha = is a difference or relationship

Making a decision does not FIX a problem, taking action does.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

281

Introduction to Hypothesis Testing Steps to Statistical Hypothesis Testing There are six steps to Hypothesis Testing: 1. State the Practical Problem. 2. State the Statistical Problem. 3. Select the appropriate statistical test and risk levels. –Your alpha may change depending on the problem at hand. An alpha of .05 is common in most manufacturing. In transactional projects, an alpha of 0.10 is common when dealing with human behavior. Being 90% confident that a change to a sale procedure will produce results is most likely a good approach. A not-so-common alpha is 0.01. This is only used when it is necessary to make the null hypothesis very difficult to reject. 4. Establish the Sample Size required to detect the difference. 5. State the Statistical Solution. 6. State the Practical Solution.

Noooot THAT practical solution!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

282

Introduction to Hypothesis Testing How Likely is Unlikely? Any differences between observed data and claims made under H0 may be real or due to chance. Hypothesis Tests determine the probabilities of these differences occurring solely due to chance and call them P-values. The a level of a test (level of significance) represents the yardstick against which p-values are measured and H0 is rejected if the P-value is less than the alpha level. The most commonly used a levels are 5%, 10% and 1%. Hypothesis Testing Risk The alpha risk or Type 1 Error (generally called the “Producer’s Risk”) is the probability that we could be wrong in saying that something is “different.” It is an assessment of the likelihood that the observed difference could have occurred by random chance. Alpha is the primary decisionmaking tool of most statistical tests.

A ctu a l   C o n d itio n s

Alpha risk can also be explained as: The risk with implementing a change when you should not. Alpha risk is typically lower than beta risk because you are more hesitant to make a mistake about claiming the significance of an X (and therefore spending money) as compared to overlooking an X (which is never revealed).

N ot  Different (H o is  True)

N ot  Different

(Fa il  to  Reject  Ho)

S ta tis tica l C o n clu s io n s Different

(Reject  Ho)

Different

(H o is  Fa lse)

C orrect Decision

Type  II Error

Type  1 Error

C orrect Decision

There of two types of error Type I with an associated risk equal to alpha (the first letter in the Greek alphabet), and of course named the other one Type II with an associated risk equal to beta. The formula reads: alpha is equal to the probability of making a Type 1 error, or alpha is equal to the probability of rejecting the null hypothesis when the null hypothesis is true.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

283

Introduction to Hypothesis Testing Alpha Risk

A lp h a   (α )   ris k s   a re   e x p re s s e d   re la tiv e   to   a   re fe re n ce   d is trib u tio n . D is trib u tio n s   in clu d e : – t-­‐d is tr ib u tio n – z -­‐d is tr ib u tio n

Th Thee    aa -­‐le -­‐levveel  l  is is    rreeppre resseennte tedd    bbyy     th thee    clo clouuddeedd    aa re reaa ss..

– χ2 -­‐ d is tr ib u tio n

SSaa m m pple le    re ressuults lts    in in    th this is    aa re reaa     le leaa dd    to to    re reje jectio ctionn    oof  f  H H 00..

– F-­‐d is tr ib u tio n  

R e g io n   o f   DO UBT

R e g io n   o f   DO UBT A cce p t   a s   ch a n ce   d iffe re n ce s  

Hypothesis Testing Risk The beta risk or Type 2 Error (also called the “Consumer’s Risk”) is the probability that we could be wrong in saying that two or more things are the same when, in fact, they are different.

A ctu a l   C o n d itio n s N ot  Different (H o is  True)

N ot  Different

(Fail  to  Reject  Ho)

S ta tis tica l C o n clu s io n s Different

(Reject  Ho)

Different

(H o is  False)

C orrect Decision

Type  II Error

Type  1 Error

C orrect Decision

Another way to describe beta risk is failing to recognize an improvement. Chances are the sample size was inappropriate or the data was imprecise and/or inaccurate. Reading the formula: Beta is equal to the probability of making a Type 2 error. Or: Beta is equal to the probability of failing to reject the null hypothesis given that the null hypothesis is false. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

284

Introduction to Hypothesis Testing Beta Risk Beta and sample size are very closely related. When calculating Sample size in SigmaXL®, we always enter the “power” of the test which is one minus beta. In doing so, we are establishing a sample size that will allow the proper overlap of distributions.

Beta  Risk  is  the  probability  of  failing  to  reject  the  null  hypothesis   when  a  difference  exists. D is trib u tio n   if   H 0 is   tru e R e je ct   H 0 α =   P r(Ty p e   1   e rr o r) α =  0 .0 5 H 0 value

A cce p t   H 0 β=   P r(Ty p e   II   e rro r)

D is trib u tio n   if   H a is   tru e µ

CCritica ritical  l  vvaalu luee    oof  f   te tesst  t  ssta tatis tistic tic

Distinguishing between Two Samples Recall from the Central Limit Theorem as the number of individual observations increase the Standard Error decreases. In this example when n=2 we cannot distinguish the difference between the Means (> 5% overlap, P-value > 0.05).

δ

Theoretical Distribution of Means When n = 2 δ=5 S=1

When n=30, we can distinguish between the Means (< 5% overlap, Pvalue < 0.05) There is a significant difference. Theoretical Distribution of Means When n = 30 δ=5 S=1

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

285

Introduction to Hypothesis Testing Delta Sigma—The Ratio between δ and S Delta (δ) is the size of the difference between two Means or one Mean and a target value. Sigma (S) is the sample Standard Deviation of the distribution of individuals of one or both of the samples under question.

Large Delta

δ

When δ /& S is large, we don’t need statistics because the differences are so large. If the variance of the data is large, it is difficult to establish differences. We need larger sample sizes to reduce uncertainty.

Large S

We want to be 95% confident in all of our estimates! All samples are estimates of the population. All statistics based on samples are estimates of the equivalent population parameters. All estimates could be wrong!

Typical Questions on Sampling These are typical questions you will experience or hear during sampling. The most common answer is “It depends.”. Primarily because someone could say a sample of 30 is perfect where that may actually be too many. Point is you don’t know what the right sample is without the test. Question: Answer:

How many samples should we take?

Well, that depends on the size of your delta and Standard Deviation .

Question:

How should we conduct the sampling?

Answer:

Well, that depends on what you want to know .

Question:

Was the sample we took large enough?

Answer:

Well, that depends on the size of your delta and Standard Deviation .

Question: Answer:

LSS Black Belt Manual XL v11

Should we take some more samples just to be sure? No, not if you took the correct number of samples in the first place!

© 2013 e-Careers Limited

286

Introduction to Hypothesis Testing The Perfect Sample Size The minimum sample size required to provide exactly 5% overlap (risk). In order to distinguish the Delta. Note: If you are working with nonNormal Data, multiply your calculated sample size by 1.1. 40

40

50

60

70

50

60

70

P o p u la tio n

Hypothesis Testing Roadmap – Continuous Data Here is a Hypothesis Testing roadmap for Continuous Data. This is a great reference tool while you are conducting Hypothesis Tests.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

287

Introduction to Hypothesis Testing Hypothesis Testing Roadmap – Continuous Data

Hypothesis Testing Roadmap – Attribute Data

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

288

Introduction to Hypothesis Testing Common Pitfalls to Avoid

While using Hypothesis Testing the following facts should be borne in mind at the conclusion stage: –  The decision is about Ho and NOT Ha. –  The conclusion statement is whether the contention of Ha was upheld. –  The null hypothesis (Ho) is on trial. –  When a decision has been made: •  Nothing has been proved. •  It is just a decision. •  All decisions can lead to errors (Types I and II). –  If the decision is to Reject Ho, then the conclusion should read There is sufficient evidence at the α level of significance to show that state the alternative hypothesis Ha. –  If the decision is to Fail to Reject Ho, then the conclusion should read There isn t sufficient evidence at the α level of significance to show that state the alternative hypothesis.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

289

Introduction to Hypothesis Testing At this point, you should be able to: §  Articulate the purpose of Hypothesis Testing §  Explain the concepts of the Central Tendency §  Be familiar with the types of Hypothesis Tests

You have now completed Analyze Phase – Introduction to Hypothesis Testing.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

290

Lean Six Sigma Black Belt Training

Analyze Phase Hypothesis Testing Normal Data Part 1

Now we will continue in the Analyze Phase with “Hypothesis Testing Normal Data Part 1”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

291

Hypothesis Testing Normal Data Part 1 Overview The core fundamentals of this phase are Hypothesis Testing, Tests for Central Tendency, Tests for Variance and ANOVA. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infe fere renntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    H H yy ppooth theessis is    Te Tesstin tingg

SSaa m mpple le    SSiz izee

H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP11

Te Tesstin tingg    M Mea ea nnss

H H yy ppooth theessis is    Te Tesstin tingg    N ND D    PP22

AAnnaa ly ly zzin ingg    RReessuults lts

H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP11 H H yy ppooth theessis is    Te Tesstin tingg    N NN ND D    PP22 W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Test of Means (t-tests) T-tests are used to compare a Mean against a target and to compare Means from two different samples and to compare paired data. When comparing multiple Means it is inappropriate to use a ttest. Analysis of variance or ANOVA is used when it is necessary to compare more than 2 Means.

They don’t look the same to me!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

292

Hypothesis Testing Normal Data Part 1 1 Sample t Here we are looking for the region in which we can be 95% sure our true population Mean will lie. This is based on a calculated average, Standard Deviation, number of trials and a given alpha risk of .05. In order for the Mean of the sample to be considered not significantly different than the target, the target must fall within the confidence interval of the sample Mean.

1 Sample t-test Sample Size One common pitfall in statistics is not understanding what the proper sample size Ta rg e t should be. If you look at the P o p u la tio n graphic, the question is: Is there a difference between my X C a n   n o t   te ll   th e   n= 2 X X d iffe re n ce XX process Mean and the desired X X X b e tw e e n   th e   s a m p le   X X X target. If we had population X X X a n d   th e   ta rg e t. data, it would be very easy – n = 3 0 C a n   te ll   th e   X no they are not the same, but d iffe re n ce X b e tw e e n   th e   s a m p le   XX they may be within an X X a n d   th e   ta rg e t. X XX acceptable tolerance (or specification window). If we S SE Mean = took a sample of 2 can we tell n a difference? No, because the spread of the distribution of averages from samples of 2 will create too much uncertainty and make it very difficult to statistically say there is a difference. T

If you remember from earlier, 95% of the area under the curve of a Normal Distribution falls within plus or minus 2 Standard Deviations. Confidence intervals are based on your selected alpha level, so if you selected an alpha of 5%, then the confidence interval would be 95% which is roughly plus or minus 2 Standard Deviations. Using your eye to guesstimate you can see that the target value falls within plus or minus 2 Standard Deviations of the sampling distribution of sample size 2. If you used a sample of 30, could you tell if the target was different? Just using your eye it appears that the target is outside the 95% confidence interval of the Mean. Luckily, SigmaXL® makes this very easy… LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

293

Hypothesis Testing Normal Data Part 1 Sample Size Instead of going through the dreadful hand calculations of sample size we will use SigmaXL®. Two of the main fields must be filled in and one selected as the Solve For. If you want to know the sample size, you must enter the difference, which is the shift that must be detected. It is common to state the difference in terms of “generic” Standard Deviations when you do not have an estimate for the Standard Deviation of the process. For example, if you want to detect a shift of 1.5 Standard Deviations enter that in difference and enter 1 for Standard Deviation. If you knew the Standard Deviation and it was 0.8, then enter it for Standard Deviation and 1.2 for the difference (which is a 1.5 Standard Deviation shift in terms of real values). If you are unsure of the desired difference, or in many cases simply get stuck with a sample size that you didn’t have a lot of control over, SigmaXL® will tell you how much of a difference can be detected. You as a practitioner must be careful when drawing Practical Conclusions because it is possible to have statistical significance without practical significance. In other words - do a reality check. SigmaXL® has made it easy to see an assortment of sample sizes and differences. Try the example shown. Notice that as the sample size increases, there is not as big an effect on the difference. If it was only necessary to see a difference of 0.9, why bother taking any more samples than 15? The Standard Deviation entered has an effect on the difference calculated. Take a few moments and explore different Standard Deviation sizes in SigmaXL® to see their effect on difference.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

294

Hypothesis Testing Normal Data Part 1 1-Sample t Example

1 .   P ra ctica l   P ro b le m : • W e  are  considering  chang ing  suppliers  for  a  part  that  we  currently   purchase  from  a  supplier  that  charg es  us  a  premium  for  the  hardening   process.     • The  proposed  new  supplier  has  provided  us  with  a  sample  of  their product.    They  have  stated  that  they  can  maintain  a  g iven  charac teristic   of  5  on  their  product. • W e  want  to  test  the  samples  and  determine  if  their  claim  is  accurate. 2 .   S ta tis tica l   P ro b le m : H o:  µN .S . =  5 H a :  µN .S. ≠ 5 3 .   1 -­‐s a m p le   t-­‐te s t (p o p u la tio n   S ta n d a rd   D e v ia tio n   u n k n o w n ,   co m p a rin g   to   ta rg e t). α =  0 .0 5              β =  0 .1 0 Let’s now try a 1-sample t example. Step 1: Take a moment and review the practical problem Step 2: The Statistical Problem is: The null hypothesis is the Mean of the new supplier is equal to 5. The alternative hypothesis is the Mean of the new supplier is not equal to 5. This is considered a 2-tailed test if you’ve heard that terminology before. Step 3: Our selected alpha level is 0.05 and beta is 0.10.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

295

Hypothesis Testing Normal Data Part 1 Hypothesis Testing Follow along in SigmaXL®, as you can see, we will be able to detect a difference of 1.24 with the sample of 9. If this was not good enough, you would need to request additional samples.

This means we will be able to detect a difference of only 1.24 if the population has a Standard Deviation of 1 unit.

Example: Follow the Road Map Now refer to the road map for Hypothesis Testing, you must first check for Normality. In SigmaXL® select “Graphical Tools>Normal Probability Plots”. For the “Numeric Data Variable (Y)” doubleclick on “Value” in the left-hand box. Once this is complete select “OK”. Since the P-value is greater than 0.05 we fail to reject the null hypothesis that the data are Normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

296

Hypothesis Testing Normal Data Part 1 1-Sample t Example Perform the one sample ttest. In SigmaXL® select “Statistical Tools>1 Sample t-Test & Confidence Intervals”. From the lefthand box select “Values” and click “Numeric Data Variable (Y) >>” . SigmaXL® provides a selection for the alternative hypothesis. We find the default is not equal to, which corresponds to our hypothesis. If your alternative hypothesis was a greater than or less than, you would have to change the default. Shown here is the SigmaXL® result for the 1-Sample t-test. SigmaXL® does not include graphical views of the Null Hypothesis.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

297

Hypothesis Testing Normal Data Part 1 Evaluating the Results

S in ce   th e   P -­‐v a lu e   o f   0 .0 3 4   is   le s s   th a n   0 .0 5 ,   re je ct   th e   n u ll   h y p o th e s is . B a s e d   o n   th e   s a m p le s   g iv e n   th e r e   is   a   d iffe r e n ce   b e tw e e n   th e   a v e ra g e   o f   th e   s a m p le   a n d   th e   d e s ire d   ta rg e t.

X

Ho

6 .   S ta te   P ra ctica l   C o n clu s io n s Th e   n e w   s u p p lie r ’ s   cla im   th a t   th e y   ca n   m e e t   th e   ta rg e t         o f   5   fo r   th e   h a rd n e s s   is   n o t   co rre ct. Manual Calculation of 1- Sample t

Le t’ s   co m p a re   th e   m a n u a l   ca lcu la tio n s   to   w h a t   th e   co m p u te r   ca lcu la te s . – C a lcu la te   t-­‐s ta tis tic   fro m   d a ta :

t=

X − Target 4.79 − 5.00 = = −2.56 s 0.247 n 9

– D e te rm in e   critica l   t-­‐v a lu e   fro m   t-­‐ta b le   in   re fe re n ce   s e ctio n . • W h e n   th e   a lte rn a tiv e   h y p o th e s is   h a s   a   n o t   e q u a l   s ig n ,   it   is   a   tw o -­‐s id e d   te s t. • S p lit   th e   α in   h a lf   a n d   re a d   fro m   th e   0 .9 7 5   co lu m n   in   th e   t-­‐ta b le   fo r   n   -­‐1   (9   -­‐ 1 )   d e g re e s   o f   fre e d o m . Here are the manual calculations of the 1-sample t, verify that SigmaXL® is correct. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

298

Hypothesis Testing Normal Data Part 1 Manual Calculation of 1- Sample t If the calculated t-value lies anywhere in the critical regions reject the null hypothesis. T - Distribution

degrees of freedom

1 2 3 4 5

.600 0.325 0.289 0.277 0.271 0.267

.700 0.727 0.617 0.584 0.569 0.559

.800 1.376 1.061 0.978 0.941 0.920

.900 3.078 1.886 1.638 1.533 1.476

.950 6.314 2.920 2.353 2.132 2.015

.975 12.706 4.303 3.182 2.776 2.571

.990 31.821 6.965 4.541 3.747 3.365

.995 63.657 9.925 5.841 4.604 4.032

6 7 8 9 10

0.265 0.263 0.262 0.261 0.260

0.553 0.549 0.546 0.543 0.542

0.906 0.896 0.889 0.883 0.879

1.440 1.415 1.397 1.383 1.372

1.943 1.895 1.860 1.833 1.812

2.447 2.365 2.306 2.262 2.228

3.143 2.998 2.896 2.821 2.764

3.707 3.499 3.355 3.250 3.169

µ!

-2.56 -2.306

2.306 α/2 =.025

α/2=.025 The data here supports the alternative

0 Critical Regions

hypothesis that the estimate for the Mean of the population is not 5.0.

Confidence Intervals for Two-Sided t-test Here is the formula for the confidence interval. Notice we get the same results as SigmaXL®.

Th e   fo rm u la   fo r   a   tw o -­‐s id e d   t-­‐te s t   is : s s ≤ µ ≤ X + t α/2,n −1 n n or

X − t α/2,n −1

X ± t crit SE mean = 4.788 ± 2.306 * .0824 4.5989 to 4.9789

4.5989

LSS Black Belt Manual XL v11

X 4.7889

4.9789

Ho

© 2013 e-Careers Limited

299

Hypothesis Testing Normal Data Part 1 1-Sample t Exercise

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

300

Hypothesis Testing Normal Data Part 1 1-Sample t Exercise: Solution Since we do not know the population Standard Deviation, we will use the 1 sample t-test to determine if we are at target.

Select the “RM Suppliers” Worksheet.

Depending on the test you are running you may need to change Ha (Not Equal To, Less Than, or Greater Than). Also ensure your desired Confidence Level is set.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

301

Hypothesis Testing Normal Data Part 1 1-Sample t Exercise: Solution (cont.) Because the null hypothesis value is within the confidence level, we “fail to reject” the null hypothesis and accept the equipment is running at the target of 32.0. Also, as you can see, the Pvalue is 0.201. Because it is above 0.05, we “fail to reject” the null hypothesis so we accept the equipment is giving product at a target of 32.0 ppm VOC.

Reject or Accept?

30.832 32.0

LSS Black Belt Manual XL v11

37.251

© 2013 e-Careers Limited

302

Hypothesis Testing Normal Data Part 1 Hypothesis Testing Roadmap

2 Sample t-test Notice the difference in the hypothesis for two-tailed vs. one-tailed test. This terminology is only used to know which column to look down in the ttable.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

303

Hypothesis Testing Normal Data Part 1 Sample Size Instead of going through the dreadful hand calculations of sample size we will use SigmaXL®. Three fields must be filled in and one left blank in the sample size window. SigmaXL® will solve for the third. If you want to know the sample size, you must enter the difference, which is the shift that must be detected. It is common to state the difference in terms of “generic” Standard Deviations when you do not have an estimate for the Standard Deviation of the process. For example, if you want to detect a shift of 1.5 Standard Deviations enter that in difference and enter 1 for Standard Deviation. If you knew the Standard Deviation and it was 0.8, then enter it for Standard Deviation and 1.2 for the difference (which is a 1.5 Standard Deviation shift in terms of real values).

If you are unsure of the desired difference, or in many cases simply get stuck with a sample size that you didn’t have a lot of control over, SigmaXL® will tell you how much of a difference can be detected. You as a practitioner must be careful when drawing Practical Conclusions because it is possible to have statistical significance without practical significance. In other words - do a reality check. SigmaXL® has made it easy to see an assortment of sample sizes and differences. Try the example shown. As you can see we used the same command here just as in the 1-sample t. Do you think the results are different? Correct, the results are different.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

304

Hypothesis Testing Normal Data Part 1 2-Sample t Example Over the next several lesson pages we will explore an example for a 2-Sample t-test. Step 1. Read Practical Problem Step 2. The null hypothesis is the Mean of BTU.In for damper 1 is equal to the Mean of BTU.In for damper 2. The alternative hypothesis is the Means are not equal. Step 3. We will use the 2-Sample t-test since the population Standard Deviations are unknown.

No, not that kind of damper!!

Now in Step 4. Open the worksheet: “Furnace” How is the data coded?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

305

Hypothesis Testing Normal Data Part 1 2-Sample t Example We will unstack the data in BTU.In by Damper.

Notice the “unstacked” data for each damper. WE NOW HAVE TWO COLUMNS.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

306

Hypothesis Testing Normal Data Part 1 2-Sample t Example Now let us perform a 2 Sample t Example. In SigmaXL® select “Statistical Tools>Power & Sample Size Calculators> 2 Sample t-Test Calculator”. For the field “Sample Sizes:” enter ‘40’. You may then use SigmaXL®’s Recall Last Dialog function to repeat the last calculation. Now enter a Sample Size of 50, because our data set has unequal sample sizes which is not uncommon. The smallest difference that can be detected is based on the smallest sample size, so in this case it is: 0.734.

Example: Follow the Roadmap…

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

307

Hypothesis Testing Normal Data Part 1 Normality Test – Is the Data Normal?

Is that normal?!

The data is considered Normal since the P-value is greater than 0.05.

Or that?!

This is the Normality Plot for damper 2. Is the data Normal? It is Normal, continuing down the roadmap…

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

308

Hypothesis Testing Normal Data Part 1 Test of Equal Variance (Bartlett’s Test) In SigmaXL® select “Statistical Tools>2 Sample Comparison Tests”.

The F-test P-value of 0.5578 indicates that there is no statistically significant difference in variance. For this example we will only focus on the Test for Equal Variances portion of the 2 Sample Comparison Test Results. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

309

Hypothesis Testing Normal Data Part 1 2 Sample t-test Equal Variance Let’s first view this data graphically with a Box Plot.

Box Plot

The Box Plots do not show much of a difference between the dampers.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

310

Hypothesis Testing Normal Data Part 1 3 Sample t-Test Let’s continue along the roadmap… Perform the 2Sample t-test; be sure to check the box “Assume equal variances”.

SigmaXL® Results Take a moment and review the SigmaXL® results.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

311

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution

To unstack the data follow the steps here. This will generate two new columns of data shown on the next page…

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

312

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution By unstacking the data we how have the Clor.Lev data separated by the distributor it came from. Now let’s move on to trying to determine correct sample size.

Select “SigmaXL>Statistical Tools>Power & Sample Size Calculators>2 Sample t-Test Calculator” .

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

313

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution We want to determine what is the smallest difference that can be detected based on our data. Fill in the Power (1-Beta) and Sample Size (N) select Difference (Mean1Mean2) to be solved for. SigmaXL® will tell us the differences we need.

The smallest difference that can be calculated is based on the smallest sample size. In this case: .7339 rounded to.734

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

314

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution Check Normality for Clor.Lev_Post_1 The results shows us a P-value of 0.304 so our data is also Normal.

Check Normality for Clor.Lev_Post_2 The results shows us a P-value of 0.941 so our data is also Normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

315

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution Test for Equal Variances Before calculating a 2 sample t-Test we must test for Equal Variances. SigmaXL® Path: “Statistical Tools > 2 Sample Comparison Tests”

For the “Numeric Data Variable (Y)” we select our stacked column ‘Clor.Lev_Post’ For our “Group Category (X)” we select our stacked column ‘Distributor’

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

316

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution Look at the P-value of 0.113. This tells us that there is no statistically significant difference in the variance in these two data sets. What does this mean….We can finally run a 2 sample t–test with Equal Variances?

Follow the command prompt shown here and enter the data as shown. Remember you must click on graphs and check the Box Plot data option. This way SigmaXL® will create a Box Plot. Equal variances can be assumed based on the test for equal variances on the previous page.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

317

Hypothesis Testing Normal Data Part 1 2 Sample t-Test: Solution Look at the Box Plot and Session Window. There is NO significant difference between the Distributors. Look at the Box Plot and 2 Sample t-Test Results. There is NO significant difference between the distributors.

Hmm, we re a lot alike!! The Box Plots show VERY little difference between the Distributors, also not the P-value in the Session Window– there is no difference between the two Distributors. Hypothesis Testing Roadmap

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

318

Hypothesis Testing Normal Data Part 1 Unequal Variance Example Open the worksheet named “2 SAMPLE UNEQUAL VARIANCE DATA”.

Don’t just sit there…. open it!!

Normality Test

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

319

Hypothesis Testing Normal Data Part 1 Test for Equal Variance

This is the output from a SigmaXL® Multi-Vari Chart. This can be created through “SigmaXL > Graphical Tools > Multi-Vari Chart”. The F-Test Statistics were obtained using SigmaXL®'s 2 Sample Comparison Test. This can be selected through “SigmaXL>Statistical Tools> 2 Sample Comparison Tests” 2-Sample t-Test Unequal Variance

The Box Plot shows no difference between the Means. The overall box is smaller for sample on the left, which is an indication for the difference in variance. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

320

Hypothesis Testing Normal Data Part 1 2-Sample t-Test Unequal Variance

By looking at the histogram of Sample 3, you can notice a big spread or variance of the data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

321

Hypothesis Testing Normal Data Part 1 2-Sample t-test Unequal Variance What does the Pvalue of 0.996 mean? After conducting a 2sample t-test there is no significant difference between the Means.

Hypothesis Testing Roadmap

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

322

Hypothesis Testing Normal Data Part 1 Paired t-test

Example

1.  Practical Problem: •  We are interested in changing the sole material for a popular brand of shoes for children. •  In order to account for variation in activity of children wearing the shoes, each child will wear one shoe of each type of sole material. The sole material will be randomly assigned to either the left or right shoe. 2. Statistical Problem: H o: µ δ = 0 H a: µ δ ≠ 0 3. Paired t-test (comparing data that must remain paired). α = 0.05 β = 0.10

Just checking your souls, er…soles!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

323

Hypothesis Testing Normal Data Part 1 Example (cont.) Now let’s open EXH_STAT Delta worksheet for analysis. Use columns labeled Mat-A and Mat-B.

Paired t-test Example In SigmaXL® open “Statistical Tools>Power & Sample Size Calculators> 1 Sample t-Test Calculator””. Enter in the appropriate Sample Size, Power Value and Standard Deviation.

Now that’s a tee test!!

Given the sample size of 10 we will be able to detect a difference of 1.15. If this was your process you would need to decide if this was good enough. In this case, is a difference of 1.15 enough to practically want to change the material used for the soles of the children’s shoes. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

324

Hypothesis Testing Normal Data Part 1 Paired t-test Example For the next test we must first calculate the difference between the two columns. We will use Excel’s native functions to perform this calculation. Select Cell E2, enter: “=C2-B2”. We can now copy this formula for the remaining cells to show the difference between Mat-A and Mat-B. We placed Mat-B first in the equation shown because it was generally higher than the values for Mat-A.

We are going to use the difference column in a One Sample t-Test however, SigmaXL® also has a Paired t-Test where the difference column is created automatically. Paired t-test Example

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

325

Hypothesis Testing Normal Data Part 1 1-Sample t

Box Plot

From the results we see that the Null Hypothesis falls outside the confidence interval, so we reject the Null Hypothesis. The P-value is also less than 0.05. Given this we are 95% confident that there is a difference in the wear between the two materials used for the soles of children’s shoes. The marker for our Hypothesized Mean has been added to illustrate our point. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

326

Hypothesis Testing Normal Data Part 1 Paired T-Test

Distinguishing between Two Samples

As you will see the conclusions are the same, but just presented differently.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

327

Hypothesis Testing Normal Data Part 1 Paired T-Test If you analyze this as a 2-sample t–test it simply compares the means of Material A to Material B. The power of the paired test is that it increases the sensitivity of the test without having to look at a series of other factors.

Paired T-Test Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

328

Hypothesis Testing Normal Data Part 1 Paired t-test Exercise: Solution Because the two labs ensured to exactly report measurement results for the same parts and the results were put in the correct corresponding row, we are able to do a paired t-test. The first thing we must do is create a new column with the difference between the two test results.

We must confirm the differences (now in a new calculated column) are from a Normal Distribution. This was confirmed with the Anderson-Darling Normality Test by doing a graphical summary under Basic Statistics.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

329

Hypothesis Testing Normal Data Part 1 Paired t-test Exercise: Solution

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

330

Hypothesis Testing Normal Data Part 1 Continuous Data Roadmap

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

331

Hypothesis Testing Normal Data Part 1 At this point, you should be able to: §  Determine appropriate sample sizes for testing Means §  Conduct various Hypothesis Tests for Means §  Properly Analyze Results

You have now completed Analyze Phase – Hypothesis Testing Normal Data Part 1.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

332

Lean Six Sigma Black Belt Training

Analyze Phase Hypothesis Testing Normal Data Part 2

Now we will continue in the Analyze Phase with “Hypothesis Testing Normal Data Part 2”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

333

Hypothesis Testing Normal Data Part 2 Overview We are now moving into Hypothesis Testing Normal Data Part 2 where we will address Calculating Sample Size, Variance Testing and Analyzing Results. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infe fere renntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    HH yy ppooth theessis is    Te Tesstin tingg HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP11 HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP22 HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP11

CCaa lcu lcula la te   te  SSaa m mpple   le  SSiz izee VVaa ria ria nnce   ce  Tes Testin tingg AAnnaa ly ly zze   e  RRes esuults lts

HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP22 W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Tests of Variance

Normal Data –  1 Sample to a target –  2 Samples – F-Test –  3 or More Samples Bartlett s Test Non-Normal Data –  2 or more samples Levene s Test The null hypothesis states there is no difference between the Standard Deviations or variances. –  Ho: σ1 = σ2 = σ3 … –  Ha = at least on is different

Now that s non-normal!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

334

Hypothesis Testing Normal Data Part 2 1-Sample Variance

A   1 -­‐s a m p le   v a r ia n ce   te s t   is   u s e d   to   co m p a r e   a n   e x p e cte d   p o p u la tio n   v a r ia n ce   to   a   ta r g e t. Stat > Basic Statistics > Graphical Summary

If   th e   ta r g e t   v a r ia n ce   lie s   in s id e   th e   co n fid e n ce   in te r v a l,   fa il to   r e je ct   th e   n u ll   h y p o th e s is . – H o :   σ2 S a m p le =   σ2 Ta rg e t – H a :   σ2 S a m p le ≠ σ2 Ta rg e t U s e   th e   s a m p le   s iz e   ca lcu la tio n s   fo r   a   1   s a m p le   t-­‐te s t   s in ce   th e y   a r e   r a r e ly   p e r fo rm e d   w ith o u t   p e rfo rm in g   a   1   s a m p le   t-­‐ te s t   a s   w e ll.

1 Sample t-test Sample Size

1 . P r a ctica l   P ro b le m : • W e   a re   co n s id e rin g   ch a n g in g   s u p p lie s   fo r   a   p a rt   th a t   w e   cu rre n tly   p u rch a s e   fro m   a   s u p p lie r   th a t   ch a rg e s   a   p re m iu m   fo r   th e   h a rd e n in g   p ro ce s s   a n d   h a s   a   la rg e   v a ria n ce   in   th e ir   p ro ce s s . • Th e   p ro p o s e d   n e w   s u p p lie r   h a s   p ro v id e d   u s   w ith   a   s a m p le   o f   th e ir   p ro d u ct.   Th e y   h a v e   s ta te d   th e y   ca n   m a in ta in   a   v a ria n ce   o f   0 .1 0 . 2 . S ta tis tica l   P r o b le m : H o :   σ2 =   0 .1 0 o r H a :   σ2 ≠ 0 .1 0

H o :   σ =   0 .3 1 H a :   σ ≠ 0 .3 1

3 . 1 -­‐s a m p le   v a r ia n ce : α =   0 .0 5         β =   0 .1 0 The Statistical Problem can be stated two ways: The null hypothesis: The variance is equal to 0.10 and the alternative hypothesis: The variance is not equal to 0.10 OR The null hypothesis: The Standard Deviation is equal to 0.31 and the alternative hypothesis: The Standard Deviation is not equal to 0.31 LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

335

Hypothesis Testing Normal Data Part 2 1-Sample Variance

Take time to notice the Standard Deviation of 0.31 falls within 95% confidence interval. Based off this data the Statistical Solution is “fail to reject the null”. What does this mean from a practical stand point? They can maintain a variance of 0.10 that is valid. Typically, shifting a Mean is easier to accomplish in a process than reducing variance. The new supplier would be worth continuing the relationship to see if they can increase the Mean slightly while maintaining the reduced variance.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

336

Hypothesis Testing Normal Data Part 2 Test of Variance Example

1 . P r a ctica l   P r o b le m : W e  want  to  determine  the  effect  of  two  different  storag e  methods on   the  rotting  of  potatoes.  Y ou  study  conditions  conducive  to  potato  rot   by  injecting  potatoes  with  bacteria  that  cause  rotting  and  subjecting   them  to  different  temperature  and  oxyg en  reg imes.  W e  can  test  the   data  to  determine  if  there  is  a  difference  in  the  Standard  Devia tion  of   the  rot  time  between  the  two  different  methods. 2 .   S ta tis tica l   P r o b le m : H o:  σ1   =  σ2 H a :  σ1   ≠ σ2 3 .   Eq u a l   v a r ia n ce   te s t (F-­‐test  since  there  are  only  2  factors.)

The Statistical problem is: The null hypothesis: The Standard Deviation of the first method is equal to the Standard Deviation of the second method. The alternative hypothesis: The Standard Deviation of the first method is not equal to the Standard Deviation of the second method. These hypotheses can also be stated in terms of variance.

Now open the worksheet “EXH_AOV”. Follow along in SigmaXL®. Note: The sample size is for each level.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

337

Hypothesis Testing Normal Data Part 2 Normality Test – Follow the Roadmap Check for Normality.

According to the graph we have Normal data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

338

Hypothesis Testing Normal Data Part 2 Test of Equal Variance

Now conduct the test for Equal Variance using the 2 Sample Comparison Test.

What is the Statistical Solution? Fail to reject.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

339

Hypothesis Testing Normal Data Part 2 Normality Test

Test for Equal Variance (Normal Data)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

340

Hypothesis Testing Normal Data Part 2 Test of Equal Variance You can see there is no statistical difference for variance in Rot based on temperature as a factor. Since the data is Normally Distributed and we have 2 samples, use F-Test statistic. Note: The Box Plot was not generated using the 2 Sample Comparison Test. It has been added as a graphical illustration. Continuous Data - Normal An alternative to using the 2 Sample Comparison Test is the 2 Sample F-Test Calculator which requires manual entry of summary statistics as shown. This calculator can be found under Statistical Tools>Basic Statistical Templates>2 Sample FTest(Compare 2 StDevs) This calculation confirms the P-value previously calculated.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

341

Hypothesis Testing Normal Data Part 2 Continuous Data - Normal This time we have Rot as the response and Temp/Oxygen as the factor.

SigmaXL®’s tests for equal variances only allow one factor, so the Temp and Oxygen are combined using Excel’s Concatenate Function to create a single factor Temp/Oxygen column. Test For Equal Variances

From the Hypothesis Testing Roadmap, we will now use Bartlett’s Test for unequal variances since there are more than 2 levels (groups) in the temp/oxygen factor.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

342

Hypothesis Testing Normal Data Part 2 Test For Equal Variances Statistical Analysis

Note that Bartlett’s Test for Equal Variance should only be used if the data is normal in each group. Since the P-Values for all Anderson Darling Tests are >0.05, we will assume Normality for each group. If we had Non-normal data, then Levene’s Test for Equal Variance would be used.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

343

Hypothesis Testing Normal Data Part 2 Tests for Variance Exercise

Tests for Variance Exercise: Solution First we want to do a graphical summary of the two samples from the two suppliers.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

344

Hypothesis Testing Normal Data Part 2 Tests for Variance Exercise: Solution In “Numeric Data Variables (Y)” enter ‘ppm VOC’ In “Group Category (X1)” enter ‘RM Supplier’ We want to see if the two samples are from Normal populations.

The P-value is greater than 0.05 for both Anderson-Darling Normality Tests so we conclude the samples are from Normally Distributed populations because we “failed to reject” the null hypothesis that the data sets are from Normal Distributions.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

345

Hypothesis Testing Normal Data Part 2 Tests for Variance Exercise: Solution (cont.) Continue to determine if they are of Equal Variance.

Because the 2 populations were considered to be Normally Distributed, the F-test is used to evaluate whether the variances (Standard Deviation squared) are equal. The P-value of the Ftest was greater than 0.05 so we “fail to reject” the null hypothesis. So once again in English: The variances are equal between the results from the two suppliers on our product’s ppm VOC level.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

346

Hypothesis Testing Normal Data Part 2 Hypothesis Testing Roadmap

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

347

Hypothesis Testing Normal Data Part 2 Purpose of ANOVA

Analysis of Variance extends the two sample t-test for testing the equality of two population Means to a more general null hypothesis of comparing the equality of more than two Means, versus them not all being equal. –  The classification variable, or factor, usually has three or more levels (If there are only two levels, a t-test can be used). –  Allows you to examine differences among means using multiple comparisons. –  The ANOVA test statistic is:

Avg SS between S2 between = 2 Avg SS within S within There s a Nova again!!

What do we want to know? Is the between group variation large enough to be distinguished from the within group variation?

X

delta (δ)

(B e tw e e n   G ro u p   V a ria tio n )

To ta l   (O v e ra ll)   V a ria tio n W ith in   G ro u p   V a ria tio n (le v e l   o f   s u p p lie r   1 )

X X X X X X X X

µ1

LSS Black Belt Manual XL v11

µ2

© 2013 e-Careers Limited

348

Hypothesis Testing Normal Data Part 2 Calculating ANOVA Take a moment to review the formulas for an ANOVA. W h e re : G   -­‐ th e   n u m b e r   o f   g ro u p s   (le v e ls   in   th e   s tu d y ) x ij =   th e   in d iv id u a l   in   th e   j th g ro u p n j =   th e   n u m b e r   o f   in d iv id u a ls   in   th e   j th g ro u p   o r   le v e l X =   th e   g ra n d   M e a n X j =   th e   M ea n   o f   th e   j th g ro u p   o r   le v e l To ta l   (O v e r a ll)   V a r ia tio n

delta (δ)  

W ith in   G r o u p   V a r ia tio n

(B e tw e e n   G r o u p   V a r ia tio n )

Within Group Variation

Between Group Variation g

∑

nj

g

(Xj − X) 2

nj

∑∑ (X

j=1

ij

− X) 2

j=1 i =1

Total Variation g

nj

∑ ∑ (X

ij

− X) 2

j=1 i =1

Calculating ANOVA

Th e   a lp h a   ris k   in cre a s e s   a s   th e   n u m b e r   o f   M e a n s   in cre a s e s   w ith   a   p a ir -­‐w is e   t-­‐te s t   s ch e m e .   Th e   fo rm u la   fo r   te s tin g   m o re   th a n   o n e   p a ir   o f   M e a n s   u s in g   a   t-­‐te s t   is : k

1 − (1 − α ) where k = number of pairs of means so, for 7 pairs of means and an α = 0.05 : 7

1 - (1 - 0.05) = 0.30 or 30% alpha risk The reason we don’t use a t-test to evaluate series of Means is because the alpha risk increases as the number of Means increases. If we had 7 pairs of Means and an alpha of 0.05 our actual alpha risk could be as high as 30%. Notice we did not say it was 30%, only that it could be as high as 30% which is quite unacceptable. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

349

Hypothesis Testing Normal Data Part 2 Three Samples We have three potential suppliers that claim to have equal levels of quality. Supplier B provides a considerably lower purchase price than either of the other two vendors. We would like to choose the lowest cost supplier but we must ensure that we do not effect the quality of our raw material.

Follow the Roadmap…Test for Normality Compare P-values.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

350

Hypothesis Testing Normal Data Part 2 Test for Equal Variance… According to Bartlett’s Test there is no significant difference in the variance of the 3 suppliers.

ANOVA There doesn’t seem to be a huge difference here. This Box Plot was not generated using Bartlett’s Test, we are using it to graphically display the data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

351

Hypothesis Testing Normal Data Part 2 ANOVA

Follow along in SigmaXL®. Note that SigmaXL®’s OneWay ANOVA uses a confidence level of 95.0%.

Looking at the P-value the conclusion is we fail to reject the null hypothesis. According to the data there is no significant difference between the Means of the 3 suppliers. Note that the Mean/CI graph shows the 95% confidence intervals on the mean for each supplier using a pooled standard deviation. The fact that the confidence intervals overlap indicates that there is no statistical evidence of a difference in Supplier Means.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

352

Hypothesis Testing Normal Data Part 2 ANOVA Before looking up the F-Critical value you must first know what the degrees of freedom is. The purpose of the ANOVA’s test statistic uses variance between the Means divided by variance within the groups. Therefore, the degrees of freedom would be three suppliers minus 1 for 2 degrees of freedom. The denominator would be 5 samples minus 1 (for each supplier) multiplied by 3 suppliers, or 12 degrees of freedom. As you can see the F-Critical value is 3.89 and since the F-Calc is 1.40 and not close to the critical value, we fail to reject the Null Hypothesis.

Sample Size Let’s check on how much difference we can see with a sample of 5. Will having a sample of 5 show a difference? After crunching the numbers, a sample of 5 can only detect a difference of 2.56 Standard Deviations. Which means that the Mean would have to be at least 2.56 Standard Deviations until we could see a difference. To help elevate this problem a larger sample should be used. If there is a larger sample you would be able to have a more sensitive reading for the Means and the variance. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

353

Hypothesis Testing Normal Data Part 2 ANOVA Assumptions

1 . O b s e rv a tio n s   a re   a d e q u a te ly   d e s crib e d   b y   th e   m o d e l. 2 . Erro rs   a re   n o rm a lly   a n d   in d e p e n d e n tly   d is trib u te d . 3 . H o m o g e n e ity   o f   v a ria n ce   a m o n g   fa cto r   le v e ls . In   o n e -­‐w a y   A N O V A ,   m o d e l   a d e q u a cy   ca n   b e   ch e ck e d   b y   e ith e r   o f   th e   fo llo w in g : 1 . C h e ck   th e   d a ta   fo r   N o rm a lity   a t   e a ch   le v e l   a n d   fo r   h o m o g e n e ity   o f   v a ria n ce   a cro s s   a ll   le v e ls . 2 . Ex a m in e   th e   re s id u a ls     (a   re s id u a l   is   th e   d iffe re n ce   in   w h a t   th e   m o d e l   p re d icts   a n d   th e   tru e   o b s e rv a tio n ). 1 . N o rm a l   p lo t   o f   th e   r e s id u a ls 2 . R e s id u a ls   v e rs u s   fits 3 . R e s id u a ls   v e rs u s   o rd e r

If   th e   m o d e l   is   a d e q u a te ,   th e   re s id u a l   p lo ts   w ill   b e   s tru ctu re le s s . Residual Plots SigmaXL® V6 does not include Residuals in One-Way ANOVA, so we will now manually calculate the Residuals. The Residuals are the individual data points subtracted by the Mean of the group. This slide uses Descriptive Statistics to calculate the Mean. This may also be done using Excel’s AVERAGE function. These group Residuals are then stacked in the column “Stacked Residuals”. Note that Residuals are available in Two-Way ANOVA and Regression Analysis which will be covered at a later point.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

354

Hypothesis Testing Normal Data Part 2 Histogram of Residuals The Histogram of Residuals should show a bell shaped curve.

Normal Probability Plot of Residuals The Normality plot of the Residuals should follow a straight line on the probability plot. (Does a pencil cover all the dots?)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

355

Hypothesis Testing Normal Data Part 2 Residuals versus Fitted Values This chart was created using a Scatter Plot of “Stacked Residuals” Vs “Supplier Mean”.

ANOVA Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

356

Hypothesis Testing Normal Data Part 2 ANOVA Exercise: Solution First let’s look at the Histogram and Descriptive Statistics for the 3 shifts. Worksheet: RM Suppliers

We want to see if the 3 samples are from Normal populations. In “Numeric Data Variables (Y)” enter ‘ppm VOC’ In “Group Category (X1)” enter ‘Shift’

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

357

Hypothesis Testing Normal Data Part 2 ANOVA Exercise: Solution

Following the Hypothesis Testing Roadmap, we will use Bartlett’s Test for Equal Variance, since there are 3 groups and each group is assumed to have Normal data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

358

Hypothesis Testing Normal Data Part 2 ANOVA Exercise: Solution If the variances are unequal then use Welch’s ANOVA instead of One-Way ANOVA.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

359

Hypothesis Testing Normal Data Part 2 ANOVA Exercise: Solution A visual display of our Residuals indicates that the data is Normal. Since our Residuals look Normally Distributed and randomly patterned, we will assume our analysis is correct. This graphical display was generated using Multiple Regression which we will cover in detail later.

The steps to create these Residual plots are as follows: 1. Select SigmaXL>Statistical Tools>Regression>Multiple Regression. 2. Select “ppm VOC” for Numeric Response (Y). 3. Select “Shift” for Categorical Predictors (X). 4. Ensure “Display Residual Plots” is checked. 5. Click OK, the residuals can be found in the Mult Reg Residuals worksheet.

We accept the alternate hypothesis that the Mean product quality is different from at least one shift.

Don t miss that shift!!

Since the confidence intervals of the Means do not overlap between Shift 1 and Shift 3, we see one of the shifts is delivering a product quality with a higher level of ppm VOC.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

360

Hypothesis Testing Normal Data Part 2 At this point, you should be able to: §  Be able to conduct Hypothesis Testing of Variances §  Understand how to Analyze Hypothesis Testing Results

You have now completed Analyze Phase – Hypothesis Testing Normal Data Part 2.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

361

Lean Six Sigma Black Belt Training

Analyze Phase Hypothesis Testing Non-Normal Data Part 1

Now we will continue in the Analyze Phase with “Hypothesis Testing Non-Normal Data Part 1”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

362

Hypothesis Testing Non-Normal Data Part 1 Overview The core fundamentals of this phase are Equal Variance Tests and Tests for Medians.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infe fere renntia tia l  l  SSta ta tis tistics tics

We will examine the meaning of each of these and show you how to apply them.

In Intro tro    to to    HH yy ppooth theessis is    Te Tesstin tingg HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP11 HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP22 Equal  Variance  Tests Equal  Variance  Tests

HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP11

Tests  for  Medians Tests  for  Medians

HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP22 W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Non-Normal Hypothesis Tests At this point we have covered the tests for determining significance for Normal Data. We will continue to follow the roadmap to complete the test for Non-Normal Data with Continuous Data. Later in the module we will use another roadmap that was designed for Discrete data. Recall that Discrete data does not follow a Normal Distribution, but because it is not Continuous Data, there are a separate set of tests to properly analyze the data.

Normal

Continuous

Non-Normal

Discrete

We can test for anything!!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

363

Hypothesis Testing Non-Normal Data Part 1 1 Sample t Why do we care if a data set is Normally Distributed? §  When it is necessary to make inferences about the true nature of the population based on random samples drawn from the population. §  When the two indices of interest (X-Bar and s) depend on the data being Normally Distributed. §  For problem solving purposes, because we don’t want to make a bad decision – having Normal Data is so critical that with EVERY statistical test, the first thing we do is check for Normality of the data. Recall the four primary causes for Non-normal data: §  Skewness – Natural and Artificial Limits §  Mixed Distributions - Multiple Modes §  Kurtosis §  Granularity

We will focus on skewness for the remaining tests for Continuous Data. Skewness is a natural state for much data. Any data that has natural or artificial limits typically exhibits a Skewed Distribution when it is operating near the limit. The other 3 causes for Nonnormality are usually a symptom of a problem and should be identified, separated and corrected. We will focus on Skewness for the remaining tests for Continuous Data. A common reaction to Nonnormal Data is to simply transform it. Please see your Master Black Belt to determine if a transform is appropriate. Often data is beaten into submission only to find out that there was an underlying cause for Non-normality that was ignored. Remember, we want you to predict whether the data should be Normal or not. If you believe your data should be Normal but it is not, there is most likely an underlying cause that can be removed which will then allow the data to show it’s true nature and be Normal. Hypothesis Testing Roadmap Now we will continue down the NonNormal side of the roadmap. Notice this slide is primarily for tests of Medians.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

364

Hypothesis Testing Non-Normal Data Part 1 Sample Size

Levene’s  test  of  equal  variance,  used  to  compa re  the  estimated   population  Standard  Deviations  from  two  or  more  samples   with  N on-­‐N ormal  distributions.

– H o:  σ1 =  σ2 =  σ3 … – H a :  A t  least  one  is  different. You have already seen this command in the last module, this is simply the application for Nonnormal Data. The question is: Are any of the Standard Deviations or variances statistically different? Follow the Roadmap… Open the worksheet “EXH_AOV”. Select “SigmaXL>Graphic al Tools > Normal Probability Plots”. As you can clearly see from the chart, this is not a normal process. Next we will see that the Anderson Darling P-values are much less than 0.05.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

365

Hypothesis Testing Non-Normal Data Part 1 Test of Equal Variance Non-Normal Distribution

Next we test for Equal Variance. From the Hypothesis Testing Roadmap, we see that since “Factors2” has 2 levels we will use the Levene’s Test in the 2 Sample Comparison Tests. If we had more than two levels we would use “SigmaXL>Statistical Tools>Equal Variance Tests>Levene” Select: “SigmaXL>Statistical Tools > 2 Sample Comparison Tests”. Since the data is Non-normal, the test highlighted by SigmaXL® is the Levene’s test and not the F-test. Test of Equal Variance Non-Normal Distribution

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

366

Hypothesis Testing Non-Normal Data Part 1 Hypothesis Test Exercise

Test for Equal Variance Example: Solution First test to see if the data is Normal or Non-Normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

367

Hypothesis Testing Non-Normal Data Part 1 Test for Equal Variance Example: Solution Since there are two variables we need to perform a Normality Test on CallsperWk1 and CallsperWk2. First select the variable ‘CallsperWk1’ and Press “OK”. Follow the same steps for ‘CallsperWk2’.

From the Descriptive Statistics and the Normal Probability Plots we can see that the data for both groups is Non-normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

368

Hypothesis Testing Non-Normal Data Part 1 Test for Equal Variance Example: Solution As you can see the data illustrates a P-value of 0.247 which is more than 0.05. As a result, there is no variance between CallperWk1 and CallperWk2. Therefore with a 95% confidence level we reject the null hypothesis.

And here s our answer……

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

369

Hypothesis Testing Non-Normal Data Part 1 Nonparametric Tests A non-parametric test makes no assumptions about Normality. For a Skewed Distribution: - The appropriate statistic to describe the central tendency is the Median, rather than the Mean. - If just one distribution is not Normal, a non-parametric should be used. Non-parametric Hypothesis Testing works the same way as parametric testing. Evaluate the Pvalue in the same manner. δ

Target

~ X

~ X1

~ X2

Mean and Median In general, nonparametric tests do the following: rank order the data, sum the data by ranks, sign the data above or below the target, and calculate, compare and test the Median. Comparisons and tests about the Median make nonparametric tests useful with very Non-normal Data. Note: SigmaXL® V6 does not report confidence intervals on the Median in Descriptive Statistics. However, Confidence Intervals on the Median are available in the Kruskal-Wallis and Mood’s Median Tests to be covered later.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

370

Hypothesis Testing Non-Normal Data Part 1 SigmaXL®’s Nonparametrics 1-Sample Sign: performs a one-sample sign test of the Median and calculates the corresponding point estimate and confidence interval. Use this test as an alternative to one-sample Z and onesample t-tests. 1-Sample Wilcoxon: performs a one-sample Wilcoxon signed rank test of the Median and calculates the corresponding point estimate and confidence interval (more discriminating or efficient than the sign test). Use this test as a nonparametric alternative to one-sample Z and one-sample ttests. Mann-Whitney: performs a Hypothesis Test of the equality of two population Medians and calculates the corresponding point estimate and confidence interval. Use this test as a nonparametric alternative to the two-sample t-test. Kruskal-Wallis: performs a Hypothesis Test of the equality of population Medians for a one-way design. This test is more powerful than Mood’s Median (the confidence interval is narrower, on average) for analyzing data from many populations, but is less robust to outliers. Use this test as an alternative to the one-way ANOVA. Mood’s Median Test: performs a Hypothesis Test of the equality of population Medians in a oneway design. Test is similar to the Kruskal-Wallis Test. Also referred to as the Median test or sign scores test. Use as an alternative to the one-way ANOVA. There are 5 basic nonparametric tests that SigmaXL® calculates. Each one has a counterpart in normal Hypothesis Testing.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

371

Hypothesis Testing Non-Normal Data Part 1 1-Sample Sign Test Here is a little trick! Dividing the sample size from a t-test estimate by 0.864 should give you a large enough sample regardless of the underlying distribution…most of the time. For instance, having a sample size of 23 using the ttest method, the sample size would increase by 3. If there is a Normal Distribution (assuming) this number would increase by 1. Truthfully, it is really possible to decrease the sample size depending on the distribution selected for the alternative. 1-Sample Example

The Statistical Problem is: The Null Hypothesis is that the Median is equal to 63 and the alternative hypothesis is the Median is not equal to 63. Open the SigmaXL® Data File: “DISTRIB1.MTW”. Next you have a choice of either performing a 1Sample Sign Test or 1-Sample Wilcoxon Test because both will test the Median against a target. For this example we will perform a 1-Sample Sign Test. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

372

Hypothesis Testing Non-Normal Data Part 1 1-Sample Example

=

For a two tailed test, choose the not equal for the alternative hypothesis.

As you can see the P-value is less than 0.05, so we must reject the null hypothesis which means we have data that supports the alternative hypothesis that the Median is different than 63. The actual Median of 65.70 is shown in the Session Window. Since the Median is greater than the target value, it seems the new process is not as good as we may have hoped. Statistical Tools >Nonparametric Tests > 1 Sample Wilcoxon

Perform the same steps as the 1-Sample Sign to use the 1-sample Wilcoxon. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

373

Hypothesis Testing Non-Normal Data Part 1 Hypothesis Test Exercise

1 Sample Example: Solution According to the Hypothesis the Mine Manager feels he is achieving his target of 2.1 tons/day. H0: M = 2.1 tons/day Ha: M ≠ 2.1 tons/day Since we are using one sample, we have a choice of choosing either a 1 Sample-Sign or 1 Sample Wilcoxon. For this example we will use a 1 Sample-Sign.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

374

Hypothesis Testing Non-Normal Data Part 1 1 Sample Example: Solution

We disagree!!

Mann-Whitney Example

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

375

Hypothesis Testing Non-Normal Data Part 1 Mann-Whitney Example When looking at the Probability Plot, Match A yields a less than .05 P-value. Now look at Graph B? Ok now you have one graph that is Non-normal Data and the other that is Normal. The good news is when performing a Nonparametric Test of 2 Samples, only one has to be Normal. With that said, now let’s perform a MannWhitney.

Perform the Mann-Whitney test. The Practical Conclusion is that there is a difference between the Medians of the two machines.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

376

Hypothesis Testing Non-Normal Data Part 1 Exercise

Exercise objective: To practice solving problem presented using the appropriate Hypothesis Test. A credit card company now understands there is no variability difference in customer calls/week for the two different credit card types. This means no difference in strategy of deploying the workforces. However, the credit card company wants to see if there is a difference in call volume between the two different card types. The company expects no difference since the total sales among the two credit card types are similar. The Black Belt was selected and told to evaluate with 95% confidence if the averages were the same. The Black Belt reminded the credit card company the calls/day were not Normal distributions so he would have to compare using Medians since Medians are used to describe the central tendency of Non-normal Populations. 1.  Analyze the problem using the Hypothesis Testing roadmap. 2.  Use the columns named CallsperWk1 and CallsperWk2. 3.  Is there a difference in call volume between the 2 different card types? Worksheet: Hypothesis Test Study

Mann-Whitney Example: Solution

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

377

Hypothesis Testing Non-Normal Data Part 1 Mann-Whitney Example: Solution

Mood’s Median Test The final 2 tests are the Mood’s Median and the Kruskal Wallis.

1 . A n  aluminum  company  wanted  to  compare  the  operation  of  its   three  facilities  worldwide.    They  want  to  see  if  there  is  a  difference   in  the  recoveries  among  the  three  locations.    A  Black  Belt  was   asked  to  help  manag ement  evaluate  the  recoveries  at  the  locations   with  9 5 %  confidence. 2 . H o:  M 1 =  M 2 =  M 3 H a :  at  least  one  is  different 3 . Use  the  Mood’s  median  test. 4 . Based  on  the  smallest  sample  of  1 3 ,  the  test  will  be  able  to  detect   a  difference  close  to  1 .5 . 5 . Statistical  C onclusions:    Use  columns  named  Recovery  and   Location  for  analysis.

= LSS Black Belt Manual XL v11

=

? © 2013 e-Careers Limited

378

Hypothesis Testing Non-Normal Data Part 1 Follow the Roadmap…Normality Instead of using the Anderson-Darling test for Normality, this time we used the graphical summary method. It gives a P-value for Normality and allows a view of the data that the Normality test does not.

Notice evidence of Outliers in at least 2 of the 3 populations. You could do a Box Plot to get a clearer idea about Outliers.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

379

Hypothesis Testing Non-Normal Data Part 1 Follow the Roadmap…Equal Variance

Check for Equal Variance using Levene’s Test. We conclude that the Variances are equal.

Mood’s Median Test

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

380

Hypothesis Testing Non-Normal Data Part 1 Kruskal-Wallis Test Using the same data set, analyze using the Kruskal-Wallis test.

The Kruskal-Wallis Test is more powerful than the Mood’s Median Test, but the Mood’s Median Test is more robust to Outliers.

Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

381

Hypothesis Testing Non-Normal Data Part 1 Pagers Defect Rate Example: Solution Let’s follow the Roadmap and check to see if the data is Normal. Take a moment to compare the 3 variables. Since our 3 variables are less than 0.05 the data is Nonnormal.

SigmaXL>Graphical Tools>Histograms and Descriptive Statistics…

The P-value is over 0.05…therefore, we fail to reject the Null Hypothesis. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

382

Hypothesis Testing Non-Normal Data Part 1 Unequal Variance

W here  do  you  g o  in  the  roadmap  if  the  variance  is  not  equal? – Unequal  variances  are  usually  the  result  of  differences  in   the  shape  of  the  distribution. • Extreme  tails • O utliers • Multiple  modes These  conditions  should  be  explored  throug h  data   demog raphics. For  S kewed  Distributions  with  compa rable  Medians  it  is   unusual  for  the  variances  to  be  different  without  some   assig nable  cause  impacting  the  process. Example This is an example of comparable products. To view these graphs open the worksheet “Var_Comp”. As you can see, Model A is Normal but Model B is Non-normal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

383

Hypothesis Testing Non-Normal Data Part 1 Example (cont.) Now let’s check the variance. Does Model B have a larger variance than Model A? The Median for Model B is much lower. How can we capitalize on our knowledge of the process? Let’s look at data demographic to help us explain the differences between the two processes.

Data Demographics What clues can explain the difference in variances? This example illustrates how Non-normal Data can have significant informational content as revealed through data demographics. Sometimes this is all that is needed to draw conclusions.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

384

Hypothesis Testing Non-Normal Data Part 1 Black Belt Aptitude Exercise

Black Belt Aptitude Exercise: Solution

Which of these graphs has Normal Data and which one doesn’t? As you can see data for Engineering, Liberal Arts and Business is Normal Data. However, the data for Science is Nonnormal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

385

Hypothesis Testing Non-Normal Data Part 1 Black Belt Aptitude Exercise: Solution (cont.)

Now let’s look at information given by SigmaXL®. As you can see the P-value is greater than 0.05. The data illustrates that there is not a difference in Variance.

Since the P-value is > .05, we fail to reject the null hypothesis, i.e., there is no difference between a potential Black Belt’s degree and performance.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

386

Hypothesis Testing Non-Normal Data Part 1 At this point, you should be able to: §  Conduct Hypothesis Testing for Equal Variance §  Conduct Hypothesis Testing for Medians §  Analyze and interpret the results

You have now completed Analyze Phase – Hypothesis Testing Non-Normal Data Part 1.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

387

Lean Six Sigma Black Belt Training

Analyze Phase Hypothesis Testing Non-Normal Data Part 2

Now we will continue in the Analyze Phase with “Hypothesis Testing Non-Normal Data Part 2”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

388

Hypothesis Testing Non-Normal Data Part 2 Overview The core fundamentals of this phase are Tests for Proportions and Contingency Tables. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    AA nnaa ly ly zz ee ““ XX ”” SSiftin iftingg In Infe fere renntia tia l  l  SSta ta tis tistics tics In Intro tro    to to    HH yy ppooth theessis is    Te Tesstin tingg HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP11 HH yy ppooth theessis is    Te Tesstin tingg    N N DD    PP22 HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP11 Tests  for  Proportions Tests  for  Proportions

HH yy ppooth theessis is    Te Tesstin tingg    N NN N DD    PP22

CC ontingency  Tables ontingency  Tables

W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Hypothesis Testing Roadmap Attribute Data

We will now continue with the roadmap for Attribute Data. Since Attribute Data is Non-normal by definition, it belongs in this module on Non-normal Data. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

389

Hypothesis Testing Non-Normal Data Part 2 Sample Size and Types of Data Sample size is dependent on the type of data.

Proportion versus a Target This formula is an approximation for ease of manual calculation.

Th is   te s t   is   u s e d   to   d e te rm in e   if   th e   p ro ce s s   p ro p o rtio n   (p )   e q u a ls   s o m e   d e s ire d   v a lu e ,   p 0 . Th e   h y p o th e s e s : – H 0 :     p   =   p 0 – H a :     p   ¹ p 0 Th e   o b s e rv e d   te s t   s ta tis tic   is   ca lcu la te d   a s   fo llo w s : (n o rm a l   a p p ro x im a tio n )

Z

obs

=

(pˆ − p ) 0

p (1 − p 0

0

)n

Th is   is   co m p a re d   to             Z crit =   Z a / 2

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

390

Hypothesis Testing Non-Normal Data Part 2 Proportion versus a Target Now let’s try an example:

Take note of the how quickly the sample size increases as the alternative proportion goes up. It would require 1402 samples to tell a difference between 98% and 99% accuracy. Our sample of 500 will do because the alternative hypothesis is 96% according to the proportion formula.

Yes sir, they’re all good!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

391

Hypothesis Testing Non-Normal Data Part 2 Proportion versus a Target Select the Confidence Interval for One Proportion as shown above. Now for the “Number of elements:” enter how many items were shipped and for the “Size of Sample” field enter the number of accurate items shipped. SigmaXL® reports the Upper and Lower CI Limits.

After you analyze the data you will see the Statistical Conclusion is to reject the Null Hypothesis. What is the Practical Conclusion…the process is not performing to the desired accuracy of 99%. Sample Size Exercise

Ex e rcis e   o b je ctiv e : To  practice  solving  the  problem   presented  using  the  appropriate  Hypothesis  Test. Y ou  are  the  shipping  manag er  and  are  in  charg e  of   improving  shipping  accuracy.    Y our  annual  bonus   depends  on  your  ability  to  prove  that  shipping   accuracy  is  better  than  the  targ et  of  8 0 %. 1 . How  many  samples  do  you  need  to  take  if  the   anticipated  sample  proportion  is  8 2 %? 2 . O ut  of  2 0 0 0  shipments  only  1 6 8 0  were  accurate. • •

LSS Black Belt Manual XL v11

Do  you  g et  your  a nnua l  bonus? W as  the  sa mple  siz e  g ood  enoug h?

© 2013 e-Careers Limited

392

Hypothesis Testing Non-Normal Data Part 2 Proportion vs Target Example: Solution Power (1-Beta) should be .9 and the Alternative Proportion 1(P1) should be 0.82. The Hypothesized Proportion should be 0.80. Keep the default Alpha of .05. As you can see the Sample Size should be at least 4073 to prove our hypothesis.

Do you get your bonus? Yes, you get your bonus since .80 is not within the confidence interval. Because the improvement was 84%, the sample size was sufficient. Answer: Use alternative proportion of .82, hypothesized proportion of .80. n=4073. Either you’d better ship a lot of stuff or you’d better improve the process more than just 2%!

N o w   le t   u s   ca lcu la te   if   w e   re ce iv e   o u r   b o n u s … O u t   o f   th e   2 0 0 0   s h ip m e n ts ,   1 6 8 0   w e re   a ccu ra te .     W a s   th e   s a m p le   s iz e   s u fficie n t?

LSS Black Belt Manual XL v11

?

X 1680 pˆ = = = 0.84 n 2000

© 2013 e-Careers Limited

393

Hypothesis Testing Non-Normal Data Part 2 Comparing Two Proportions SigmaXL® gives you a choice of using the normal approximation or the exact method. We will use the exact method. The formula is an approximation for ease of manual calculation.

Th is   te s t   is   u s e d   to   d e te rm in e   if   th e   p ro ce s s   d e fe ct   ra te   (o r   p ro p o rtio n ,   p )   o f   o n e   s a m p le   d iffe rs   b y   a   ce rta in   a m o u n t   D   fro m   th a t   o f   a n o th e r   s a m p le   (e .g .,   b e fo re   a n d   a fte r   y o u r   im p ro v e m e n t   a ctio n s ) Th e   h y p o th e s e s : H 0 :     p 1 -­‐ p 2 =   D H a :     p 1 -­‐ p 2 ¹ D Th e   te s t   s ta tis tic   is   ca lcu la te d   a s   fo llo w s :

Zobs =

pˆ1 − pˆ 2 − D pˆ1 (1 − pˆ1 ) n1 + pˆ 2 (1 − pˆ 2 ) n 2

Th is   is   co m p a re d   to   Z critica l =   Z a / 2

Catch   s ome   Z ’s! Catch some Z’s!!

Sample Size and Two Proportions Practice

Answers: 34,247 32,986 4,301 5,142 5,831 5,831

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

394

Hypothesis Testing Non-Normal Data Part 2 Proportion versus a Target In SigmaXL® click Statistic Tools > Power &Sample Size Calculators>2 Proportion Test Calculator. For the field “Proportion 1 (P1):” type .85 and for the field “Power (1-Beta):” type .90; The last field “Proportion 2 (P2):” enter .95 then click OK.

A sample of at least 188 is necessary for each group to be able to detect a 10% difference. If you have reason to believe your improved process is has only improved to 90% and you would like to be able to prove that improvement is occurring the sample size of 188 is not appropriate. Recalculate using .90 for proportion 2 and leave proportion 1 at .85. It would require a sample size of 918 for each sample! Comparing Two Proportions The data shown was gathered for two processes.

Th e   fo llo w in g   d a ta   w e re   ta k e n : To ta l   S a m p le s

A ccu ra te

B e fo re   Im p r o v e m e n t

600

510

A fte r   Im p ro v e m e n t

225

212

C a lcu la te   p ro p o rtio n s : B e fo re   Im p r o v e m e n t:     6 0 0   s a m p le s ,   5 1 0   a ccu ra te

pˆ1 =

X1 510 = = 0.85 n1 600

A fte r   Im p ro v e m e n t:     2 0 0   s a m p le s ,   2 2 0   a ccu ra te

pˆ 2 =

X 2 212 = = 0.942 n 2 225

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

395

Hypothesis Testing Non-Normal Data Part 2 Comparing Two Proportions To compare two proportions in SigmaXL® select Statistical Tools>Basic Statistical Templates>2 Proportion Test & Fisher’s Exact.

Note: Fisher’s exact P-values should be used for any real world problem. The approximate P-values based on the Normal Distribution are provided for instructional purposes, e.g., comparing to hand calculations. The normal approximation uses a pooled estimate of proportion for the test. Boris and Igor Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

396

Hypothesis Testing Non-Normal Data Part 2 2 Proportion vs Target Example: Solution

Firs t   w e   n e e d   to   ca lcu la te   o u r   e s tim a te d   p 1 a n d   p 2 fo r   B o ris   a n d   Ig o r.

Boris

pˆ1 =

X1 47 = = 0.132 n1 356

Ig or

pˆ 2 =

X 2 99 = = 0.173 n 2 571

Poised for the competition!!

Results: As you can see we Fail to reject the null hypothesis with the data given. One conclusion is the sample size is not large enough. It would take a minimum sample of 1673 to distinguish the sample proportions for Boris and Igor.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

397

Hypothesis Testing Non-Normal Data Part 2 2 Proportion vs Target Example: Solution

The Fisher’s exact P-value (2-sided, Ha:P1≠P2) is .096 so we fail to reject the Null Hypothesis.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

398

Hypothesis Testing Non-Normal Data Part 2 Contingency Tables

C o n tin g e n cy   Ta b le s a re   u s e d   to   s im u lta n e o u s ly   co m p a re   m o re   th a n   tw o   s a m p le   p ro p o rtio n s   w ith   e a ch   o th e r. It   is   ca lle d   a   C o n tin g e n cy   Ta b le   b e ca u s e   w e   a re   te s tin g   w h e th e r   th e   p ro p o rtio n   is   co n tin g e n t   u p o n ,   o r   d ep e n d e n t   u p o n   th e   fa cto r   u s e d   to   s u b g ro u p   th e   d a ta . Th is   te s t   g e n e ra lly   w o rk s   th e   b e s t   w ith   5   o r   m o re   o b s erv a tio n s   in   e a ch   ce ll.     O b s e rv a tio n s   ca n   b e   p o o le d   b y   co m b in in g   ce lls . S o m e   e x a m p le s   fo r   u s e   in clu d e : – R e tu rn   p ro p o rtio n   b y   p ro d u ct   lin e – C la im   p ro p o rtio n   b y   cu s to m er – D e fect   p ro p o rtio n   b y   m a n u fa ctu rin g   lin e Th e   n u ll   h y p o th e s is   is   th a t   th e   p o p u la tio n   p ro p o rtio n s   o f   e a ch   g ro u p   a re   th e   s a m e . –

H 0 :     p 1 =   p 2 =   p 3 =   … =   p n

–

H a :     a t   le a s t   o n e   p   is   d iffe re n t

S ta tis ticia n s   h a v e   s h o w n   th a t   th e   fo llo w in g   s ta tis tic   fo rm s   a   ch i-­‐s q u a re   d is trib u tio n   w h e n   H 0 is   tru e : 2

∑

(observed − expected) expected

W h e re   “ o b s e rv e d ” is   th e   s a m p le   fre q u e n cy ,   “ e x p e cte d ” is   th e   ca lcu la te d   fre q u e n cy   b a s e d   o n   th e   n u ll   h y p o th e s is ,   a n d   th e   s u m m a tio n   is   o v e r   a ll   ce lls   in   th e   ta b le .

That? ..oh, that’s my contingency table!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

399

Hypothesis Testing Non-Normal Data Part 2 Test Statistic Calculations

C h i-­‐s q u a r e   Te s t 2 o

r

χ =∑ i =1

c

∑

(Oij − E ij ) 2 E ij

j=1

(F * F ) E ij = row col Ftotal

W h e re : O   =   th e   o b s e rv e d   v a lu e   (fro m   s a m p le   d a ta ) E   =   th e   e x p e cte d   v a lu e r   =     n u m b e r   o f   ro w s c   =   n u m b e r   o f   co lu m n s F r o w =   to ta l   fre q u e n cy   fo r   th a t   ro w

2 χ critical = χ α,2 ν

From    the  C hi-­‐S quare  Table

F co l =   to ta l   fre q u e n cy   fo r   th a t   co lu m n F to ta l   =   to ta l   fre q u e n cy   fo r   th e   ta b le n   =   d e g re e s   o f   fre e d o m   [(r -­‐1 )(c-­‐1 )]

Wow!!! Can you believe this is the math in a Contingency Table. Thank goodness for SigmaXL®. Now let’s do an example.

Contingency Table Example

Can’t you clowns get the entries correct?!! Note the data gathered in the table. Curley isn’t looking too good right now (as if he ever did). LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

400

Hypothesis Testing Non-Normal Data Part 2 Contingency Table Example The sample data are the “observed” frequencies. To calculate the “expected” frequencies, first add the rows and columns. Then calculate the overall proportion for each row.

The sample data are the observed frequencies. To calculate the expected frequencies, first add the rows and columns:

Defective OK Total

Moe 5 20 25

Larry Curley Total 8 20 33 30 25 75 38 45 108

Then calculate the overall proportion for each row:

Moe Defective 5 OK 20 Total 25

Larry Curley Total 8 20 33 0.306 30 25 75 0.694 38 45 108

33/108 = 0.306 75/108 = 0.694

Now use these proportions to calculate the expected frequencies in each cell.

Defective Proportion = 0.306 OK Proportion = 0.694 Moe Defective 5 OK 20 Total 25

0.694 * 38 = 26.4

LSS Black Belt Manual XL v11

Larry Curley Total 8 20 33 0.306 30 25 75 0.694 38 45 108

0.306*45 = 13.8

© 2013 e-Careers Limited

401

Hypothesis Testing Non-Normal Data Part 2 Contingency Table Example

N e x t   ca lcu la te   th e   χ2 v a lu e   fo r   e a ch   ce ll   in   th e   ta b le :

(observed - expected)2 expected

Moe Defective 0.912 OK 0.401

Larry 1.123 0.494

Curley 2.841 1.250

(20 − 13.8)2 13.8

= 2.841

Fin a lly ,   a d d   th e s e   n u m b ers   to   g e t   th e   o b s erv e d   ch i -­‐s q u a re : 2 = 0.912 +1.123 + 2.841+ χ obs 0.401+ 0.494 +1.250 2 χ obs = 7.02

The final step is to create a summary table including the observed chi-squared.

A   s u m m a ry   o f   th e   ta b le : Observed Expected 2 D e fe ctiv e χ Observed Expected

OK

χ2

LSS Black Belt Manual XL v11

Moe 5 7.6

Larry 8 11.6

Curley 20 13.8

0.912 20 17.4

1.123 30 26.4

2.841 25 31.3

0.401

0.494

1.250

2 = 7.02 χ obs

© 2013 e-Careers Limited

402

Hypothesis Testing Non-Normal Data Part 2 Contingency Table Example

G ra p h ica l   S u m m a ry : S in ce   th e   o b s erv e d   ch i-­‐s q u a re   e x ce e d s   th e   critica l   ch i-­‐ s q u a re ,   w e   re je ct   th e   n u ll   h y p o th e s is   th a t   th e   d e fe ct   ra te   is   in d ep e n d e n t   o f   w h ich   p e rs o n   e n te rs   th e   o rd ers . C hi-­‐square  probability  density  function  for  n  =  2 0.5 0.4 0.3

f

A ccept Reject

0.2

2 = 7.02 χobs

0.1 0.0 0

1

2

3

4

5

chi-square

LSS Black Belt Manual XL v11

6

7

8

2 = 5.99 χcrit

© 2013 e-Careers Limited

403

Hypothesis Testing Non-Normal Data Part 2 Contingency Table Example (cont.) For the Chi Square for TwoWay (contingency) tables if your data is in stacked column format use the “Chi Square Test.” This data can be found in the “Stooges” worksheet.

As you can see the data confirms: to reject the null hypothesis and the Practical Conclusion is: The defect rate for one of these stooges is different. In other words, defect rate is contingent upon the stooge.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

404

Hypothesis Testing Non-Normal Data Part 2 Quotations Exercise

Ex e rcis e   o b je ctiv e : To  practice  solving  the  problem   presented  using  the  appropriate  Hypothesis  Test. • •

Y ou  a re  the  quota tions  ma na g er  a nd  your  team  thinks  tha t  the   rea son  you  don’t  g et  a  contra ct  depends  on  its  complexity.   Y ou  determine  a  wa y  to  mea sure  complexity  a nd  cla ssify  lost   contra cts  a s  follows:

Price Lead Time Technology

Low 8 10 5

Med 10 11 9

High 12 9 16

1 . W rite  the  null  and  alternative  hypothesis. 2 . Does  complexity  have  an  effect?

Contingency Table Example: Solution

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

405

Hypothesis Testing Non-Normal Data Part 2 Contingency Table Example: Solution (cont.) After analyzing the data we can see the P-value is 0.426 which is larger than 0.05. Therefore, we accept the null hypothesis.

Instructor notes: 1. Ho: plow = pmed = phigh Ha: at least one is different 2. Obs Chi square = 3.856 Crit Chi square = 9.488 df = (3-1)(3-1) Fail to reject. There is no basis that they don’t get contracts because of their complexity.

Overview

Contingency Tables are another form of Hypothesis Testing. They are used to test for association (or dependency) between two classifications. The null hypothesis is that the classifications are independent. A Chi-square Test is used for frequency (count) type data. If the data is converted to a rate (over time) then a continuous type test would be possible. However, determining the period of time that the rate is based on can be controversial. We do not want to just pick a convenient interval; there needs to be some rational behind the decision. Many times we see rates based on a day because that is the easiest way to collect data. However, a more appropriate way would be to look at the rate distribution per hour.

Per hour?!

LSS Black Belt Manual XL v11

Per day?!

Per month?!

© 2013 e-Careers Limited

406

Hypothesis Testing Non-Normal Data Part 2 At this point, you should be able to: §  Calculate and explain test for proportions §  Calculate and explain contingency tests

You have now completed Analyze Phase – Hypothesis Testing Non-Normal Data Part 2.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

407

Lean Six Sigma Black Belt Training

Analyze Phase Wrap Up and Action Items

Now we will conclude the Analyze Phase with “Wrap Up and Action Items.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

408

Wrap Up and Action Items Analyze Phase Wrap Up Overview

Six Sigma Behaviors

• • • • • •

Embracing  chang e C ontinuous  learning   Being  tenacious  and  courag eous Make  data -­‐b ased  decisions   Being  rig orous Thinking  outside  of  the  box

Ea Each ch    ““ppla layyeerr”” in in    th thee    SSix ix    SSig igm maa    pprrooce cessss    m muusst  t  bbee AA    RROOLE   LE  M MOODDEL EL fo r   th e   S ix   S ig m a   cu fo r   th e   S ix   S ig m a   cultu lturree.. A Six Sigma Black Belt has a tendency to take on many roles, therefore these behaviors help throughout the journey.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

409

Wrap Up and Action Items Analyze Deliverables Sample size is dependent on the type of data.

• Listed  below  are  the  A nalyz e  Phase  deliverables  that  each  candid ate   will  present  in  a  Power  Point  presentation  at  the  beg inning  of  the   C ontrol  Phase  training .   • A t  this  point  you  should  all  understand  what  is  necessary  to  provide   these  deliverables  in  your  presentation. – – – – – – – – –

Team  Members  (Team  Meeting  A ttendance) Primary  Metric Secondary  Metric(s) Data  Demog raphics Hypothesis  Testing  (applicable  tools) Modeling  (applicable  tools) Strateg y  to  reduce  X’s Project  Plan     It’s Issues  and  Barriers

your show!! It’s   y our   s how!

Analyze Phase - The Roadblocks Each phase will have roadblocks. Many will be similar throughout your project.

Look for the potential roadblocks and plan to address them before they become problems: –  Lack of data –  Data presented is the best guess by functional managers –  Team members do not have the time to collect data –  Process participants do not participate in the analysis planning –  Lack of access to the process

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

410

Wrap Up and Action Items DMAIC Roadmap

C hampion/ Process  O wner

Now you should be able to prove/disprove the impact “X’s” have on a problem.

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

Analyze Phase Over 80% of projects will realize their solutions in the Analyze Phase – then we must move to the Control Phase to assure we can sustain our improvements.

Vital  Few  X’s  Identified Sta te  Practica l  Theories  of  Vita l  Few  X’s  Impact  on  Problem Tra nsla te  Practica l  Theories  into  Scientific  Hypothesis Select  A nalysis  Tools  to  Prove/ Disprove  Hypothesis C ollect  Da ta Perform  Sta tistica l  Tests Sta te  Practica l  C onclusion

Statistically Sig nificant?

N

Y

Update  FMEA

N

Practically Sig nificant? Y Root C ause Y

N Identify  Root  C a use

Ready  for  Improve  and  C ontrol

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

411

Wrap Up and Action Items Analyze Phase Checklist

Analyze Questions Define Performance Objectives Graphical Analysis •  Is existing data laid out graphically? •  Are there newly identified secondary metrics? •  Is the response discrete or continuous? •  Is it a Mean or a variance problem or both? Document Potential X s Root Cause Exploration •  Are there a reduced number of potential X s? •  Who participated in these activities? •  Are the number of likely X s reduced to a practical number for analysis? •  What is the statement of Statistical Problem? •  Does the process owner buy into these Root Causes? Analyze Sources of Variability Statistical Tests •  Are there completed Hypothesis Tests? •  Is there an updated FMEA? General Questions •  Are there any issues or barriers that prevent you from completing this phase? •  Do you have adequate resources to complete the project?

Planning for Action This is a template that should be used with each project to assure you take the proper steps – remember, Six Sigma is very much about taking steps. Lots of them and in the correct order.

WHAT

W HO

W H EN

WHY

W H Y   N O T

HOW

Q ualitative  screening  of  vital  from  controllable  trivial  Xs Q ualitative  screening  for  other  factors Q uantitative  screening  of  vital  from  controllable  trivial  Xs Ensure  compliance  to  problem  solving  strateg y Q uantify  risk  of  meeting  needs  of  customer,  business  and  people Predict  risk  of  sustainability C hart  a  plan  to  accomplish  desired  state  of  culture A ssess  shift  in  process  location Minimiz e  risk  of  process  failure Modeling  C ontinuous  or  N on  C ontinuous  O utput A chieving  breakthrough  in  Y  with  minimum  efforts Validate  Financial  Benefits

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

412

Wrap Up and Action Items At this point, you should: §  Have started to develop a project plan to meet the deliverables §  Have identified ways to deal with potential roadblocks §  Be ready to apply the Six Sigma method through your project

You’re on your way!! You have now completed the Analyze Phase. Congratulations!

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

413

Lean Six Sigma Black Belt Training

Improve Phase Welcome to Improve

Now that we have completed the Analyze Phase we are going to jump into the Improve Phase. Welcome to Improve will give you a brief look at the topics we are going to cover.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

414

Welcome to Improve Overview Well, now that the Analyze Phase is over, on to a more difficult phase. The good news is….you’ll hardly ever use this stuff, so pay close attention! We will examine the meaning of each of these and show you how to apply them.

W e lco m e   to   Im p ro v e P ro ce s s   M o d e lin g :   R e g r e s s io n A d v a n ce d   P ro ce s s   M o d e lin g :   M LR D e s ig n in g   Ex p e rim e n ts Ex p e rim e n ta l   M e th o d s Fu ll   Fa cto r ia l   Ex p e rim e n ts Fra ctio n a l   Fa cto r ia l   Ex p e rim e n ts W ra p   U p   &   A ctio n   Ite m s

C hampion/ Process  O wner

DMAIC Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  Xs  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

We are currently in the Improve Phase and by now you may be quite sick of Six Sigma, really! In this module we are going to look at additional approaches to process modeling. Its actually quite fun in a weird sort of way! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

415

Welcome to Improve Improve Phase

A nalysis  C omplete

Identify  Few  Vital  X’s

Experiment  to  O ptimiz e  Value  of  X’s

Simulate  the  N ew  Process

Validate  N ew  Process  

Implement  N ew  Process

Ready  for  C ontrol

After completing the Improve Phase you will be able to put to use the steps as depicted here.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

416

Lean Six Sigma Black Belt Training

Improve Phase Process Modeling Regression

Now we will continue in the Improve Phase with “Process Modeling: Regression”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

417

Process Modeling Regression Overview

W W eelco lcom m ee    to to    Im Im ppro rovvee

CC orrela orrelation tion

PPro roce cessss    M Mooddeelin lingg :  :  RReegg rreessssio ionn

Introduction  to  Reg Introduction  to  Regression ression

AA ddvvaa nnce cedd    PPro roce cessss    M Mooddeelin lingg :  :   M MLR LR

Simple  Linea Simple  Linear  Reg r  Regression ression

D Deessig ig nnin ingg    Ex Ex ppeerim rim eennts ts Ex Ex ppeerim rim eennta ta l  l  M Meeth thooddss Fu Full   ll  Fa Fa cto ctorria ia l  l  Ex Ex ppeerim rim eennts ts Fra Fra ctio ctionnaa l  l  Fa Fa cto ctorria ia l  l   Ex Ex ppeerim rim eennts ts W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

In this module of Process Modeling we will study Correlation, Introduction to Regression and Simple Linear Regression. These are some powerful tools in our data analysis tool box. We will examine the meaning of each of these and show you how to apply them. Correlation

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

418

Process Modeling Regression Correlation Coefficient Ho: No Correlation

Ho ho ho….!

Ha: There is Correlation

Ha ha ha….!

The Correlation Coefficient (always) assumes a value between –1 and +1. The Correlation Coefficient of the population, R, is estimated by the sample Correlation Coefficient, r:

The null hypothesis for correlation is: there is no correlation, the alternative is there is correlation. The correlation coefficient (always) assumes a value between –1 and +1. The correlation coefficient of the population, large R, is estimated by the sample correlation coefficient, small r and is calculated as shown. Types and Magnitude of Correlation

The graphics shown here are labeled as the type and magnitude of their correlation: Strong, Moderate or Weak correlation. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

419

Process Modeling Regression Limitations of Correlation To properly understand regression you must first understand correlation. Once a relationship is described, then a regression can be performed.

• • • •

A  strong  positive  or  neg ative  correlation  between  X  and  Y  does  not  indicate   causality. C orrelation  provides  an  indica tion  of  the  streng th  but  does  not   provide  us   with  an  exact  numerical  relationship  (i.e.  Y = f(x)). The  mag nitude  of  the  correlation  coefficient  is  somewha t  relative  and  should   be  used  with  caution. Just  like  any  other  statistic,  you  need  to  assess  whether  the  correlation   coefficient  is  statistically  sig nificant,  as  well  as  practically sig nificant.

•

A s  usual,  statistical  sig nificance  is  judg ed  by  comparing  a  p -­‐value  with  the   chosen  deg ree  of  alpha  risk.

•

G uidelines  for  practical  sig nificance  are  as  follows:  

A strong positive – If  |  r  |  >  0 .8 0 ,  relationship  is  practically  sig nificant or negative – If  |  r  |  <  0 .2 0 ,  relationship  is  not  practically  sig nificant correlation between X and reaa   o   of  f  nneeggaativ tivee A re a   o f   p o s itiv e AAre N o   lin e a r   co rre la tio n Y does not lineeaar  r  co corre rrelalatio tionn lin e a r   co rre la tio n lin indicate causality. + 1 .0 -­‐1 .0 -­‐0 .8 -­‐0 .2 0 .2 0 .8 0 Correlation provides an indication of the strength but does not provide us with an exact numerical relationship. Regression however provides us with that data more specifically a y equals f of x equation. Just like any other statistic, be sure to assess the correlation coefficient is both statistically significant and practically significant. Correlation Example

We will use some data from a National Football League player, Walter Payton formerly of the Chicago Bears. Open the worksheet “RB Stats Correlation” as shown here. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

420

Process Modeling Regression Correlation Analysis

Get outta my way!!

To generate a graph with the correlation data and a Trendline follow the sequence shown with our data set. Correlation Example SigmaXL® V6 does not include Lowess Smoothing. If a trend line is selected, it can easily be modified using Excel’s Chart tools. In this example it appears that there is strong correlation in the data.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

421

Process Modeling Regression Correlation Example (cont.) Now we will generate the Correlation Coefficient using SigmaXL®. Follow the SigmaXL® command path shown here and select the variables “payton carries” and “payton yards” as shown above. The Correlation Coefficient is high which corresponds to the graph on the previous slide that shows positive correlation. The P-value is low at . 000 so we reject the null hypothesis by saying that there is significant correlation between Payton’s carries and the number of yards.

Regression Analysis Correlation ONLY tells us the strength of a relationship while Regression gives the mathematical relationship or the prediction model. The last step to proper analysis of Continuous Data is to determine the Regression Equation. The Regression Equation can mathematically predict Y for any given X. The Regression Equation from SigmaXL is the BEST FIT for the plotted data.

Prediction Equations: Y = a + bx

(Linear or 1st order model)

Y = a + bx + cx2

(Quadratic or 2nd order model)

Y = a + bx + cx2 + dx3

(Cubic or 3rd order model)

Y = a (bx)

(Exponential)

Looking for the best fit!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

422

Process Modeling Regression Simple vs. Multiple Regression

In Simple Regression there is only one X commonly referred to as a predictor or regressor. Multiple Regression allows many Y’s. Recall we are only presenting Simple Regression in this phase and will present Multiple Regression in detail in the next phase.

Regression Analysis Graphical Output

There are two ways to perform a Simple Regression. One is the Scatter Plot as shown. The Regression Equation can be found in the top right corner. A Simple Regression can also be performed in SigmaXL® using the Multiple Regression tool, which will be covered in the next slide. Follow the SigmaXL® command prompt shown here, select “payton yards” for Response (Y) and “payton carries” for the Predictor (X1). LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

423

Process Modeling Regression Regression Analysis Statistical Output Now we will perform the Simple Linear Regression using SigmaXL®'s Multiple Regression Tool to get a more detailed statistical analysis. Select SigmaXL>Statistical Tools>Regression> Multiple Regression. Select “payton yards” for Numeric Response (Y) and “payton carries” for Continuous Predictors (X). The difference between R squared and adjusted R squared is not terribly important in Simple Regression. In Multiple Regression where there are many X’s it becomes more important. We’ll look at that in the next module.

Regression (Prediction) Equation The Regression Analysis generates a prediction model based on the best fit line through the data represented by the equation shown here. To predict the number of yards that Payton would run if he had 250 carries you simply fill in that value in the equation and solve.

R e g re s s io n   A n a ly s is :   P a y to n   y a rd s   v e rs u s   P a y to n   ca r rie s The  reg ression  equation  is                                                         Payton  yards  =  -­‐1 6 3 .4 9 7  +  4 .9 1 6 2 2  Payton  carries                

C o n s ta n t

Le v e l   o f   X C o e fficie n t

To  predict  how  many  yards  Payton  would  run  if  he  had  2 5 0  carries use  the   prediction  equation  above.    

LSS Black Belt Manual XL v11

Payton yards = -163.497 + 4.91622(250) = 1,065.6

© 2013 e-Careers Limited

424

Process Modeling Regression Regression (Prediction) Equation (cont.) You could make a rough estimate by using a Scatter Plot. To get an exact estimate use SigmaXL®’s Predicted Response Calculator located in the “Multiple Regression” worksheet.

Regression Graphical Output

Using Excel’s native functions we are able to modify the fitted line plot to both Quadratic and Cubic models. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

425

Process Modeling Regression Regression Graphical Output (cont.)

Use the best fitting equation by looking at the R-Sq value. If it improves significantly, or if the assumptions of the residuals are better met as a result of utilizing the quadratic or cubic equation you should use it. Here there is no big difference so we will stick with the linear model. Residuals Regression Analysis relies on assumptions about the residuals; differences between predicted and actual Y values. Then we analyze the residuals to look for evidence of an outlier, which could mean a typo or some assignable cause, or nonlinearity. As in ANOVA, the residuals should: –  Be Normally Distributed (normal plot of residuals) –  Be independent of each other •  no patterns (random) •  data must be time ordered (residuals vs. order graph) –  Have a constant variance (visual, see residuals versus fits chart, should be (approximately) the same number of residuals above and below the line, equally spread.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

426

Process Modeling Regression Residuals (cont.)

These graphs are found on the “Mult Reg Residuals” sheet.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

427

Process Modeling Regression Residual Analysis Standardized residuals greater than 2 and less than -2 are usually considered large. We will discuss the meaning of this a bit later. The Residuals Table can be found on the “Mult Reg Residuals” worksheet.

Normal Probability Plot of Residuals This Normal Probability Plot of Standardized Residuals can be found in the “Mult Reg Residuals” worksheet next to the Multiple Regression results. This chart is displayed starting in cell R1.

As you can see the Normal probability plot of residuals evaluates the Normally Distributed response assumption. The residuals should lay near the straight line to within a fat pencil. Looking at a Normal probability plot to determine normality takes a little practice. Technically speaking however, it is inappropriate to generate an Anderson-Darling or any other Normality test that generates a pvalue to determine normality. The reason is that residuals are not independent and do not meet a basic assumption for using the Normality tests. Dr. Douglas Montgomery of Arizona State University coined the phrase “fat pencil test” much to the chagrin of many of his colleagues. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

428

Process Modeling Regression Residuals vs Fitted Values Residuals versus Fitted Values evaluates the Equal Variance assumption. Here you want to have a random scattering of points. You DO NOT want to see a “funnel effect” where the residuals gets bigger and bigger as the Fitted Value gets bigger or smaller. Note: The horizontal line at 0 was manually added as a reference.

Residuals vs Order of Data

Residuals versus the order of data is used to evaluate the independence assumption. It should not show trends either up or down and should have approximately the same number of points above and below the zero line. The horizontal line at 0 was manually added as a reference. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

429

Process Modeling Regression Modeling Y=f(x) Exercise

Modeling Y=f(x) Exercise: Question 1 Solution

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

430

Process Modeling Regression Modeling Y=f(x) Exercise: Question 1 Solution

You could also use Recall SigmaXL® Dialog to quickly recreate the Scatter Plot.

Fitted Line Plot!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

431

Process Modeling Regression Modeling Y=f(x) Exercise: Question 2 Solution (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

432

Process Modeling Regression Modeling Y=f(x) Exercise: Question 3 Solution

If Dorsett carries the football 325 times the predicted value would be determined that Dorsett would carry the football for 1462.63 yards – approximately! Modeling Y=f(x) Exercise: Question 4 Solution All three assumptions have been satisfied.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

433

Process Modeling Regression At this point, you should be able to: §  Perform the steps in a Correlation and a Regression Analysis §  Explain when Correlation and Regression is appropriate

You have now completed Improve Phase – Process Modeling Regression.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

434

Lean Six Sigma Black Belt Training

Improve Phase Advanced Process Modeling

Now we will continue with the Improve Phase “Advanced Process Modeling MLR”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

435

Advanced Process Modeling Overview

W W eelco lcom m ee    to to    Im Im ppro rovvee PPro roce cessss    M Mooddeelin lingg :  :  RReegg rreessssio ionn AA ddvvaa nnce cedd    PPro roce cessss    M Mooddeelin lingg :  :   M MLR LR D Deessig ig nnin ingg    Ex Ex ppeerim rim eennts ts

Review  C Review  C orr./ orr./ Reg Regression ression N N on-­‐ on-­‐LLinea inear  Reg r  Regression ression Tra Transforming nsforming  Process  Da  Process  Data ta Multiple  Reg Multiple  Regression ression

Ex Ex ppeerim rim eennta ta l  l  M Meeth thooddss Fu Full   ll  Fa Fa cto ctorria ia l  l  Ex Ex ppeerim rim eennts ts Fra Fra ctio ctionnaa l  l  Fa Fa cto ctorria ia l  l   Ex Ex ppeerim rim eennts ts W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

The core fundamentals of this phase are as shown. We will examine the meaning of each of these and show you how to apply them. Correlation and Linear Regression Review

Recall the Simple Linear Regression and Correlation covered in a previous module. The essential tools presented here describe the relationship between two variables. A independent or input factor and typically an output response. Causation is NOT always proved; however, the tools do present a guaranteed relationship. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

436

Advanced Process Modeling Correlation Review The Pearson Correlation Coefficient, represented here as “r”, shows the strength of a relationship in correlation. The coefficient can vary ONLY between -1 and +1 while a zero value describes NO relationship, meaning no correlation. The P-value proves the statistical confidences of our conclusion representing the Possibility that a relationship exists. Simultaneously; the Pearson Correlation Coefficient shows the “strength” of the relationship. For example, P-value standardized at .05, then 95% confidence in a relationship is exceeded by the two factors tested. Linear Regression Review Presented here Stirrate is directly related to impurity of the process; the relationship between the two, is one unit Stir Rate causes . 4566 Impurity increase. Stir Rate locked at 30 and Impurity calculated by 30 times .4566, subtracting .289 gives us a 13.4 Impurity. Granted; that we have an error in our model, the red points do not lie on the blue line. The dependent response variable is Impurity and the Stirrate is the independent predictor, as both variables in this example are perpetual.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

437

Advanced Process Modeling Correlation Review Numerical relationship is left out when speaking of Correlation. Correlation shows potency of linear relationship, mathematical relationship is shown by and through the Prediction Equation of Regression. As shown, these Correlations or Regressions are not proven casual relationships. We are attempting to PROVE statistical commonality. Exponential, quadratic, simple linear relationships or even predictable outputs (Y) concern REGRESSION equations. More complex relationships are approaching.

Simple vs. Multiple Regression Review Simply Regressions have one X and are referenced as the regressors or predictors; multiple X’s give reason to output or response variable, this is Multiple Regression accounts. Strength of the regression known quantity by R squared and dictates overall variation in output (Y), independent variable subjected to the regression equation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

438

Advanced Process Modeling Regression Step Review How to run a Regression The basic steps to follow in Regression are as follows: is directed here. Using a 1.  Create Scatter Plot with Trendline (Graphical Tools>Scatterplot) Scatter Plot, and understanding the 2.  Determine Correlation (Statistical Tools>Correlation Matrix – P-value less than 0.05) variation between the X’s and Y’s, then activate a 3.  Run Regression (Statistical Tools>Regression>Multiple Regression) (Unusual Observations?) Correlation analysis allowing a potential linear 4.  Evaluate R2, adjusted R2 and P-values relationship indication. 5.  Consider quadratic or cubic Trendline. Add Non-linear terms to Third step is to find regression model if necessary existing linear 1.  Add quadratic terms mathematical 2.  Add cubic terms One step relationships which calls 6.  Analyze residuals to validate assumptions at a time….! for a Prediction Equation 1.  Normally distributed then fourth to find the 2.  Equal variance potency or strength of the 3.  Independence linear relationship if one 4.  Confirm one or two points do not overly influence model. exists. Linear Regression accompanied by the variation of the input gives a variety of output results and a completion of the fifth step denoted, the amount percentage a given output has. It also includes the answer to strength of statistical confidence within our Linear Regression. To conclude a Linear Regression exists; majority has that a 95% statistical confidence or above has to be obtained. If unsatisfied conclusions are drawn, as a point of contingency, step 6 is essential. At present, in step 6, we contemplate the potential Non-linear Regression. However, this is only necessary if we can not find a Regression Equation (statistical and practical) variation of output by way of scoping the input or by analyzing the model error for correctness. Step 7, depicted subsequently, validates residuals are a necessity for a valid model. Simple Regression Example Recalling tools learned in the Analyze Phase, presented here is a Simple Regression example examining a piece of equipment pertaining to a mining company. This diagram plots output to input, following the Regression steps. Notice how the equipment is agitated by output of PGM concentrate. Opening the worksheet “Concentrator” will show how output is always applied to the Y axis (dependent) as input is always applied to the X axis (independent). LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

439

Advanced Process Modeling Example Correlation Identifying the existing Linear Regression is the second step. Having the Pearson Correlation Coefficient at .847 and a P-value less than .05, we see with a very strong statistical confidence in a Linear Regression. If no Correlation existed the coefficient would be closer to zero, remember? Example Regression Line

Now finding the Prediction Equation of the linear relationship, two factors; output response and input variable. Grams per ton of the PGM concentrate is the output and the RPM of the agitator is the input. Knowing that a positive slope exists, by a greater than zero Correlation Coefficient indicates the agitators RPM increases in correlation with the PGM concentrate. The slope of Linear Regression equals 1.333. Did you recall that the Pearson correlation coefficient exceeded zero? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

440

Advanced Process Modeling Example Linear Regression Select SigmaXL>Statistical Tools>Regression>Multiple Regression. Select “PGM concentrate (g/ ton)” as Numeric Response (Y) and “Agitator RPM” as Continuous Predictor (X). Ensure that “Display Residuals” is checked and “Standardized Residuals” are selected.

Shown here is the Multiple Regression output (Single X, Simple Linear Regression) explaining 70% of the process variation. Highlighted above we see a potentially large residual. This was added manually for illustration purposes. SigmaXL® highlights standardized residual values greater than 3 or less than -3 to minimize false alarms. R squared, and R squared adjusted pertain to our full Regression analysis. With these concerns the addition of Non-linear Regression terms might be in consideration.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

441

Advanced Process Modeling Example Regression Line

Notice how the new line is a more appropriate demonstration of our data since the curvature better fits the plotted points. This is the essence of choosing quadratic Regression. This model option can be used in Excel as follows: 1. Select the Trendline 2. Right Click and select “Format Trendline” 3. In the Trendline Options tab, select Polynomial Trend/Regression Type. Order 2 for quadratic, Order 3 for cubic.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

442

Advanced Process Modeling Residual Analysis Example In order to create a quadratic model using SigmaXL®’s Multiple Regression tool, you will need to square the data being used as your Continuous Predictor. Then select SigmaXL > Statistical Tools> Regression> Multiple Regression. Select both your original and squared columns as continuous predictors. Ensure “Display Residual Plots” is checked and standardized residuals are selected.

Linear and Non-Linear Regression Example We have here both Regression models. In terms of R squared being higher in percentage rate on the Non-linear model as apposed to that of the Linear we see more process variation. In addition, S presents estimated Standard Deviation of errors, Non-linear model has a lower decimal.

Linear Model

More variation is explained using the Non-linear model since the RSquared is higher and the S statistic is lower which is the estimated Standard Deviation of the error in the model.

Non- Linear Model:

Let us now consider the model error. You need not be perplexed, model error has many variables. Output dependency on the impact of other input variables and measurement system errors of output and inputs can be causes.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

443

Advanced Process Modeling Residual Analysis Example By clicking the Residuals worksheet, we now see all analyses presented and must keep in mind our assumptions to consider the possibilities of a valid Regression. Residuals do not have a pattern across the data collected, however, they do have a similar variation across the board of Fitted Values. Moreover, in a valid Regression of all residuals will be distributed. Similarities between the residuals across the Fitted Values in the upper right graph show no monumental differences as to variation. Random placement of the residuals are proven by the bottom right graph; no pattern is in essence. Looking for Normality the bottom left graph (the Histogram) indicates we have a bell curve, as does the upper right graph proving residuals placed near the straight line. Now, have we met the necessary requirements of the criteria? With these randomly dispersed residual data points finding the impact of just a single one is the confirmation. Non-Linear Relationships Summary

M e th o d s   to   fin d   N o n -­‐lin e a r   R e la tio n s h ip s : – S ca tte r   P lo t   in d ica tin g   cu rv a tu re . – U n u s u a l   o b s e rv a tio n s   in   Lin e a r   R e g re s s io n   m o d e l. – Tre n d s   o f   th e   R e s id u a l v e rs u s   th e   Fitte d   V a lu e s P lo t   in   s im p le   Lin e a r   R e g re s s io n . – S u b je ct   m a tte r   e x p e rt   k n o w le d g e   o r   te a m   e x p e rie n ce . When identifying Non-linear Relationships, looking at the graphical variation of output to input on any given Scatter Plot the Non-linear relationship is self evident. Using step four of the Regression Analysis methodology, unusual observation will ask us to focus deeper at Fitted Line Plots to see what is the solution for the historical data. To detect Non-linearity carefully look at the Residuals vs. Fitted Values graph of a Linear Regression. Finding clustering and/or trends of data one could conclude a Non-linear Regression. Relying on a team or expert who has prior knowledge can avail much information, also.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

444

Advanced Process Modeling Types of Non-Linear Relationships The simple Linear model, the quadratic model, the logarithm model and the inverse model define the more conventional relationships between outputs and inputs.

Oh,  which which  formula f ormula   u se?! Oh, toto   use?!!

Mailing Response Example

Clip ‘em!!

Open the worksheet “Mailing Response vs. Discount”. This shows transactions by a retail store chain giving the relationship between discount percentages and the customer response. With the input variable displayed in C1 and output displayed in C2, Belts need to establish which discount rate will yield a 10% response from customers.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

445

Advanced Process Modeling Mailing Response Scatter Plot The output vs. the input is graphically plotted with the output plotted on the Yaxis. Notice we have some curvature in the customer response.

Mailing Response Correlation Now we are testing for a Linear relationship by running a Correlation. The results of the analysis are a strong confidence level since the Pvalue is less than . 05. Do you notice the Pearson Correlation Coefficient is almost 1.0? That indicates a strong correlation. From SigmaXL®’s User Guide: Pearson Correlation Coefficient (r) 0.9 Statistical Tools> Regression> Multiple Regression. Select both your original and squared columns as continuous predictors. Select SigmaXL > Statistical Tools> Regression> Multiple Regression.

I found some Residuals!!

Confidence and Prediction Intervals Keeping in mind the original question, the store wants 10% of the coupons redeemed by their customers so what discount rate will generate this response? We will use the Predicted Response Calculator to answer this question. This calculator is located to the right of the regression report. Here we must use the Multiple Regression Tool rather than the Scatter Plot because SigmaXL®’s Scatter Plots provide prediction and confidence intervals only for a Linear (1st Order) Trendline. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

448

Advanced Process Modeling Confidence and Prediction Intervals (cont.) Our analysis tells us that to get at least a 10% response from customers, we must offer a 19% discount with our coupons. This can be obtained through trial and error entry of “% discount” and calculated “Discount – Sq” (Enter “=K12^2” in cell K13). Having less data available to predict the Regression Equation usually causes the Confidence Interval to flare out at the extreme ends. If a prediction equation exists, it would be found within the red lines indicating the Confidence Interval at the 95% confidence level.

Considering the question of yielding 10% or more, finding the Regression Equation is of menial importance compared to estimating where the data ought to predict the relationship. The Prediction Interval will provide a degree of confidence in how the customers will respond. This estimate is of great importance.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

449

Advanced Process Modeling Residual Analysis Confirming the validity, taking into consideration our residuals and completing step six is next. Having a variation of outputs is due to a high level in R-squared, but from that information we can not draw the conclusion it’s a sufficient model. We can have confidence in our model because all three assumptions are satisfied; outputs are Normally and Randomly Distributed across the observation order and have similar variance across the Fitted Values. The store should give a discount of 19% expecting at least a 10% response from customers.

Now does the present data for the response fit the equation as predicted?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

450

Advanced Process Modeling Transforming Process Data

In   th e   ca s e   w h e re   d a ta   is   N o n -­‐lin e a r   it   is   p o s s ib le   to   p e rfo rm   R e g re s s io n   u s in g   tw o   d iffe re n t   m e th o d s : – N o n -­‐lin e a r   R e g re s s io n   (a lre a d y   d is cu s s e d ) – Lin e a r   R e g re s s io n   o n   tra n s fo rm e d   d a ta Eith e r   th e   X   o r   Y   m a y   b e   tra n s fo rm e d . A n y   s ta tis tica l   to o ls   th a t   re q u ire s   tra n s fo rm a tio n   u s e s   th e s e   m e th o d s . A d v a n ta g e s   o f   tra n s fo rm in g   d a ta : – Lin e a r   R e g re s s io n   is   e a s ie r   to   v is u a lly   u n d e rs ta n d   a n d   m a na g e. – N o n -­‐n o rm a l   d a ta   ca n   b e   ch a n g e d   to   r e s e m b le   N o r m a l   d a ta   fo r   s ta tis tica l   a n a ly s e s   w h e re   N o rm a lity   is   re q u ire d . D is a d v a n ta g e s   o f   tra n s fo rm in g   d a ta : – D ifficu lt   to   u n d e rs ta n d   tr a n s fo rm e d   u n its . – D ifficu lt   w ith o u t   a u to m a tio n   o r   co m p u te rs . Majority has it that Belts find data that is abnormally distributed. We have learned how to do Nonlinear Regression, but another approach is to transform it into Linear Regression. Outputs or inputs can be transformed and many people will wonder, “What's the point?” Simplicity is the answer and has a great deal of value.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

451

Advanced Process Modeling Effect of Transformation Using a mathematical function we have transformed this data. This example shows how taking a square root of this data yields a Normal distribution. The challenge then is to find the appropriate transform function.

Transforming Data Using SigmaXL®

Select worksheet: Transform In finding an appropriate transform SigmaXL® performs a function to aid the Belt, this is known as Box Cox Transformation. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

452

Advanced Process Modeling Box Cox Transform Selecting a transform, in the upper graph SigmaXL® presents a lambda of .5, the lambda is a mathematical function applied to the data. In taking a square root, you can notice two probabilities of plots in the graphs below. The right plot obviously shows a new data set after having been transformed by the square root and the left showing Non-normal distribution with red dots away from the blue line symbolized by a P-value of under .05.

The transformed data is stored in the worksheet: “Box-Cox” column “Transformed Data (Y**0.500000)”. This tool can also be found under “Process Capability > Nonnormal> Box-Cox Transformation” and “Control Charts> Nonnormal> Box-Cox Transformation>”. Box-Cox is also included with automated distribution fitting (Process Capability > Nonnormal>Distribution Fitting)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

453

Advanced Process Modeling Transforming Without the Box Cox Routine Using Excel, calculate the square root of each observation in Pos Skew and store in E, calling it “Transformed”.

Finding that the new data is Normally Distributed after creating the transformed data set is necessary. Remembering from the Measure Phase the “Graphical Tools > Normal Probability Plot” and “Statistical Tools>Descriptive Statistics” command is now of great importance. Interestingly enough the Box Cox found the best transformation was the same square root we executed.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

454

Advanced Process Modeling Multiple Linear Regression R e g re s s io n s   a re   ru n   o n   h is to r ica l   p r o ce s s   d a ta .     It   is   N O T   a   fo r m   o f   e x p e rim e n ta tio n . M u ltip le   Lin e a r   R e g re s s io n   in v e s tig a te s   m u ltip le   in p u t   v a ria b le s ’ e ffe ct   o n   a n   o u tp u t   s im u lta n e o u s ly . – If   R 2 is   n o t   a s   h ig h   a s   d e s ire d   in   th e   S im p le   Lin e a r   R e g re s s io n . – P ro ce s s   k n o w le d g e   im p lie s   m o re   th a n   o n e   in p u t   a ffe cts   th e   o u tp u t. Th e   a s s u m p tio n s   fo r   r e s id u a ls   w ith   S im p le   R e g re s s io n s   a re   s till   n e ce s s a ry   fo r   M u ltip le   Lin e a r   R e g re s s io n s . A n   a d d itio n a l   a s s u m p tio n   fo r   M LR   is   th e   in d e p e n d e n ce   o f   p re d icto r s   (X ’ s ). – M IN ITA B TM ca n   te s t   fo r   m u ltico llin e a rity   (co rre la tio n   b e tw e e n   th e   p re d icto r s   o r   X ’ s ).

M o d e l   e rr o r   (r e s id u a ls )   is   im p a cte d   b y   th e   a d d itio n   o f   m e a s u re m e n t   e r ro r   fo r   a ll   th e   in p u t   v a ria b le s .

In a quick review, we only do Regression on historical data and Regression is not applied to experimental data. Furthermore, we covered performing Regression involving one input and one output. Now taking into account Multiple Linear Regressions and when they are applicable, allows us to identify Linear Regression including one output and more than one input at the same time. If you haven’t identified enough of the output variation, recall briefly R-squared measures the amount of variation for the output in Correlation with the input you selected. In looking at the equations here we can assume that in Multiple Linear Regressions each input are independent of one another, no Correlation exists. Having the inputs independent of one another gives each of them their own slope. Also we see the epsilon at the end of the equation representing the fact that every Regression has model error.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

455

Advanced Process Modeling Definitions of MLR Equation Elements Th e   d e fin itio n s   fo r   th e   e le m e n ts   o f   th e   M u ltip le   Lin e a r   R e g re s s i o n   m o d e l   a re   a s   fo llo w s :

Y = β0+ β1X1 + β2X2 + β3X3 + ε Y   =   Th e   r e s p o n s e   (d e p e n d e n t)   v a ria b le .   X 1 ,   X 2 ,   X 3 :   Th e   p re d icto r   (in d e p e n d e n t)   in p u ts .     Th e   p re d icto r   v a ria b le s   u s e d   to   e x p la in   th e   v a ria tio n   in   th e   o b s e rv e d   re s p o n s e v a ria b le ,   Y . β0 :   Th e   v a lu e   o f   Y   w h e n   a ll   th e   e x p la n a to ry   v a ria b le s   (th e   X s )   a re e q u a l   to   z e ro . β1 ,   β2 ,   β3 (P a rtia l   R e g re s s io n   C o e fficie n t):     Th e   a m o u n t   b y   w h ich   th e   re s p o n s e   v a ria b le   (Y )   ch a n g e s   w h e n   th e   co rre s p o n d in g   X i   ch a n g e s   b y   o n e   u n it   w ith   th e   o th e r   in p u t   v a ria b le s   re m a in in g   co n s ta n t.   ε (Erro r   o r   R e s id u a l):   Th e   o b s e rv e d   Y   m in u s   th e   p re d icte d   v a lu e   o f   Y   fro m   th e   R e g re s s io n .

Simple linear equations and multiple linear equations are very similar, however each in Multiple Linear Regression there is partial regression coefficient and beta one and beta zero apply to Simple Linear Regressions. Earlier we did Regressions in this module, do you recall the residuals we had? Residuals are defined as the observed value minus the predicted value. MLR Step Review

Th e   b a s ic   s te p s   to   fo llo w   in   m u ltip le   lin e a r   reg re s s io n   a re : 1 . C re a te   m a trix   p lo t   (G ra p h > M a trix   P lo t) 2 . R u n   B e s t   S u b s e ts   R e g re s s io n   (S ta t> R e g r e s s io n > B e s t   S u b s e ts ) 3 . Ev a lu a te   R 2 ,   a d ju s te d   R 2   ,   M a llo w s ’ C p ,   n u m b e r   o f   p re d icto rs   a n d   S . 4 . Ite ra tiv e ly   d e te rm in e   a p p ro p ria te   R e g re s s io n   m o d e l.   (S ta t> R e g re s s io n >   R e g r e s s io n   > O p tio n s )

5 . A n a ly z e   re s id u a ls   (S ta t> R e g r e s s io n > R e g re s s io n   > G ra p h s ) 1 . N o rm a lly   d is trib u te d 2 . Eq u a l   v a ria n ce 3 . In d e p e n d e n ce 4 . C o n firm   o n e   o r   tw o   p o in ts   d o   n o t   o v e rly   in flu e n ce   m o d e l. 6 . V e rify   y o u r   m o d e l   b y   ru n n in g   p re s e n t   p ro ce s s   d a ta   to   co n firm   y o u r   m o d e l   e rro r.

With many different input variables on hand and only one output it can be so tedious to find if variations come from one particular input, using a Matrix Plot can greatly speed up the process and it will show which is impacting the output the most. After narrowing the field of variables use the best given command to complete the Multiple Linear Regression, we identify the correct command by examining R-squared, R-squared adjustable, #’s of predictors, S variable and Mallows Cp; following this we must iteratively confirm inputs are statistically significantly. We have then only confirmation of this valid model and we MUST especially in consideration for Multiple Linear Regressions process and witness the presently performing Regression. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

456

Advanced Process Modeling Multiple Linear Regression Model Selection

It’s in our best interest to use the least confusing Multiple Linear Regression model, using these particular guidelines.

Flight Regression Example

Select the “Flight Regression MLR” worksheet to see historical data being analyzed by an airplane manufacturer. Output is listed as flight speeds and the other columns contain input variables. With these we will build a Scatter Plot Matrix and witness the possibility of relationships among the variables come to fruition. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

457

Advanced Process Modeling Flight Regression Example Matrix Plot Now we are given a fairly confusing graph of outputs and inputs to interpret. Do not be discouraged, this is just a plethora of sporadically plotted, outputs and inputs, flight speeds vs. altitudes. Seeing at least two inputs having Correlation shows the need to continue with a Multiple Linear Regression. The lower half has identical data as the upper half of the outputs just the axis are not reversed.

Flight Regression Example Model Selection

Select “Statistical Tools > Regression > Multiple Regression”. Select “Flight Speed” as Numeric Response (Y), and Select all inputs as Continuous Predictors (X). SigmaXL® V6 currently includes Multiple Regression but does not include Best Subsets or Stepwise Regression. However, you can easily add or remove terms from the model using Recall SigmaXL Dialog. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

458

Advanced Process Modeling Flight Regression Example Model Selection (cont.)

The VIF for temp indicates it should be removed from the model.

Variance Inflation Factor (VIF) detects Correlation among predictors. •  VIF = 1 indicates no relation among predictors •  VIF > 1 indicates predictors are correlated to some degree •  VIF between 5 and 10 indicates Regression Coefficients are poorly estimated and are unacceptable.

Do you notice any similarities here? A foreign column has appeared, labeled VIF, this indicates if a high Correlation among inputs exists. Temp has a high VIF, so we will remove it.

The VIF values are NOW acceptable. Evaluate the P-values: •  If p > 0.05, the term(s) should be removed from the Regression.

Remove Altitude, re-run model.

Use “Recall SigmaXL Dialog” and remove the “Temp” variable. Note that “Altitude” now has a P-Value > 0.05. Again use “Recall SigmaXL Dialog” and remove “Altitude”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

459

Advanced Process Modeling Flight Regression Example Model Selection (cont.)

The P-value for Turbine Angle is P > 0.05 which indicates it should be removed and re-run.

Re-run the Regression

After removing “Altitude” from the model we now see that “Turbine Angle” is not statistically significant.

Shown here is the entire Regression output for a complete discussion of the final Multiple Linear Regression model. We have 2 predictor variables and all are statistically significant. Also shown above is a portion of the residuals report showing a high leverage observation and large standardized residual. If possible these data points should be examined. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

460

Advanced Process Modeling Flight Regression Example Residual Analysis

How do we do this? Graph it and use the appropriate commands to analyze.

Now having a final model, it is VITAL to confirm the residuals are correct and the model is valid. Select the “Mult Reg Residuals” worksheet. It appears our model is valid and the Residuals are satisfactory! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

461

Advanced Process Modeling At this point, you should be able to: §  Perform Non-Linear Regression Analysis §  Perform Multiple Linear Regression Analysis (MLR) §  Examine Residuals Analysis and understand its effects

You have now completed Improve Phase – Advanced Process Modeling.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

462

Lean Six Sigma Black Belt Training

Improve Phase Designing Experiments

Now we are going to continue with the Improve Phase “Designing Experiments”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

463

Designing Experiments Overview Within this module we will provide an introduction to Design of Experiments, explain what they are, how they work and when to use them.

W W eelco lcom m ee    to to    Im Im ppro rovvee PPro roce cessss    M Mooddeelin lingg :  :  RReegg rreessssio ionn AA ddvvaa nnce cedd    PPro roce cessss    M Mooddeelin lingg :  :   M LR M LR

Rea Reasons  for  Experiments sons  for  Experiments

D Deessig ig nnin ingg    Ex Ex ppeerim rim eennts ts

GG ra raphical  A phical  Analysis nalysis

Ex Ex ppeerim rim eennta ta l  l  M Meeth thooddss

DO DO E  Methodolog E  Methodologyy

Fu Full   ll  Fa Fa cto ctorria ia l  l  Ex Ex ppeerim rim eennts ts Fra Fra ctio ctionnaa l  l  Fa Fa cto ctorria ia l  l   Ex Ex ppeerim rim eennts ts W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Project Status Review

• U n d e r s ta n d   o u r   p r o b le m   a n d   it’ s   im p a ct   o n   th e   b u s in e s s .   (D e fin e ) • Es ta b lis h e d   fir m   o b je ctiv e s / g o a ls   fo r   im p r o v e m e n t.   (D e fin e ) • Q u a n tifie d   o u r   o u tp u t   ch a r a cte r is tic.   (D e fin e ) • V a lid a te d   th e   m e a s u r e m e n t   s y s te m   fo r   o u r   o u tp u t   ch a r a cte r is tic.   (M e a s u r e ) • Id e n tifie d   th e   p r o ce s s   in p u t   v a r ia b le s   in   o u r   p r o ce s s .   (M e a s u r e ) • N a r r o w e d   o u r   in p u t   v a r ia b le s   to   th e   p o te n tia l   “ X ’ s ” th r o u g h   S ta tis tica l   A n a ly s is .   (A n a ly z e ) • S e le cte d   th e   v ita l   fe w   X ’ s   to   o p tim iz e   th e   o u tp u t   r e s p o n s e (s ).   (Im p r o v e ) • Q u a n tifie d   th e   r e la tio n s h ip   o f   th e   Y ’ s   to   th e   X ’ s   w ith   Y = f(x ).   (Im p r o v e )

Keep an eye on where you’ve been!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

464

Designing Experiments Six Sigma Strategy

This is reoccurring awareness. By using tools we filter the variables of defects. When talking of the Improve Phase in the Six Sigma methodology we are confronted by many Designed Experiments; transactional, manufacturing, research. Reasons for Experiments Th e   A n a ly z e   P h a s e   n a rro w e d   d o w n   th e   m a n y   in p u ts   to   a   critica l   fe w ,   n o w   it   is   n e ce s s a ry   to   d e te rm in e   th e   p ro p e r   s e ttin g s   fo r   th e   v ita l   fe w   in p u ts   b e ca u s e : –

Th e   v ita l   fe w   p o te n tia lly   h a v e   in te ra ctio n s .

–

Th e   v ita l   fe w   w ill   h a v e   p re fe rre d   ra n g e s   to   a ch ie v e   o p tim a l   re s u lts .

–

C o n firm   ca u s e   a n d   e ffe ct   re la tio n s h ip s   a m o n g   fa cto rs   id e n tifie d   in   a n a ly z e   p h a s e   (e .g .   re g re s s io n )

U n d e rs ta n d in g   th e   re a s o n   fo r   a n   e x p e rim e n t   ca n   h e lp   in   s e le ctin g th e   d e s ig n   a n d   fo cu s in g   th e   e ffo rts   o f   a n   e x p e rim e n t. R e a s o n s   fo r   e x p e rim e n tin g   a re : –

P ro b le m   S o lv in g     (Im p ro v in g   a   p ro ce s s   re s p o n s e )

–

O p tim iz in g     (H ig h e s t   y ie ld   o r   lo w e s t   cu s to m e r   co m p la in ts )

–

R o b u s tn e s s     (C o n s ta n t   re s p o n s e   tim e )

–

S cre e n in g     (Fu rth e r   s cr e e n in g   o f   th e   critica l   fe w   to   th e   v ita l   fe w   X ’ s )

Desig n  you’re where  y going ou’re  g-oing -­‐ be   s ure   et   there! Design where be  sure youy ou   getg there!! Designs of Experiments help the Belt to understand the cause and effect between the process output or outputs of interest and the vital few inputs. Some of these causes and effects may include the impact of interactions often referred to synergistic or cancelling effects. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

465

Designing Experiments Desired Results of Experiments Designed experiments allows us to describe a mathematical relationship between the inputs and outputs. However, often the mathematical equation is not necessary or used depending on the focus of the experiment.

P ro b le m   S o lv in g – Elimina te  defective  products  or  services. – Reduce  cycle  time  of  ha ndling  tra nsa ctiona l  processes. O p tim iz in g – Ma thema tica l  model  is  desired  to move  the  process  response. – O pportunity  to  meet  differing  customer  requirements  (specifica tions  or   VO C ). R o b u s t   D e s ig n – Provide  consistent  process  or  product  performa nce.   – Desensitiz e  the  output  response(s)  to  input  va ria ble  cha ng es  including   N O IS E  va ria bles. – Desig n  processes  knowing  which  input  va ria bles  a re  difficult  to   ma inta in. S cre e n in g – Pa st  process  data  is  limited  or  sta tistica l  conclusions  prevented  g ood   na rrowing  of  critica l  fa ctors  in  A na lyz e  Pha se

When  iti t  rains rains  it i t  PPORS!! OR S ! When DOE Models vs. Physical Models Here we have models that are the result of designed experiments. Many have difficulty determining DOE models from that of physical models. A physical model includes: biology, chemistry, physics and usually many variables, typically using complexities and calculus to describe. The DOE model doesn’t include any variables or complex calculus: it includes most important variables and shows variation of data collected. DOE will focus on the specific region of interest.

What are the differences between DOE modeling and physical models? –  A physical model is known by theory using concepts of physics, chemistry, biology, etc... –  Physical models explain outside area of immediate project needs and include more variables than typical DOE models. –  DOE describes only a small region of the experimental space.

The objective is to minimize the response. The physical model is not important for our business objective. The DOE Model will focus in the region of interest.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

466

Designing Experiments Definition for Design of Experiments D e s ig n   o f   Ex p e r im e n ts (D O E)   is   a   s cie n tific   m e th o d   o f   p la n n in g   a n d   co n d u ctin g   a n   e x p e rim e n t   th a t   w ill   y ie ld   th e   tru e   ca u s e -­‐a n d -­‐e ffe ct   re la tio n s h ip   b e tw e e n   th e   X   v a ria b le s   a n d   th e   Y   v a ria b le s   o f   in te re s t. D O E   a llo w s   th e   e x p e rim e n te r   to   s tu d y   th e   e ffe ct   o f   m a n y   in p u t   v a ria b le s   th a t   m a y   in flu e n ce   th e   p ro d u ct   o r   p ro ce s s   s im u lta n e o u s ly ,   a s   w e ll   a s   p o s s ib le   in te ra ctio n   e ffe cts   (fo r   e x a m p le   s y n e rg is tic   e ffe cts ).   Th e   e n d   re s u lt   o f   m a n y   e x p e rim e n ts   is   to   d e s crib e   th e   re s u lts   a s   a   m a th e m a tica l   fu n ctio n .   y   =   f   (x ) Th e   g o a l   o f   D O E   is   to   fin d   a   d e s ig n   th a t   w ill   p ro d u ce   th e   in fo rm a tio n   re q u ire d   a t   a   m in im u m   co s t.

Design of Experiment shows the cause and effect relationship of variables of interest X and Y. By way of input variables, designed experiments have been noted within the Analyze Phase then are executed in the Improve Phase. DOE tightly controls the input variables and carefully monitors the uncontrollable variables.

Properly designed DOE’s are more efficient experiments.

One Factor at a Time is NOT a DOE Let’s assume a Belt has found in the Analyze Phase that pressure and temperature impact his process and no one knows what yield is achieved for the possible temperature and pressure combinations.

O n e   Fa cto r   a t   a   Tim e (O FA T)   is   a n   e x p e rim e n ta l   s ty le   b u t   n o t   a   p la n n e d   e x p e rim e n t   o r   D O E. Th e   g ra p h ic   s h o w s   y ie ld   co n to u rs   fo r   a   p ro ce s s   th a t   a re   u n k n o w n   to   th e   e x p e rim e n te r.     Yield Contours Are Unknown To Experimenter

75

Pressure (psi)

80

Trial 1 2 3 4 5 6 7

Temp 125 125 125 125 125 130 120

Press 30 31 32 33 34 33 33

Yield 74 80 85 92 86 85 90

135 85 If a Belt inefficiently did a One 6 130 Factor at a Time experiment 90 1 3 2 5 O ptimum  identified 4 125 (referred to as OFAT), one with  O FA T 95 120 7 variable would be selected to change first while the other True  O ptimum  available variable is held constant, 34 35 30 31 32 33 with  DO E once the desired result was Temperature (C) observed, the first variable is set at that level and the second variable is changed. Basically, you pick the winner of the combinations tested.

The curves shown on the graph above represent a constant process yield if the Belt knew the theoretical relationships of all the variables and the process output of pressure. These contour lines are familiar if you’ve ever done hiking in the mountains and looked at an elevation map which shows contours of constant elevation. As a test we decided to increase temperature to achieve a higher yield. After achieving a maximum yield with temperature, we then decided to change the other factor, pressure. We then came to the conclusion the maximum yield is near 92% because it was the highest yield noted in our 7 trials. With the Six Sigma methodology, we use DOE which would have found a higher yield using equations. Many sources state that OFAT experimentation is inefficient when compared with DOE methods. Some people call it hit or miss. Luck has a lot to do with results using OFAT methods. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

467

Designing Experiments Types of Experimental Designs DOE is iterative in nature and may require more than one experiment at times. As we learn more about the important variables, our approach will change as well. If we have a very good understanding of our process maybe we will only need one experiment, if not we very well may need a series of experiments. Fractional Factorials or screening designs are used when the process or product knowledge is low. We may have a long list of possible input variables (often referred to as factors) and need to screen them down to a more reasonable or workable level. Full Factorials are used when it is necessary to fully understand the effects of interactions and when there are between 2 to 5 input variables. Response surface methods (not typically applicable) are used to optimize a response typically when the response surface has significant curvature. Value Chain Full factorial designs are generally noted as 2 to the k where k is number of input variables or factors and 2 is the number of levels all factors used. In the table, two levels and four factors are shown; by using the formula, how many runs would be involved in this design? 16 is the answer, of course.

LSS Black Belt Manual XL v11

Th e  g en era l  n o ta tio n  u s ed  to  d es ig n a te  a  fu ll  fa cto ria l   d es ig n  is  g iv en  b y :

•W h ere  k  is  th e   n u m b er  o f  in p u t  v a ria b les  o r  fa cto rs . – 2  is  th e  n u m b er  o f   “ lev els ” th a t  w ill  b e  u s ed  fo r  ea ch   fa cto r. • Q u a n tita tiv e  o r  q u a lita tiv e  fa cto rs  ca n  b e  u s ed .

© 2013 e-Careers Limited

468

Designing Experiments Visualization of 2 Level Full Factorial Let’s consider a 2 squared design which means we have 2 300 levels for 2 factors. The factors Temp of interest are temperature and 350 2 pressure. There are several 500 ways to visualize this 2 level Press Full Factorial design. In 600 Uncoded levels for factors experimenting we often use what’s called coded variables. Coding simplifies the notation. T P T*P The low level for a factor is -1 -1 +1 minus one, the high level is plus +1 -1 -1 one. Coding is not very friendly -1 +1 -1 when trying to run an +1 +1 +1 experiment so we use uncoded Coded levels for factors or actual variable levels. In our example 300 degrees is the low level, 500 degrees is the high level for temperature. 2

(+1,+1)

(-1,+1)

600

Press

500

(+1,-1)

(-1,-1) 300F

Temp

350F

Fo u r   e x p e rim e n ta l   ru n s : • Te m p   =   3 0 0 ,   P re s s   =   5 0 0 • Te m p   =   3 5 0 ,   P re s s   =   5 0 0 • Te m p   =   3 0 0 ,   P re s s   =   6 0 0 • Te m p   =   3 5 0 ,   P re s s   =   6 0 0

Back when we had to calculate the effects of experiments by hand it was much simpler to use coded variables. Also when you look at the prediction equation generated you could easily tell which variable had the largest effect. Coding also helps us explain some of the math involved in DOE. Fortunately for us, SigmaXL® calculates the equations for both coded and non-coded data.

Graphical DOE Analysis - The Cube Plot

LSS Black Belt Manual XL v11

C o n s id er   a   2 3 d e s ig n   o n   a   ca ta p u lt... 8.2

A

4.55

Run Start Number Angle 3.35

Stop Angle

The representation here has two cubed designs and 2 levels of three factors and shows a treatment combination table using coded inputs level settings. The table has 8 experimental runs. Run 5 shows start angle, stop angle very low and the fulcrum relatively high.

1.5

5.15

2.4

Fulcrum 2.1

Start Angle

0.9

B

C

Response

Stop Angle

Fulcrum

Meters Traveled

1

-­‐1

-­‐1

-­‐1

2.10

2

1

-­‐1

-­‐1

0.90

3

-­‐1

1

-­‐1

3.35

4

1

1

-­‐1

1.50

5

-­‐1

-­‐1

1

5.15

6

1

-­‐1

1

2.40

7

-­‐1

1

1

8.20

8

1

1

1

4.55

W h a t   a re   th e   in p u ts   b e in g   m a n ip u la te d   in   th is   d e s ig n ? H o w   m a n y   ru n s   a re   th e re   in   th is   e x p erim e n t?    

© 2013 e-Careers Limited

469

Designing Experiments Graphical DOE Analysis - The Cube Plot (cont.) The Main Effects Plot shown here displays the effect that the input values have on the output response. The Y axis is the same for each of the plots so they can be compared side by side. Which has the steepest Slope? What has the largest impact on the output?

Hint: Check the slope!!

Answer > Fulcrum

Main Effects Plots’ Creation In order to create the Main Effects Plot we must be able to calculate the average response at the low and high levels for each Main Effect. The coded values are used to show which responses must be used to calculate the average Let’s review what is happening on this slide. How many experimental runs were operated with the start angle at the high level or 1. The answer is 4 experimental runs shows the process to run with the start angle at the high level. The 4 experimental runs running with the start angle at the high level are run number 2, 4, 6 and 8. If we take the 4 distances or process output and take the average, we see the average distance when the process had the start angle running at the high level was 2.34 meters. The second dot from the left in the Main Effects Plots shows the distance of 2.34 with the start angle at a high level.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

470

Designing Experiments Interaction Definition

Interactions occur when variables act together to impact the output of the process. Interactions plots are constructed by plotting both variables together on the same graph. They take the form of the graph below. Note that in this graph, the relationship between variable “A” and Y changes as the level of variable “B” changes. When “B” is at its high (+) level, variable “A” has almost no effect on Y. When “B” is at its low (-) level, A has a strong effect on Y. The feature of interactions is non-parallelism between the two lines.

Degrees of Interaction Effect Degrees of interaction can be related to nonparallelism and the more non-parallel the lines are the stronger the interaction.

S ome Interaction High

Y

Low

N o  Interaction BB+ B+

Full  Reversal

High

High

BY

Low

B+

B-

Y B+ Low

+ + + A A A A common S trong  Interaction Moderate  Reversal misunderstanding is High High that that the lines BBmust actually cross each other for an Y Y interaction to exist B+ but that’s NOT true. B+ B+ Low Low The lines may cross + + A A at some level OUTSIDE of the experimental region, but we really don’t know that. Parallel lines show absolutely no interaction and in all likelihood will never cross.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

471

Designing Experiments Interaction Plot Creation Calculating the points to plot the interaction is not as straight forward as it was in the Main Effects Plot. Here we have four points to plot and since there are only 8 data points each average will be created using data points from 2 experimental runs. This plot is the interaction of Fulcrum with Start Angle on the distance. Starting with the point indicated with the green arrow above we must find the response data when the fulcrum is set low and start angle is set high (notice the color coding SigmaXL® uses on the right side of the chart). The point indicated with the purple arrow is where fulcrum is set high and start angle is high. Take a few moments to verify the remaining two points plotted. Interaction Plot (data means) for Distance 6.5

-1 1

5.5

Mean

Start Angle

4.5 3.5 2.5

(4 .5 5  +  2 .4 0 )/ 2  =  3 .4 8

1.5

(0 .9 0  +  1 .5 0 )/ 2  =  1 .2 0 Run # 1 2 3 4 5 6 7 8

-1

Fulcrum

Start Angle Stop Angle -­‐1 -­‐1 1 -­‐1 -­‐1 1 1 1 -­‐1 -­‐1 1 -­‐1 -­‐1 1 1 1

1

Fulcrum -­‐1   -­‐1 -­‐1 -­‐1 1 1 1 1

Distance 2.10 0.90 3.35 1.50 5.15 2.40 8.20 4.55

Let’s review what is happening here. The dot indicated by the green arrow is the Mean distance when the fulcrum is at the low level as indicated by a -1 and when the start angle is at the high level as indicated by a 1. Earlier we said the point indicated by the green arrow had the fulcrum at the low level and the start angle at the high level. Experimental runs 2 and 4 had the process running at those conditions so the distance from those two experimental runs is averaged and plotted in reference to a value of 1.2 on the vertical axis. You can note the red dotted line shown is for when the start angle is at the high level as indicated by a 1.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

472

Designing Experiments Graphical DOE Analysis - The Interaction Plots Based on how many factors you select SigmaXL® will create a number of interaction plots. Here there are 3 factors selected so it generates the 3 interaction plots. These are referred to as 2way interactions.

SigmaXL® also plots the mirror images, just in case it is easier to interpret with the variables flipped. These mirror images present the same data but visually may be easier to understand.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

473

Designing Experiments DOE Methodology

1 . D e fin e   th e   p ra ctica l   p ro b le m 2 . Es ta b lis h   th e   e x p e rim en ta l   o b je ctiv e 3 . S e le ct   th e   o u tp u t   (res p o n s e )   v a ria b le s 4 . S e le ct   th e   in p u t   (in d e p e n d e n t)   v a ria b le s 5 . C h o o s e   th e   le v e ls   fo r   th e   in p u t   v a ria b le s 6 . S e le ct   th e   e x p erim e n ta l   d e s ig n 7 . Ex e cu te   th e   e x p e rim e n t   a n d   co llect   d a ta 8 . A n a ly z e   th e   d a ta   fro m   th e   d e s ig n e d   e x p e rim e n t   a n d   d ra w   s ta tis tica l   co n clu s io n s 9 . D ra w   p ra ctica l   s o lu tio n s 1 0 .R e p lica te   o r   v a lid a te   th e   e x p e rim e n ta l   re s u lts   1 1 .Im p le m e n t   s o lu tio n s

Generate Full Factorial Designs in SigmaXL® It is easy to generate Full Factorial Designs in SigmaXL®. Follow the command path shown here. This is the Factorial/ Screening Design dialog. The next slide will explain the different options available to you through this dialog box. In the “Select Design” drop down selection, you can choose full factorial or fractional factorial designs. Resolution III designs are screening designs and should be used with caution. Resolution IV designs can be tricky because there are aliased two-way interactions. It is best, if possible, to use Resolution V or higher designs. These design options will be discussed in detail later.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

474

Designing Experiments Create Three Factor Full Factorial Design

Let’s create a three factor Full Factorial Design using the SigmaXL® command shown at the top of the slide. The design we selected will give us all possible experimental combinations of 3 factors using 2 levels for each factor. Be sure to change the “Number of factors:” to 3. Also be sure not to select the “8-Run, 2**3, FullFactorial” line within the “Designs” box. In the “Randomize Runs” box, one can change the order of the experimental runs. To view the design in standard order (not randomized for now) be sure to uncheck the default of “Randomize Runs”. “Un-checking” means no checkmark is in the white box next to “Randomize Runs”. Now, we need to enter the names of the three factors as well as the “Low” and “High” values that we want as levels. Remember when we discussed noncoded levels? The process settings of 140 and 180 for the start angle are examples of noncoded levels.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

475

Designing Experiments Three Factor Full Factorial Design Here is the worksheet SigmaXL® creates. If you had left the “Randomize Runs” selection checked, your design would be in a different order than shown. Notice the structure of the last 3 columns where the factors are shown. The first factor, Start Angle, goes from low to high as you read down the column. The second factor, Stop Angle, has 2 low then 2 high all the way down the column and the third factor, Fulcrum, has 4 low then 4 high. Notice the structure just keeps doubling the pattern. If we had created a 4 factor Full Factorial Design the fourth factor column would have had 8 rows at the low setting then 8 rows at the high setting. You can see it is very easy to create a Full Factorial Design. This standard order as we call it is not however the recommended order in which an experiment should be run. We will discuss this in detail as we continue through the modules.

Hold on! Here we go….! One warning to you as a new Belt using SigmaXL®… never copy, paste, delete or move DOE columns, SigmaXL® may not recognize the design you are attempting to use. Is our experiment done? Not at all. The process must now be run at the 8 experimental set of conditions shown above and the output or outputs of interest must be recorded yellow column(s). After we have collected the data we will then analyze the experiment. Remember the 11 step DOE methodology from earlier?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

476

Designing Experiments At this point, you should be able to: § 

Determine the reason for experimenting

§ 

Describe the difference between a physical model and a DOE model

§ 

Explain an OFAT experiment and its primary weakness

§ 

Shown Main Effects Plots and interactions, determine which effects and interactions may be significant

§ 

Create a Full Factorial Design

You have now completed Improve Phase – Designing Experiments.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

477

Lean Six Sigma Black Belt Training

Improve Phase Experimental Methods

Now we will continue with the Improve Phase “Experimental Methods”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

478

Experimental Methods Experimental Methods Within this module we will go through a basic introduction to Designing Experiments

Welc Welcome  to  Improve ome  to  Improve PProc roces esss    M Modeling odeling:  :  RReg egres resssion ion Advanc Advanced   ed  PProc roces esss    M Modeling odeling:  :   ML R ML R Des Desig igning ning    EE xperiments xperiments

Methodology Methodology

EE xperimental   xperimental  M Methods ethods

CC ons onsiderations iderations

FFull   ull  FFac actorial   torial  EE xperiments xperiments

SS teps teps

FFrac ractional   tional  FFac actorial   torial  EE xperiments xperiments Wrap   Wrap  UUp   p  & &  Ac  Action   tion  IItems tems

DOE Methodology In this module we will describe the 11 step DOE methodology some basic concepts and lots of fun and exciting terminology. Once again great content for dinner conversation later tonight!

1 . D e fin e   th e   P ra ctica l   P ro b le m 2 . Es ta b lis h   th e   Ex p e rim e n ta l   O b je ctiv e 3 . S e le ct   th e   O u tp u t   (re s p o n s e )   V a ria b le s 4 . S e le ct   th e   In p u t   (in d e p e n d e n t)   V a ria b le s 5 . C h o o s e   th e   Le v e ls   fo r   th e   in p u t   v a ria b le s 6 . S e le ct   th e   Ex p e rim e n ta l   D e s ig n 7 . Ex e cu te   th e   e x p e rim e n t   a n d   C o lle ct   D a ta 8 . A n a ly z e   th e   d a ta   fro m   th e   D e s ig n e d   Ex p e rim e n t   a n d   d ra w   S ta tis tica l   C o n clu s io n s 9 . D ra w   P ra ctica l   S o lu tio n s 1 0 .R e p lica te   o r   v a lid a te   th e   e x p e rim e n ta l   re s u lts   1 1 .Im p le m e n t   S o lu tio n s

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

479

Experimental Methods Questions to Design Selection

So you’ve decided to use Designed Experiments. Shown here are ten basic Project Management considerations before running any experiment. This is obviously not an exhaustive list, but certainly some important questions to consider and answer. What is behind some of these questions? Let’s briefly discuss a few aspects individually. 1.  Access to a process is necessary for proper monitoring and execution of a project. If restricted access for whatever reason exists, then work around must exist. 2.  If the team members or subject matter experts aren’t fully involved, then potential conflicts or unrealistic designs may be awaiting you for a poor experiment. 3.  If the Process Owners and stakeholders are unknown to you before execution of an experiment rude awakenings such as cancellations, scheduling conflicts and other nightmares can occur. 4.  No one wants to be told what will happen to the process they are managing so if you don’t involve them in the experimental design even if it involves reviewing the team’s designed experiment, how do you expect cooperation? 5.  If the Process Owners don’t understand what your DOE is, how can they assist you? 6.  Does your DOE intend to make a wide range of quality product or potentially produce an unacceptable product in the quest to improve the process? If the Process Owner has never known what your DOE intentions were, how can they not be upset if they are surprised by the results of the DOE? 7.  Time and money impact scheduling, randomization, testing concerns. All of these must be considered especially when using the actual process. 8.  It is often desirable to run DOE’s in a pilot plant or facility but this is not often the case. If a pilot facility is to be used, do the results match the process when translated outside of the laboratory? 9.  Noise variables cannot be controlled, by definition, but if ambient weather is considered to have an effect on your process, why would you execute an experiment when a cold or warm front is passing through your area. This is one example of a known disturbance being designed around. 10.  Manage your project to know if the DOE is intended to stretch the boundaries of conceived product creation or work well within a small experimental area. There are many considerations to consider. Often learning comes through experience so if you are unsure about your future experiment in this project or another, consult with mentors or Six Sigma belts. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

480

Experimental Methods Questions to Design Selection (cont.)

These questions need be answered before running an experiment.

DOE Methodology Step 1 First define the problem in a practical sense. Will we achieve all that is necessary? Might it require multiple experiments? Notice an example of this shown here.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

481

Experimental Methods DOE Methodology Step 2 In Step 2, we have to determine the critical characteristics and the desired outcome. This gives us our critical characteristic.

DOE Methodology Step 3 Step 3 is knowing that a DOE is going to be performed, does it makes sense to go an extra mile? Let’s get our money’s worth by measuring more than one output if it could benefit us in any way.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

482

Experimental Methods DOE Methodology Step 4 Step 4 is to select the Input or independent Variables. At this point you should have a decent understanding of the variables that need to be explored as a result of the work accomplished in the previous phases.

DOE Methodology Step 5 Step 5 is to choose the levels for the input variables. The factor levels must be considered to create the desired change in the output response as identified in Step 3. Poor choices for input variable level settings could very well render an experiment useless so be smart.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

483

Experimental Methods DOE Methodology Step 5 (cont.) Do not set the levels too wide, this may cause our experiment to lose very valuable output response. Making an assumption by way of drawing what you have in your mind of what it will look like, helps a great deal.

Be aware you do not want to set the factor levels too low either. We could be shown no difference in output to input relationship.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

484

Experimental Methods DOE Methodology Step 5 (cont.) Input variable level settings should be set far enough apart to detect a difference in the response and to have enough statistical confidence in the change of the output relative to the experimental noise. Assume this graphic was a sketch generated from our basic understanding of the theory. We don’t know exactly what factor setting would produce the output response but we do know the general shape of the curve. Notice that we stayed away from the sharp peak. It is very easy to slide off such a steep peak, unless your process controls are very tight it would be better to find the nice robust region where the output response is high but flat, meaning that the factor settings can change a bit, but it does not have much effect on the output response. If the concern for spending too much time on this comes up, also, consider how many defects are taken in when the statistical significance is deemed inadequate. You might think we have spent too much time on just setting the levels for the input variables or factors in your experiment. However, consider the learning of others who have had to go back to their Process Owners or Champions and explain that no factors were deemed statistically significant because the design was inadequate. DOE Methodology Step 6 Step 6 is to select the Experimental Design.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

485

Experimental Methods DOE Methodology Step 6 (cont.) Step 6 involves selecting the Experimental Design. DOE’s can be designed in many ways but balanced and orthogonal designs are highly encouraged. SigmaXL® will always design a balanced and orthogonal design if you use the program to design your experiment.

Balanced  and  orthog onal  desig ns  are  hig hly  encourag ed  and  the   definition  of  balanced  and  orthog onal  is  covered  in  a  later  module. C enter  Points  are  used  for  investig ating  curvature  and  advanced   desig ns.    C enter  Points  are  covered  in  a  later  module. Blocking  can  be  used  to  account  for  noise  variables  and  is  covered  in  a   later  module.

I’m  keeping k eepingout   out   the   N oise   coach!! I’m the Noise coach!!!

Remember our advice that subject matter experts along with your team members should pay attention to their experience and the previously gathered and analyzed data. If curvature is suspected, center points are used to confirm if curvature exists within the experimental region. Remembering that noise variables can’t be controlled but managed around, blocking is a technique for managing your experiment around noise variables considered of importance. Remember, you are interested in understanding the effects and interactions of your controlled variables so you want statistical confidence. Randomization has an impact on your statistical confidence because your experimental Noise is spread across the runs. What would happen if another unknown significant variable changed halfway during our experiment? It is possible that an unknown significant variable such as machine warm up time could get confused with the C variable because without randomization all the low levels would be generated first and then all the high levels.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

486

Experimental Methods DOE Methodology Step 6 (cont.) Determining sample size is very similar to what we did in the Analyze Phase. There are a few distinctions. Much of the values are self-explanatory. As in the Analyze Phase, we are typically solving for the number of replicates, but you can work the numbers backwards as we did before and estimate how big an effect could be detected.

Select the number of replicates to achieve the accuracy that you require for your DOE. Ensure Randomize Runs is unchecked. This will simplify the interpretation of the worksheet.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

487

Experimental Methods DOE Methodology Step 6 (cont.) A rep is a replication which is an independent observation of the run that represents variation from experimental run to experimental run. A replication is NOT a duplicate or a repeat. Look at the two designs shown here. The first is a single replicate design, which means there is only one value for each unique experimental run. The terminology is a bit confusing, but don’t worry. The replicated design has double the runs. The design is fully randomized whenever possible but the above are shown in standard order to make the worksheets easier to interpret. Notice how experimental run #1 and #9 have the three factors which are start angle, stop angle and fulcrum, running with the same combination of levels and then experimental run #9 is a replicate of run #1.

LSS Black Belt Manual XL v11

Replication Single Replicate Design

Replicated Design (2)

© 2013 e-Careers Limited

488

Experimental Methods DOE Methodology Step 6 (cont.)

DOE Methodology Step 7 Step 7 is to Execute the Experiment and Collect Data.

7 . Ex e cu te   th e   Ex p e r im e n t   a n d   C o lle ct   D a ta • • •

• •

•

Discuss  the  experimenta l  scope,  time  and  cost  with  the  process  owners   prior  to  the  experiment. Some  tea m  members  must  be  present  during  the  entire  experiment. A fter  the  experiment  has  started,  are  you  g etting  output  responses  you   expected? – If  not,  quickly  evaluate  for  N oise  or  other  factors  and  consider stopping  or  ca nceling  the  experiment. Use  a  log  book  to  make  notes  of  observations,  other  factor  setting s,  etc. C ommunicate  with  the  opera tors,  technicia ns,  sta ff  about  the   experimental  deta ils  a nd  why  the  experiment  is  being  discussed  b efore   running  the  experiment. – This  communication  ca n  prevent   “helping ” by  the  operators,   technicia ns,  etc.  that  mig ht  da mag e  your  experimental  desig n. A lert  the  la boratory  or  qua lity  technicians  if  your  experiment  will   increa se  the  number  of  samples  arriving  during  the  experiment.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

489

Experimental Methods DOE Methodology Step 8 Step 8 is to Analyze the data from the Designed Experiment and draw Statistical Conclusions.

8 . A n a ly z e   th e   D a ta   fr o m   th e   D e s ig n e d   Ex p e r im e n t   a n d   d r a w   S ta tis tica l   C o n clu s io n s • G raphical  A nalysis  has  already  been  covered  in  the  previous   modules. • Further  analysis  of  “reducing ” the  model  to  the  sig nificant  terms   will  be  covered  in  the  next  module. • Further  analysis  of  “reducing ” the  model  to  the  sig nificant  terms   will  be  covered  in  the  next  module. • The  final  model  fitting  will  occur. • Terms  in  the  final  DO E  equation  will  have  statistical  confidence you  needed. • Diag nose  the  residuals  similarly  to  that  of  Reg ression  A nalysis. • Details  of  this  step  are  covered  in  the  next  module.

DOE Methodology Step 9 Step 9 is to Draw Practical Solutions.

9 . D r a w   P r a ctica l   S o lu tio n s • This  will  be  covered  in  detail  in  the  next  module. • Even  if  terms  or  factors  are  statistically  sig nificant,  for  prac tical   sig nificance  the  term  mig ht  be  removed. • “S tat> DO E> Factorial> Response  O ptimiz er” will  help  the  project  team   find  where  the  vital  few  factors  need  to  be  targ eted  to  achieve   the   desired  output  response. – This  will  be  covered  in  detail  in  the  next  module. • This  step  is  how  the  project  team  determines  the  project’s  potential   success. • Immediately  share  the  results  with  the  process  owner  for  feedbac k  on   implementation  of  the  experimental  results.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

490

Experimental Methods DOE Methodology Step 10 Step 10 is to Replicate or Validate the Experimental Results.

1 0 . R e p lica te   o r   V a lid a te   th e   Ex p e r im e n ta l   R e s u lts • A fter  finding  the  Practical  Results  from  Step  9 ,  verify  the  results: – Set  the  factors  at  the  Practical  Results  found  with  Step  9  and  see   if  the  process  output  responds  as  expected.    This  verification   replicates  the  result  of  the  experiment. – Do  not  forg et  your  model  has  some  error.

DOE Methodology Step 11 And the final step is to Implement Solutions. We spend so much time with the 11 step methodology for a couple of reasons. One, it is easy to get confused or excited about running a Designed Experiment. Two, experiments are easy to design with the help of SigmaXL® but difficult to execute appropriately and achieve statistical results unless you follow a planning approach as we have discussed here. Overall there is a lot that can be overlooked or not done properly, take your time and follow this process, it WILL ensure better results.

1 1 . Im p le m e n t   S o lu tio n s • If  the  objective  of  the  experiment  was  accomplished  and  the  Business   C ase  is  satisfied,  then  proceed  to  the  C ontrol  Plan  which  is  covered   in  the  C ontrol  Phase. • Do  not  just  run  experiments  and  not  implement  the  solutions. • Further  experiments  may  need  to  be  desig ned  to  further  chang e  the   output  to  satisfy  the  Business  C ase. – This  possible  need  for  another  experiment  is  why  we  stated  in   earlier  modules  that  DO E’s  can  be  an  iterative  process.

You will probably not fully appreciate all the comments in the modules of this phase until you have designed, managed, executed and analyzed a few real life experiments for yourself.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

491

Experimental Methods At this point, you should be able to: §  Be able to Design, Conduct and Analyze an Experiment

You have now completed Improve Phase – Experimental Methods.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

492

Lean Six Sigma Black Belt Training

Improve Phase Full Factorial Experiments

Now we will continue in the Improve Phase with “Full Factorials”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

493

Full Factorial Experiments Full Factorial Experiments In this module we will discuss the Full Factorial in detail.

W W eelco lcom m ee    to to    Im Im ppro rovvee PPro roce cessss    M Mooddeelin lingg :  :  RReegg rreessssio ionn AA ddvvaa nnce cedd    PPro roce cessss    M Mooddeelin lingg :  :   M MLR LR D Deessig ig nnin ingg    Ex Ex ppeerim rim eennts ts Ex Ex ppeerim rim eennta ta l  l  M Meeth thooddss Fu Full   ll  Fa Fa cto ctorria ia l  l  Ex Ex ppeerim rim eennts ts Fra Fra ctio ctionnaa l  l  Fa Fa cto ctorria ia l  l   Ex Ex ppeerim rim eennts ts

Mathematical  Models Mathematical  Models Balance  and  O Balance  and  O rthog rthogona onality lity Fit  and  Diag Fit  and  Diagnose  Model nose  Model CC enter  Points enter  Points

W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Why Use Full Factorial Designs Two level Full Factorial designs are the most powerful and efficient set of experiments. They are used to: Investigate multiple factors at only two levels, requiring fewer runs than multi-level designs. To investigate large number of factors simultaneously in relatively few runs. To provide insight into potential interactions. Are frequently used in industrial DOE applications because of simplicity and ease of analysis. To obtain a mathematical relationship between X’s and Y’s. And to determine a numerical, mathematical relationship to identify the most important or critical factors in the experiments.

Ok, let s do some experimenting!!

Full Factorial designs are used when: • 

There are five or fewer factors.

• 

You know the critical factors and need to explain interactions.

• 

Optimizing processes.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

494

Full Factorial Experiments Mathematical Output of Experiments

• T he  end  res ult  of  a  D O E  is  a  mathematical  function  to  des cribe  the   res ults  of  the  experiment. • F or  the  2k  F actorial  des igns  this  module  dis cus s es ,  linear   relations hips  are  covered. • All  models  will  have  s ome  error  as  s hown  by  the  ε in  the  below   equation.

• T he  mathematical  equation  below  is  the  prediction  from  the   experimental  data.  Notice  there  is  no  error  term  in  this  form. ˆ is  the  predicted  output  res pons e  as  a  function  of  the  input   • Y variables  us ed  in  the  experiment.

This may look similar to regression, but the important difference is that DOE is considered true cause and effect because of the controlled nature of experimentation. This is an important tool in manufacturing environments. The only difference between the model equation and the prediction equation shown is that the prediction equation is simplified for describing the data gathered in the experiment and using it to predict future events. Just because you end up with a prediction equation in an experiment does not mean it is a good predictive model. We will discuss this further when we introduce center points.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

495

Full Factorial Experiments Linear Mathematical Model

T he  linear  model  is  s ufficient  for  mos t  indus trial  experimental   objectives . T he  linear  model  can  explain  res pons e  planes  and  twis ted  res pons e  s urfaces   becaus e  of  interactions . – T he  following  is  a  linear  prediction  model  us ed  in  a  two-­‐level  full  or   fractional  factorials .

Surface Plot of % Reacted

Surface Plot of % Reacted

65

65

55

60

% Reacted

% Reacted 1

55 0 -1

Ct

0

-1 1

Cn

1 45

0 -1

T

0

Cn

-1 1

Linear Models are usually sufficient for most industrial experimental objectives. This goes back to the difference between a physical model and a DOE model. Just because we know by theory that the model should not be linear, it may express itself as sufficiently Linear in the particular design space. People can get confused between the concept of curvature and twisted response planes. We do not have enough information (not enough levels for each variable) to describe true curvature. Take a piece of paper which will represent 2 input variables. Lift opposite corners. That is a graphical representation of an interaction. The response plane (paper) is twisted. Now lift up the paper to eye level and rotate until the projection looks like a curved line. We are simply looking at the projection of the twisted plane with Linear Models. There may be true curvature in the real world, we simply can’t describe it with a Linear Model. HOWEVER, in most manufacturing processes the Linear Model is very powerful because of the constrained design space. Draw a box on the paper and hold it up by two opposite corners. Depending on how much twist you give the paper and how big the box is you will either see a curve or not in the defined space. The surface plot on the left has no significant interaction, but both Main Effects are significant. The surface plot on the right shows a significant interaction with T and Cn.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

496

Full Factorial Experiments Quadratic Mathematical Model True curvature can be described using the Quadratic Model. The squared term in the model gives us the ability to describe true curvature. With the ability of describing curvature comes a cost. The experiment gets much bigger. Central composite designs are an example of a Quadratic Model. Here is a surface plot of true curvature in a Quadratic Model. This shape is referred to as a saddle for obvious reasons. Q uadratic  Models  can  be  obtained  with  des igns  not  des cribed  in  this  module. Q uadratic  Models  explain  curvature,  maximums ,  minimums  and  twis ted   maximums  and  minimums  when  interactions  are  active. – T he  following  is  the  quadratic  prediction  model  us ed  in  s ome  res pons e   s urface  models  not  covered  in  this  training. – T he  s impler  2 k   models  do  not  include  enough  information  to  generate   the  Q uadratic  Model.    

Surface Plot of C6

21

16

C6 11

6 -1.5

-1.0

-0.5

A

0.0

0.5

1.0

1.5

0.0 -0.5 -1.0 -1.5

0.5

1.0

1.5

B

Nomenclature for Factorial Experiment The nomenclature for 2 level designs is 2 to the K. If you had an experiment with 3 factors it would be a 2 cubed design. If you simply do the math, that is the number of experimental runs in the basic design.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

497

Full Factorial Experiments Treatment Combinations Treatment combinations, or experimental runs, show how to set the levels for each of the factors. Minuses and plusses can be used to indicate low and high factor level settings, Center Points are indicated with zeros. If the process is evaluated with combinations of the temperature set at 10 and 20 degrees and pressure at 50 and 100 psi, an example of an experimental run or treatment combination would be 20 degrees and 50 psi.

A 22 design has 2 factors at 2 levels.

No, those are 2 X 4 s!!

Meaning - 4 treatment combinations to consider and analyze. Temperature Pressure

10

20

50

1

2

100

3

4

Treatment combination for run number 2 is: Temperature at 20 deg and Pressure at 50 psi.

Standard Order of 2 Level Designs Dr. Frank Yates created this standard order to aid in calculating the effects of each effect by hand. Thank goodness we no longer have to perform hand calculations. It is common to draw a cube for a 2 cubed design as shown.

The Design Matrix for 2k factorials are shown in standard order (not randomized).

The low level is indicated by a - and the high level by a + .

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

498

Full Factorial Experiments Full Factorial Design with 4 Factors Here we have standard notation for 2 to the 4 design and above using 2 cubes, a common representation; now for the low levels of the 4 the factor and one for the high.

Full Factorial Design Let’s walk through and design a 2 cubed design again for practice. You can name the columns A, B and C or any name you’d like. This table created with the factors is referred to as a table of contrasts. The contrast columns are the minus ones and plus ones in the factor columns. In order to calculate contrast columns for interactions, we need the contrast columns for the main factors. Warning, whatever you do, do not change the names of the columns by simply typing over the names. SigmaXL® creates a model that it uses for the analysis later. If it can’t find the column names used to generate the worksheet, it will give an error message.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

499

Full Factorial Experiments Balanced Design Factorial designs should be balanced for proper interpretation of the mathematical equation. An experiment is balanced when each factor has the same number of experimental runs at both high and low levels. Summing the signs of the column contrast should yield a zero. In this example, there are 2 minuses and 2 plusses. Balance simplifies the math necessary to analyze the experiment.

Factorial  Desig ns  should  be  balanced  for  proper  interpretation  of  the   mathematical  equation. A n  experiment  is  balanced  when  each  factor  has  the  same  number  of   experimental  runs  at  both  hig h  and  low  levels. Summing  the  sig ns  of  the  column  contrast  should  yield  a  z ero. Balance  simplifies  the  math  necessary  to  analyz e  the  experiment. – If  you  always  use  the  desig ns  MIN ITA B TM provides,  they  will  always  be   balanced.

1 2 3 4 ∑ Xi

A + + 0

B + + 0

SigmaXL® creates balanced, orthogonal designs. If they aren’t changed, this isn’t a problem.

Orthogonal Design An orthogonal design allows each effect in an experiment to be measured independently, these are vectors which are at 90 degrees to each other. When every interaction for all possible variable pair sums to zero, the design is orthogonal.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

500

Full Factorial Experiments Biomedical Production Example

In  this  example  we  will  walk  throug h  the  1 1  Step  DO E  methodolog y.   The  biomedical  firm  is  attempting  to  increase  the  yield  of  a  specific   protein  expression  for  use  in  research  by  universities  and   pharmaceutical  companies. 1 . D e fin e   th e   P r a ctica l   P r o b le m •Increase  the  yield  by  5 0 %  of  current  production.    The  Measurement  System   A na lysis  for  yield  ha s  been  verified.    The  baseline  for  the  primary  metric  of   yield  is  at  5 0 %.    The  objective  of  the  Project  C ha rter  required   the  team  to   achieve  at  least  a  5 0 %  increase  in  yield. 2 . Es ta b lis h   th e   Ex p e r im e n ta l   O b je ctiv e • Maximiz e  the  yield.

3 . S e le ct   th e   O u tp u t   (re s p o n s e )   V a ria b le s • Y ield  of  protein  expression  is  the  only  output  of  interest. • It  is  desirable  to  chang e  the  yield  from  5 0 %  to  at  least  7 5 %. 4. • • • •

S e le ct   th e   In p u t   (in d e p e n d e n t)   V a ria b le s Temperature   C oncentration C atalyst N oise  and  other  variables  such  as  ambient  room  temperature  and  technician   will  be  recorded  during  the  experiment.

5 . C h o o s e   th e   Le v e ls   fo r   th e   In p u t   V a ria b le s • The  following  levels  were  determined  with  tools  from  the  A nalyz e Phase  such   as  Reg ression,  Box  Plots,  Hypothesis  Testing  and  Scatter  Plots.   The  levels   were  set  far  enoug h  to  attempt  larg e  yield  chang es  to  g et  statistical   confidence  in  our  results. – Temperature  C  (2 5 ,  4 5 )   – C oncentration  %  (5 ,  1 5 ) – C atalyst  (Supplier  A ,  Supplier  B)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

501

Full Factorial Experiments Biomedical Production Example (cont.) When creating the worksheet in SigmaXL® be sure to change the default in the “Number of Replicates” window to 2.

Enter the names of the factors and their levels here in SigmaXL®. This is where these are created so remember to do it here, it will not carry through if you only do it in the worksheet itself. SigmaXL® V6 does not support discrete factors in DOE so the high and low levels must be coded. We recommend 0,1 as shown. Type “Yield” in the “Response Name” as shown. If we had more than one response we would change the “Number of Responses” and label the “Response Names”. You will almost always use the randomization selection when creating designs for real experiments. There are some exceptions that we will cover later in this module. Again, we will use Standard Order to make the worksheet easier to interpret.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

502

Full Factorial Experiments Biomedical Production Example (cont.) In the shaded ‘Yield’ field is where we will place the experimental results.

Select the “3 Factor DOE” worksheet which contains the data shown above. Note that supplier is coded as 0,1. There is no “in between” value for the 2 different suppliers. In an actual experiment you would type in the yield response information in the created worksheet. Over the next several slides we will walk through the analysis. Here we go… We first need to estimate the effects for ALL possible effects in the design, including all main effects and all interaction effects. Then we will decide which ones are important to describing the variation in the data set. We will remove the effects that are not important to describing the variation in the data set and re-run the model with only those effects. This is similar to the work you have already done in Regression Analysis. After we have run the final model fit we will check our Residual Analysis to validate our assumptions, the same as in Regression. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

503

Full Factorial Experiments Biomedical Production Example (cont.) The Pareto Chart shows us the significant effects based on the selected alpha level. At this point, Temperature and the interaction of Temperature with supplier are the significant effects.

Look for the Factorial Fit information. We interpret this based on the same way as we have interpreted as we do any other statistical test. What does this tell us….there are 2 significant effects that should be in this model.

Since we have removed the insignificant factors we need to go back and refit the model. Even though there were only two significant effects we must include all Main Effects in the model that are involved in an interaction.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

504

Full Factorial Experiments Biomedical Production Example (cont>) We need to create some Factorial Plots before evaluating the Residuals. Follow the SigmaXL® path shown here.

The steep slope on a Main Effects Plot means that variable is significant. Flat lines as shown for concentration and supplier indicate they are not significant.

The interaction plot shows you all the plots with the variables you selected in the previous SigmaXL® command. The interaction of interest for our example is temperature with supplier. Here it looks like high temperature with supplier 1 gives the highest yield which in our case is exactly what we want.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

505

Full Factorial Experiments Biomedical Production Example (cont>) Review the fitted Analysis of Variance table. This provides a lot of information that we will explore later in the module, for now notice the P-value.

This shows us our Residual plots for yield. The interpretation is the same as we’ve used in the past for Regression.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

506

Full Factorial Experiments Biomedical Production Example (cont.) The Residuals versus Variables are most important when deciding what level to set an insignificant factor. A typical guideline is a difference of a factor of 3 in the spread of the Residuals between the low and high levels of an insignificant input variable. In this case concentration was not significant, but we still need to make a decision on how to set it for the process. The low level for concentration has a smaller spread of Residuals, but there is not a difference of 3:1. Other considerations for setting the Variable are cost and reducing cycle time.

Step 9 is to draw your Practical Solutions. The Solver Add-in is included in the Microsoft Excel Package. To access it, Click Tools > Add-Ins (Excel 2007: Office Button | Excel Options | Add-Ins > Manage Excel Add-Ins, click Go…). Ensure that the Solver Add-in is checked. If the Solver Add-in does not appear in the Add-ins available list, you will need to re-install Excel to include all add-ins. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

507

Full Factorial Experiments Biomedical Production Example (cont.)

Using Excel’s Solver we will find the optimal predicted response. We will select to be changing cells K26 and K27, the yellow fields. Our optimization will be subject to the following constraints: K27 = Binary L26 = -1

- This limits the options for Supplier to 1 or 0. - This limits the Temp to ensure our maximum of 45, or the coded value 1 - This limits the Temp to ensure our minimum of 25, or the coded value -1

By clicking solve, we are given the optimal result. Please note, we will set Concentration to 5%. Since Concentration is insignificant, we will reduce it to the minimum value to save on cost and potentially to minimize variation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

508

Full Factorial Experiments Biomedical Production Example (cont.) Now that we have completed one example we are going to add to your knowledge base by covering Center Points and run through another example adding further explanation of the statistics as well.

Center Points As you can see in the graphic there may be an unknown hump in the Response Curve, by adding the Center Point it allows us to calculate an additional statistic. If there is significant curvature in the model all we know is that the model is not Linear. We don’t know what it is, just what it is not.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

509

Full Factorial Experiments Center Point Clues Pseudo Center Points are used when there are discrete input variables in the model. The model can be collapsed creating real Center Points if the discrete input variables are not significant. If the desire was to maximize the response (as shown in graphic) then the model doesn’t matter. The model is an important tool to predict output response inside the design space. If the experimenter decides to set up another experiment to continue in the direction indicated, then predicting is not an issue.

A  C enter  Point  is  always  a  g ood  insurance  policy,  but  is  most  effective   when  all  the  input  factors  are  C ontinuous. A  g uideline  is  to  run  2 -­‐4  C enter  Point  runs  distributed  uniformly  throug h   the  experiment  when  all  the  input  factors  are  continuous  in  a  Full  or   Fractional  Factorial. Y

M a x im iz e   R e s p o n s e D o e s   it   m a tte r   th a t   th e   lin e a r   m o d e l   is   in a p p ro p ria te ?

“-”

“c”

“+”

x

Panel Cleaning Example

In  this  example  we  will  walk  throug h  the  1 1  step  DO E  methodolog y for   a  panel  cleaning  machine  using  C enter  Points  in  the  analysis.  The   manufacturing  firm  is  attempting  to  start  up  a  new  panel  cleaning   machine  and  would  like  to  g etting  it  running  quickly.    They  have experience  with  this  type  of  machine,  but  they  do  not  have  experience   with  this  particular  model  of  equipment. 1 . D e fin e   th e   P r a ctica l   P ro b le m • Start  the  new  equipment  as  efficiently  as  possible.  The  need  for  the  new   equipment  was  determined  in  the  A na lyz e  Phase. • A  Measurement  System  A na lysis  has  been  completed  and  modified  to  bring   within  a cceptable  g uidelines.

2 . Es ta b lis h   th e   Ex p e r im e n ta l   O b je ctiv e • Hit  a  targ et  for  W idth  of  4 0  + / -­‐ 5 . • Minimiz e  variation  as  much  as  possible.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

510

Full Factorial Experiments Panel Cleaning Example (cont.) Na2S2O8 is Sodium Persulfate; please 3 . S e le ct   th e   O u tp u t   (r e s p o n s e )   V a r ia b le s use that any time • W idth  of  conductor  is  the  only  response. you see that notation. 4 . S e le ct   th e   In p u t   (in d e p e n d e n t)   V a r ia b le s • Dwell  Time • Temperature • N a 2S2O 8 • The  experts  believe  that  ambient  temperature  and  humidity  will  have   no  effect  on  the  process.  Monitors  will  be  placed  in  the  room  to record  temperature  and  humidity. 5 . C h o o s e   th e   Le v e ls   fo r   th e   In p u t   V a r ia b le s – Dwell  Time  (  4 ,  6 )  minutes – Temperature  (4 0 ,  8 0 )  C – N a 2 S 2 O 8   (1 .8 ,  2 .4 )  g m/ lit

Use the “Panel Cleaning DOE” worksheet You actually know the answer already since the sample size is the same as the previous example and they were both 2 cubed designs. Look at your worksheet and find the Center Point runs. Why are the Center Points uniformly distributed?

Center Points not only tell us something about how well the linear model works, but is also a reality check for our data. By eyeballing the Center Point data as our experiment progressed we can see if anything has effected our experiment that we were not expecting. If your Center Points are dramatically different from each other, you’ve got a problem -- somewhere. They should be fairly close in magnitude, at least within normal variation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

511

Full Factorial Experiments Creating Designs with Center Points You most likely already know how to create a design with Center Points added. Simply go through the usual steps to create a design and include Center Points.

Your design should look different than the one in the illustration because we more likely than not have a different random seed that generated the designs. It is possible that our designs are the same, but trying to calculate the odds of that occurring is not worth the bother. You should have 19 rows in your design, so if you do not, go back and fix it.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

512

Full Factorial Experiments Creating Designs with Center Points Do the same for the Center Point you want in the middle and end of the design. We have color coded our example for ease of understanding. The rows you move most likely will be different. Use Excel’s Sort to sort the worksheet by Run Order (Data>Sort). You should now have a worksheet that has a Center Point at or near the beginning, middle and end. If your original design had the Center Points roughly in those positions, great that saved a little work.

Panel Cleaning Example Let’s continue with the Panel Cleaning Example. Use the “Panel Cleaning DOE” worksheet.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

513

Full Factorial Experiments Panel Cleaning Example (cont.) Analyze the experiment in SigmaXL®. For fun since you’ve already done this once in this module, stop reading and work on your own for a while. When you think you know what should be removed from the model, go ahead and do it.

So how did it go? Looks like the significant effects are Sodium Persulfate, temperature, the interaction of temp with Sodium Persulfate and dwell time in that order of importance.

The P-values from the analysis in the session agree as well.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

514

Full Factorial Experiments Panel Cleaning Example (cont.) Re-fit the model by removing the insignificant factors if you have not already done this. Be sure to generate the necessary Standardized Residual Plots.

Here we are going to define the calculations in the ANOVA table. When working with 2 level designs you will always have 1 degree of freedom for each effect (including interactions) which is calculated as 2 levels minus 1 equals 1 degree of freedom. In the ANOVA table for Main Effects we have 3 degrees of freedom for the 3 Main Effects placed in the model. There is one degree of freedom for the temperature Sodium Persulfate interaction.

The Residual error is broken into 2 sources. The 3 degrees of freedom for lack of fit are from the 3 interaction effects that were removed from the model because they were not significant in explaining the variation of the data. The 10 degrees of freedom come from replication. The 8 runs from the original design generated 8 degrees of freedom, in this case there were 2 replicates minus 1 equals 1 degree of freedom for each run in the design. Add to that 2 degrees of freedom from the Center Points (3 Center Points minus 1 equals 2 degrees of freedom) and we have a total of 10 degrees of freedom for pure error. Pure error can be defined as the failure of things treated alike to act alike which are the replicates. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

515

Full Factorial Experiments Panel Cleaning Example (cont.)

Continuing here with some definitions…. The SS or Sum of Squares calculations are simply an unscaled or unadjusted measure of dispersion or spread of the data. Seq or Sequential Sum of Squares and Adj or Adjusted Sum of Squares are the same for DOE analyses. (There may be differences in Regression Analysis). Adj MS or Adjusted Mean Square takes the Sum of the Squares number and scales it using the number of degrees of freedom for that calculation. Mean Squares are the equivalent of variance. Here we use the F statistic. An F statistic is simply variance divided by variance. In the case of DOE it is the Variance of an effect divided by the variance due to residual error. In this platform, SigmaXL® sums the sum of the squares for certain elements of the model to report in the ANOVA table instead of keeping them separate. The F statistic with respect to the Main Effects is calculated by taking 199.779 and dividing by 1.348 which equals 148.18. The associated P-value is 0.000 which is less than 0.05 so our conclusion is that the model is significant. Notice in this example the curvature is not significant which means our assumption of linearity is good. Also the P-value for lack of fit is not significant. That means the effects we removed from the model really do not belong in the model. If there was significant lack of fit, that would indicate that some of the effects that were removed from the model actually belong in the model. The last to discuss here is the prediction equation. Please note here the coefficients for the Prediction Equation are based on uncoded units. In other words, you can use this equation directly in real units.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

516

Full Factorial Experiments Prediction Equation Take a few minutes to study the equations. They really are simply “plug and chug”. Please note, we have taken liberties with rounding numbers! You won’t actually have to do this by hand because that is exactly what the response optimizer does in SigmaXL®.

Panel Cleaning Example The most interesting thing to look at here is the interaction plot. The temperature with Sodium Persulfate interaction shows there is very little difference in the predicted response as long as Sodium Persulfate is held at the high level. But if the concentration of Sodium Persulfate is lowered, temperature and in particular 40 degrees lowers the width more rapidly than if temperature was set at 80 degrees.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

517

Full Factorial Experiments Panel Cleaning Example (cont.) There are no assumption violations within the plots shown here.

As depicted here the Residuals Versus Factor Plots do NOT show any differences in the variation of the data from the low to the high values.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

518

Full Factorial Experiments Panel Cleaning Example (cont.) Here we will use Excel’s Solver (Data>Solver) to draw some Practical Conclusions. Play with Solver and see what you can do remembering that the original objective was to hit a target of 40 +/- 5 for the width.

Are there other solutions? Explore your options by modifying the constraints in Solver or through experimentation with the Predicted Response Calculator. Solver does an excellent job of optimizing according to the data. What it does not know are all the quirks of your equipment, cost of raw materials, increasing throughput, etc. Is it possible to achieve the target value of 40 with Sodium Persulfate set at the minimum value (to minimize cost)? It looks like we can get close, but we can’t hit the target. We know our lower specification limit is 35 and it looks like we can get to 38 with the Sodium Persulfate at the low level, temp and dwell time high. Is the good enough? Maybe, maybe not. If you knew the spread of the data or variation and it was small you could capitalize on that capability by using 38 as the target instead of 40 and still guarantee your customer they would never see any product with widths smaller than 35. Imagine if you were working with gold or platinum. What effect could that have on the bottom line? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

519

Full Factorial Experiments Panel Cleaning Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

520

Full Factorial Experiments Panel Cleaning Example (cont.) Now we will look at SigmaXL®’s Contour/Surface Plots to visualize the solution set of input variable level settings in order to achieve the desired result. As shown here we generate 3 different graphs as a result of changing the set point for dwell time. The areas highlighted in red (produced manually to aide interpretation) are the solution set for adjusting temperature and Sodium Persulfate to get a predicted response between 35 and 45. This is an alternative to the Response Optimizer.

It’s a wrap……. Fun stuff, right?!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

521

Full Factorial Experiments At this point, you should be able to: §  Understand how to create Balanced and Orthogonal Designs §  Explain how Fit, Diagnose and Center Points factor into an Experiment

You have now completed Improve Phase – Full Factorial Experiments.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

522

Lean Six Sigma Black Belt Training

Improve Phase Fractional Factorial Experiments

Now we will continue with the Improve Phase “Fractional Factorial Designing Experiments”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

523

Fractional Factorial Experiments Fractional Factorial Experiments Within this module we will explore how to conduct a Fractional Factorial Experiment.

Welc Welcome  to  Improve ome  to  Improve PProc roces esss    M Modeling odeling:  :  RReg egres resssion ion Advanc Advanced   ed  PProc roces esss    M Modeling odeling:  :   ML ML RR Des Desig igning ning    EE xperiments xperiments EE xperimental   xperimental  M Methods ethods FFull   ull  FFac actorial   torial  EE xperiments xperiments

Des Designs igns CC reation reation

FFrac ractional   tional  FFac actorial   torial  EE xperiments xperiments Wrap   Wrap  UUp   p  & &  Ac  Action   tion  IItems tems

GGenerators enerators CC onfounding   onfounding  & &    RR es esolution olution

Why Use Fractional Factorial Designs?

Fractional Factorial Designs are a powerful sub-set of Factorial Designs. As the name implies, you may expect they are some fraction of the original Factorial Designs – and you’d be correct. The question is what fraction? We’ve shown two 4 factor designs side by side so you can contrast the two designs. Notice the Fractional Factorial Design requires only a fraction of the experimental runs to evaluate 4 input factors. In this case, it is a half fraction. As with most things in life there is a price to be paid for reducing the number of runs required which we will go through in detail in this module. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

524

Fractional Factorial Experiments Why Use Fractional Factorial Designs (cont.) Fractional Factorial designs are also used to study Main Effects and 2-way interactions if the experimenter and team has good process knowledge and can assume higher order interactions are negligible. There is the cost in a nutshell. In exchange for reducing the overall experiment’s size you will give up the ability to evaluate higher order interactions. It turns out this is a pretty good assumption in many cases. We’ll talk about this more later.

F ractional  F actorial  D es igns  are  als o  us ed  to: •

•

S tudy  Main  E ffects  and  2-­‐way  interactions  if  the  experimenter  and  team  has   good  proces s  knowledge  and  can  as s ume  higher  order  interactions   are   negligible. R educe  time  and  cos t  of  experiments  becaus e  the  number  of  runs  h ave   been  lowered. – As  the  number  of  factors  increas es ,  the  number  of  runs  required   to  run  a  full  2 k factorial  experiment  als o  increas es  (even  without  repeats  or  replicates ) • 3  factors :  2x2x2                  =  8  runs • 4  factors :  2x2x2x2          =  16  runs • 5  factors :  2x2x2x2x2  =  32  runs  etc … .

•

B e  an  initial  experiment  that  can  be  augmented  with  another  frac tion  to   reduce  confounding  and  es timate  factors  of  interes t.

T he   answer   i s   i n   there   The answer is in somewhere!!

there somewhere!!!

Fractional Factorial designs are also used to reduce the time and cost of experiments because the number of runs have been lowered. As the number of factors increases, the number of runs required to run a full 2k factorial experiment also increases (even without repeats or replicates) as you already know. 3 factors: requires 8 runs 4 factors: requires 16 runs 5 factors: requires 32 runs etc…. The number of runs required for a Fractional Factorial will depend on how many factors are included in the design and how much fractioning can be tolerated based on the facts of the process. Fractionals are also used as an initial experiment that can be augmented with another fraction to reduce confounding and estimate factors of interest. We’ll define this as we advance through the module.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

525

Fractional Factorial Experiments Nomenclature for Fractional Factorials The general notation for a Fractional Factorial is similar to that of a Full Factorial. Take a few moments and read through the definitions for the notation. Let’s look at the 2 to the 5 minus 1 example here: How many factors are in the experiment? That is the first number in the exponent or in this case, 5. At this point we are not ready to discuss the resolution since we have not covered it yet.

Th e   g e n e ra l   n o ta tio n   fo r   Fra ctio n a l   Fa cto ria ls   is : – – – –

2R

k  =  number  of  fa ctors  to  be  investig a ted p  =  number  of  fa ctors  a ssig ned  to  a n  intera ction  column  (a lso  ca lled   “deg ree  of  fra ctiona ting ” with  1 = 1 / 2 ,  2 = 1 / 4 ,3 = 1 / 8 ,  etc.) R  =  desig n  resolution  (III,  IV,  V,  etc.).      It  deta ils  a mount  of confounding  to  compa re  desig n  a lterna tives 2 k-­‐p   =  the  number  of  experimenta l  runs

The  example  clarifies  how  to  use  the  nomenclature. • • •

k -p

How  ma ny  fa ctors  in  the  experiment? How  ma ny  runs  if  no  repea ts  or  replica tes? W ha t  fra ctiona l  desig n  is  this  (1 / 8 ,  1 / 4  or  1 / 2 )?

5-1

2V

How many runs if no repeats or replicates? Simply do the math. 2 to the 5 minus 1 is the same as 2 to the fourth which is 8 runs. What Fractional Design is this? Since this design uses only half the number of runs as a Full Factorial with 5 factors it is a half fraction. Half-Fractional Experiment Creation

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

526

Fractional Factorial Experiments Half-Fractional Experiment Creation Having 4 runs can not project 4 factor therefore, this would have 3 degrees of freedom, so the answer is a big fat NO. Why  is  the  des ig n,  s hown  as  orang e  rows ,  c alled  a  “half” frac tion?    T his  is  the  des ig n   jus t  c reated  on  the  previous  s lide.    T his  is  a  half  frac tion  s in c e  a  full  2x 2x 2x 2  fac torial   would  take  16  runs .    With  the  half  frac tion  we  c an  es timate  the   effec ts  of  4  fac tors  in  8   runs .    What  is  the  c os t?    We  los e  the  ability  to  s tudy  the  hig he r  order  interac tion   independently!

Half Fraction: Alias Structure: D = ABC Note D settings are the same as the ABC interaction

A -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1

B -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1

C -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1

D -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1

AxB 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1

AxC 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1

BxC 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1

AxBxC -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1

C ould  we  c reate  a  quarter  frac tion  ex periment  out  of  the  above   matrix  and  s till  s tudy  four  fac tors  at  onc e? Why  or  why  not?

Graphical Representation of Half-Fraction Why would we call this a half fraction? Because half the number of runs is necessary as apposed to that of a Full Factorial. We  have  dis cus s ed  half-­‐fractional  E xperimental  D es igns  for  4  factors : T he  graphical  repres entation  s hows  the  8  runs  we  created  on  the   previous  2   s lides . T op  line  of  previous  s lide

- A +

- A + - C +

B

-

+ C + -

D

+

R emember  that  D  is  confounded  with  the  A B C  interaction  in  this  h alf-­‐fractional   des ig n.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

527

Fractional Factorial Experiments Design Generators Don’t worry – SigmaXL® will take care of this! THANK YOU SigmaXL®!!!!

D es ign   G enerators   a re   a n   e as ier   technique   to   us e   than   to   g enerate   the   F ractional   F actorial   D es igns   by   hand   a s   done   in   the   previous   s lides . D es ign   G enerators   help   us   E AS IL Y   find  the   c onfounding   within   the F ractional   D es ign. A   D es ign   G enerator   is   the   m athematical   definition   for   how   to   beg in   alias ing   a   F ull   F actorial   to   c reate   a   F ractional   F actorial. E xample   of   a   D es ign   G enerator:

Des ig n   G enerator         D  =  A B C T his   m eans   the   D   c olumn   is   the   s ame   a s   the   A B C   interac tion   c olumn;   they   c annot   b e   d is ting uis hed   from   eac h   o ther   s o   a re   c alled  “c onfounded”.

This graph helps us visually draw the conclusion of the data that we already have. We have highlighted in green two boxes and this can very simply be filled in by the data expressed by the generator; A times B times C equals D.

Des ig n   G enerator         D   =   A B C • B ecaus e   of   the   D es ign   G enerator   we   c an   now   fill   out   the   D   c olumn – F or   e ach   row   of   D ,   multiply   the   v alues   in   the   c olumns   of   A ,   B   a nd   C   together   a nd   c reate   the   c olumn   • Y ou   may   c orrectly   s us pect   s ome   2 -­‐factor   interactions   a re   confounded • C reate   c ontras t   c olumns   for   A D,   B D,   C D   us ing   a   s imilar   technique us ed   to   c reate   the   c olumn   for   D A

B -1 1 -1 1 -1 1 -1 1

LSS Black Belt Manual XL v11

C -1 -1 1 1 -1 -1 1 1

AB -1 -1 -1 -1 1 1 1 1

AC 1 -1 -1 1 1 -1 -1 1

BC 1 -1 1 -1 -1 1 -1 1

D

AD

BD

CD

1 1 -1 -1 -1 -1 1 1

© 2013 e-Careers Limited

528

Fractional Factorial Experiments Design Generators (cont.)

SigmaXL® Aliasing This SigmaXL® output gives the summary of what you did on the previous slides much quicker than we can do by hand. The reason we have you did things manually earlier is to being to appreciate and understand the SigmaXL® output generated below the data table after you create a Fractional Factorial design with 4 factors, half fraction with no Center Points or replicates and the number of blocks equal to 1. You should get the same output. Try it. Notice after the design structure an alias structure is indicated. We can see the AB 2-way interaction is Confounded with the CD 2-way interaction meaning we cannot distinguish if the interaction is statistically significant whether it is a result of the AB or CD interaction or a combination.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

529

Fractional Factorial Experiments So What is “Confounding”? C onfounding  is  the  consequence  a n  experimenter  a ccepts  for  not  running  a   Full  Fa ctoria l  Desig n. W hen  using  the  “C onfounding ” or  “A lia s” pa ttern  we  a ssume  tha t  the   hig her  order  intera ctions  in  a  C onfounded  effect  a re  not  sig nifica nt. – S pa rsity  of  effects  principle  indica tes  tha t  hig her  order  intera ctions   a re  very  ra re. • “ W h ile   in te ra ctio n s   a re   im p o rta n t   th e y   d o   n o t   a b o u n d … ,   in te ra ctio n s   th a t   a re   m o re   co m p le x   th a n   th o s e   in v o lv in g   tw o   fa cto rs   a r e   ra re ” Th o m a s   B .   B a rk e r

In  the  past  example,  the  D  fa ctor  wa s  C onfounded  with  the  A BC  3 -­‐w a y   intera ction.    W hen  the  effect  is  a ssig ned  to  D  which  is  C onfounded  with   A BC ,  we  assume  beca use  of  the  spa rsity  of  effects  principle  the   effect  is   entirely  beca use  of  the  D  fa ctor. Remember  when  two  items  such  a s  a n  intera ction  with  a  Ma in  Effect  a re   C onfounded,  one  ca nnot  disting uish  if  the  sta tistica l  sig nifica nce  is  a  result   of  the  Ma in  Effect  or  the  intera ction  or  a  combina tion.

A lia s in g   is   a n o th e r   te rm   fo r   “ C o n fo u n d in g ” . Confounded Effects With Fractionals Using more enhance visuals, here is another Fractional Design structure, notice how the Alias structure A is Confounded with the two way interaction. The light green box indicates this to be true the most obvious.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

530

Fractional Factorial Experiments Experimental Resolution Remember  R  in  the  nomenclature  referenced  the  Resolution. This  useful  visual  aid  remembers  definitions  of  the   C onfounding  desig nated  by  the  Resolution.

Main Effects

Two Way Interactions

k-­‐p

2R

Fully Saturated Design Resolution III Hold up Three Fingers, One on one hand and Two on the other. This illustrates the Confounding of main effects with two way interactions.

Resolution IV Next hold up four fingers The Confounding is main effects with three way interactions or… Main Effects

Three Way Interactions

Two way interactions Confounded with other two way interactions. Two Way Interactions Two Way Interactions

The  visual  aid  is  shown  throug h  Resolution  V.

Main Effects

Four Way Interactions

k -p

2R

Resolution V Hold up Five Fingers, One on one hand and Four on the other. This illustrates the Confounding of main effects with four way interactions or …

Two way interactions Confounded with three way interactions. Two Way Interactions

LSS Black Belt Manual XL v11

Three Way Interactions

© 2013 e-Careers Limited

531

Fractional Factorial Experiments SigmaXL® Fractional Factorial Design Creation We have already seen this SigmaXL® after a Fractional Factorial Design was created. SigmaXL® automatically tells us the Resolution and if we use the hands technique to remember the Aliasing type of structure, we can save time. The Resolution can get very complicated with those screening Fractional Factorial Designs with factors more than 5 so this helps is desirable.

2V (5 -1) Fractional Design Resolution V

Example  of  a  very  useful  Fractiona l  Desig n  often  used  for  screening  desig ns.

E

B C A

P ro s 5  factors  (Ma in  Effects) 1 0  2 -­‐w a y  intera ctions Main  Effects  only  C onfounded   with  ra re  4 -­‐w a y  intera ctions

LSS Black Belt Manual XL v11

D

Cons 1 6  trials  to  g et  5  Ma in  Effects 2 nd  order  interactions  a re   C onfounded  with  3 rd  order

Run

A

B

C

D

1

-1

-1

-1

-1

E 1

2 3 4

1 -1 1

-1 1 1

-1 -1 -1

-1 -1 -1

-1 -1 1

5 6

-1 1

-1 -1

1 1

-1 -1

-1 1

7 8

-1 1

1 1

1 1

-1 -1

1 -1

9

-1

-1

-1

1

-1

10 11 12 13

1 -1 1 -1

-1 1 1 -1

-1 -1 -1 1

1 1 1 1

1 1 -1 1

14 15

1 -1

-1 1

1 1

1 1

-1 -1

16

1

1

1

1

1

© 2013 e-Careers Limited

532

Fractional Factorial Experiments SigmaXL®’s Display of Available Designs SigmaXL® does not include a visual display of Factorial Designs.

DOE Methodology We have included a copy of the methodology here for you to use when following our practical example for Fractional Factorials.

1. 2. 3. 4. 5. 6. 7. 8.

Define the Practical Problem Establish the Experimental Objective Select the Output (response) Variables Select the Input (independent) Variables Choose the Levels for the input variables Select the Experimental Design Execute the Experiment and collect data Analyze the Data from the designed experiment and draw Statistical Conclusions 9. Draw Practical Solutions 10. Replicate or Validate the Experimental Results 11. Implement Solutions

Just followsimple these simple steps ….. Just follow these steps…..!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

533

Fractional Factorial Experiments Fractional Factorial Example

This is a two to the eighth minus four power design with a resolution four design. This design has 16 runs as you see in the slide with all eight factors at two levels.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

534

Fractional Factorial Experiments Fractional Factorial Example (cont.)

Take a look at what Confounding exists before you jump into analysis. SigmaXL® does not report Confounding with 3-way interactions.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

535

Fractional Factorial Experiments Fractional Factorial Example (cont.) We chose to set alpha to 0.1 initially but this is not required. We find the factors with important Main Effects are E, H and B. The 2-way interactions AC, AF and AE seem important at an alpha level of 0.1.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

536

Fractional Factorial Experiments Fractional Factorial Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

537

Fractional Factorial Experiments Fractional Factorial Example (cont.)

Statistical Conclusions to maintain terms in the model must consider: cons §

Maintaining hierarchical order

§

A§2 way A 2 interaction -way interaction must have mustthe have involved the involved factorsfactors in the model in the model also also

§

High statistical confidence with the P

§

A higher R

§

Proper residuals and few to no unusual observations

ider:

-value -valueless lessthan thanyour youralpha alpharisk risk

-sq or model explanation of the process changes is desired

unusual No, No, nonounusual observations here… observations here…!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

538

Fractional Factorial Experiments Fractional Factorial Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

539

Fractional Factorial Experiments Fractional Factorial Example (cont.)

Practical Conclusions to keep in the model include: !  !  !  ! 

! 

Simple models can be useful depending on the project or process requirements Terms with practically large enough significance even if statistically significant Impact of R-sq by removing a term with low effects Ability to set and control the controllable inputs in the model may decide on the use of terms !  Robust designs or minimal variation requirements may require close inspection of interactions effects on the Y If multiple outputs are involved in the process requirements, balancing of requirements will be necessary

That s a lot of juggling….!

10.  Replicate or Validate the Experimental Results !  After we have determined with 95% statistical confidence, we must replicate the results to confirm our assumptions; such as which 2-way interactions were significant among the Confounded ones !  If the results do not match the expected results OR the project goal, further experimentation may be needed !  In this case, we were able to achieve 29.8 on average with the process setting of B, E and H and so the results are considered successful in the project

We win, we win…!!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

540

Fractional Factorial Experiments Fractional Factorial Example (cont.)

1 1 . Im p le m e n t   S o lu tio n s § W ork  with  the  Process  O wners  and  develop  the  C ontrol  Plans   to  sustain  your  success

Fractional Factorial Exercise

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

541

Fractional Factorial Experiments At this point, you should be able to: •  Explain why & how to use a Fractional Factorial Design •  Create a proper Fractional Factorial Design •  Analyze a proper model with aliased interactions

Not that kind of model!!! You have now completed Improve Phase – Fractional Factorial Experiments.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

542

Lean Six Sigma Black Belt Training

Improve Phase Wrap Up and Action Items

Congratulations on completing the training portion of the Improve Phase. Now comes the exciting and challenging part…implementing what you have learned to real world projects.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

543

Wrap Up and Action Items Improve Phase Overview—The Goal This is a summary of the purpose for the Improve Phase. Avoid getting into analysis paralysis, only use DOE’s as necessary. Most problems will NOT require the use of Designed Experiments however to qualify as a Black Belt you at least need to have an understanding of DOE as described in this course.

Th e   g o a l   o f   th e   Im p ro v e   P h a s e   is   to : • Determine  the  optimal  levels  of  the  variables  which  are   sig nificantly impacting  your  Primary  Metric. • Demonstrate  a  working  knowledg e  of  modeling  as  a  means  of   process  optimiz ation.

Improve Phase Action Items

• Listed  below  are  the  Improve  Phase  deliverables  that  each  candid ate   will  present  in  a  Power  Point  presentation  at  the  beg inning  of  the   C ontrol  Phase  training .   • A t  this  point  you  should  all  understand  what  is  necessary  to  provide   these  deliverables  in  your  presentation. – – – – – – – –

Tea m  Members  (Tea m  Meeting  A ttenda nce) Prima ry  Metric S econda ry  Metric(s) Experiment  Justifica tion Experiment  Pla n  /  O bjective Experiment  Results   Project  Pla n     Issues  a nd  Ba rriers

It’s It’s  your y our  show!! s how!

Before beginning the Control Phase you should prepare a clear presentation that addresses each topic shown here.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

544

Wrap Up and Action Items Six Sigma Behaviors

• Being  tenacious,  courag eous • Being  rig orous,  disciplined • Making  data -­‐b ased  decisions • Embracing  chang e  &  continuous  learning • Sharing  best  practices

Walk Walk   the the   Walk!! Walk !

Ea Each ch    ““ppla layyeerr”” in in    th thee    SSix ix    SSig igm maa    pprrooce cessss    m muusst  t  bbee AA    RROOLE   LE  M MOODDEL EL fo forr    th thee    SSix ix    SSig igm maa    cu cultu lturree.. Improve Phase - The Roadblocks

Look  for  the  potential  roadblocks  and  plan  to  address  them  before  they   become  problems:   – Lack  of  data – Data  presented  is  the  best  g uess  by  functional  manag ers   – Team  members  do  not  have  the  time  to  collect  data – Process  participants  do  not  participate  in  the  analysis  planning – Lack  of  access  to  the  process

Each phase will have roadblocks. Many will be similar throughout your project.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

545

Wrap Up and Action Items

C hampion/ Process  O wner

DMAIC Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

A ssess  Sta bility,  C apability  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Improve

A nalyz e

Measure

Establish  Tea m

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  Xs  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

The objective of the Improve Phase is simple – utilize advanced statistical methods to identify contributing variables OR more appropriately optimize variables to create a desired output. Improve Phase Over 80% of projects will realize their solutions in the Analyze Phase – Designed Experiments can be extremely effective when used properly, it is imperative that a Designed Experiment is justified. From an application and practical standpoint, if you can identify a solution by utilizing the strategy and tools within the Measure and Analyze Phases, then do it. Do not force Designed Experiments. Remember, your sole objective in conducting a Lean Six Sigma project is to find a solution to the problem. You created a Problem Statement and an Objective Statement at the beginning of your project. However you can reach a solution that achieves the stated goals in the Objective Statement, than implement them and move on to another issue – there are plenty! LSS Black Belt Manual XL v11

A nalysis  C omplete

Identify  Few  Vital  X’s

Experiment  to  O ptimiz e  Value  of  X’s

Simulate  the  N ew  Process

Validate  N ew  Process  

Implement  N ew  Process

Ready  for  C ontrol

© 2013 e-Careers Limited

546

Wrap Up and Action Items Improve Phase Checklist

These are questions that the participant should be able to answer in clear, understandable language at the end of this phase. Planning for Action WHAT

WHO

W H EN

WHY

W H Y   N O T

HOW

A  DO E  to  meet  your  problem  solving  strateg y Scheduling  your  experimental  plan Executing  your  planned  DO E A nalysis  of  results  form  your  DO E O btain  mathematical  model  to  represent  process Planning  the  pilot  validation  for  breakthroug h Present  statistical  promise  to  process  owner Prepare  for  implementation  of  final  model Schedule  resources,  for  implementation  timeline C onclude  on  expected  financial  benefits

Over the last decade of deploying Six Sigma it has been found that the parallel application of the tools and techniques in a real project yields the maximum success for the rapid transfer of knowledge. Thus we have developed a follow up process that involves planning for action between the conclusion of this phase and the beginning of the Control Phase. It is imperative that you complete this to keep you on the proper path. Thanks and good luck! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

547

Wrap Up and Action Items At this point, you should: §  Have a clear understanding of the specific action items §  Have started to develop a project plan to complete the action items §  Have identified ways to deal with potential roadblocks §  Be ready to apply the Six Sigma method within your business

You’re on your way!! You have now completed Improve Phase – Wrap Up and Action Items.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

548

Lean Six Sigma Black Belt Training

Control Phase Welcome to Control

Now that we have completed the Improve Phase we are going to jump into the Control Phase. Welcome to Control will give you a brief look at the topics we are going to cover.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

549

Welcome to Control Overview These are the modules we will cover in the Control Phase as we attempt to insure that the gains we have made with our project remain in place.. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    CCoonntr trooll AA ddvvaa nnce cedd    Ex Ex ppeerim rim eennts ts AA ddvvaa nnce cedd    CCaa ppaa bbility ility Le Leaa nn    CCoonntro trols ls D Deefe fect   ct  CCoonntro trols ls SSta ta tis tistica tica l  l  PPrrooce cessss    CCoonntr trool  l   (S (SPPCC)) SSix ix    SSig ig m m aa    CCoonntro trol  l  PPla la nnss W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

C hampion/ Process  O wner

DMAIC Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

550

Welcome to Control Control Phase Finality with Control Plans

Improvement  S elected Develop  Training  Plan Implement  Training  Plan Develop  Documentation  Plan Implement  Documentation  Plan   Develop  Monitoring  Plan Implement  Monitoring  Plan Develop  Response  Plan Implement  Response  Plan Develop  Plan  to  A lig n  S ystems  and  S tructures A lig n  S ystems  and  S tructures Verify  Financial  Impact

G o  to  N ext  Project

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

551

Lean Six Sigma Black Belt Training

Control Phase Advanced Experiments

Now we will continue in the Control Phase with “Advanced Experiments”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

552

Advanced Experiments Overview This module is the Advanced DOE module. At first thought, you might wonder why this is covered in the Control Phase instead of the Improve Phase. We include the Advanced DOE in this Control Phase to emphasize the iterative nature of Design of Experiments. The iterative nature can include a quick, statistically based technique for finding the highest or lowest response output known as the steepest ascent or descent. We cover this methodology in depth including an example and summary.

Beginnings of Control Phase You’ve already narrowed to the “vital few” with the Define, Measure, Analyze and Improve Phases. Just because you’ve found the “vital few”, may not mean you have the final results desired from the project scope. The Control Phase involves controlling the X’s where you need the Y to perform. If you haven’t achieved the output desired, one more DOE tool exists to help find where the inputs should be.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

553

Advanced Experiments Reminder of Iterative Nature for DOE DOE is an iterative process, the approach taken depends on the information that is known. Steepest ascent/decent is another method used to increase our knowledge and is used in conjunction with factorials and/or response surface methods.

Purpose The purpose of performing a Designed Experiment is to determine: v  The mathematical relationship Y=F(x1, x2, x3,…). v  Which X's most impact Y, and therefore need to be controlled v  The level of each X to achieve the desired mean Y v  The level of each X to minimize the variability of Y A DOE is needed only if this information cannot be obtained from passive analysis of the process. v  The danger of NOT running a Designed Experiment is the ability to prove cause and effect. §  Regressions, correlations or multi-linear regressions show relationships but cannot prove cause-effect relationships §  DOE’s prove cause and effect because variables are changed and the effect is measured in the output(s) of interest Steepest ascent/descent designs use proven cause-effect relationships and achieve quick improving results for a project.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

554

Advanced Experiments Steepest Ascent The method of steepest ascent guides you toward a target outside the original inference space. The method takes the most economical or shortest route towards the target by staying on the path of steepest ascent.

Steepest Ascent/Descent This methods starts with a Full or Fractional Factorial as the base to determine the direction of steepest ascent/decent. v This method works best when there is no significant curvature in the model used to determine direction, linearity is an assumption The direction of ascent is determined using the coefficients in the Prediction Equation. This method works best with a small number of variables; just 2 or 3.

Inference Space How can the Prediction Equation from the original experiment miss the mark?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

555

Advanced Experiments 2-Factor Example for Steepest Ascent

Stepping Along the Path of Steepest Ascent

Our simulated process will be run at the dotted points along the line so we can observe the “Y” or the output.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

556

Advanced Experiments Taking a New Direction When Appropriate At some point, once a local maximum has been detected, another factorial DOE may be necessary to determine the next direction.

Steepest Ascent Steps Step 1: Obtain the coefficients for the prediction equation from a factorial DOE (must use coded variables) Step 2: Select the Base factor: • Most difficult to adjust • Discrete levels • Largest coefficient (This is recommended) Step 3: Determine the step size, in coded units, that you will move in the direction of the Base Factor Step 4: Determine the step size for the other factors Step 5: Move along the path and run the process at each step, continue along the path until either the target value is achieved, or until a local maximum is reached Step 6: If necessary, conduct another DOE to determine a new steepest ascent path, and repeat steps 1-5

Y = b0 + b1X1 + b 2 X 2 + b3X3 LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

557

Advanced Experiments Example of Projection Vector Method

Choosing the Step Size

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

558

Advanced Experiments Other Factor Step Size

Work through each step to find the optimum result.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

559

Advanced Experiments Process Results from Steepest Ascent

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

560

Advanced Experiments At this point, you should be able to: §  Use the results of a DOE to determine how to further optimize a process using the steepest ascent/descent method

You have now completed Control Phase – Advanced Experiments.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

561

Lean Six Sigma Black Belt Training

Control Phase Advanced Capability

Now we will continue in the Control Phase with “Advanced Capability”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

562

Advanced Capability Overview Within this module we will explore using Process Capability to show a difference in process performance as a result of your project efforts as well as review it as a monitoring tool to ensure sustainability of improved efforts.

Beginnings of Control Phase You’ve already narrowed to the “vital few” with the Define, Measure, Analyze and Improve Phases. Just because you are able to achieve results with your project or through a DOE does not mean you have Process Capability. This module in the Control Phase gives you tools and ideas to tackle Special Causes that may be hampering your Process Capability even if you found your “vital few” to get an improved average. By this time you should have made improvements with your project. How do you know? Well the obvious is by continually monitoring your primary metric, which we know you have been doing, right? Within this module we are going to look at another method to prove your project’s impact on the process with a more quantified approach. We will compare the Capability established in the Measure Phase to a Capability Analysis here in the Control Phase. Ready to have some fun…

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

563

Advanced Capability Capability and Monitoring §  If the project was important enough to warrant the time and attention of you and your team, it is important enough to ensure that performance levels are maintained §  Monitoring the improved process is a key element of the Control Plan §  Reporting Capability and Stability should be used together as primary components of the monitoring plan §  In the Measure Phase, Capability was used to establish baseline performance by assessing what had occurred in the relevant past §  In the Control Phase, Capability becomes a predictive (inferential) tool to predict the expected process performance, usually based on a sample. Your project is clearly important, so much so that time and resources were allocated to it! One aspect that is absolutely critical to your Control Phase action items and project closure is Capability Analysis as a predictive measure. Recall in the Measure Phase we emphasized “taking a snapshot” not worrying about Stability. Well now that you have fixed some stuff it’s time to be concerned about Stability to ensure your efforts stick.

Capability Studies §  Are intended to be periodic, estimations of a process’s ability to meet its requirements §  Can be conducted on both Discrete and Continuous Data §  Are most meaningful when conducted on stable processes §  Can be reported as Sigma Level which is optimal (short term) performance §  These concepts should be remembered from using the Six Sigma toolset applied so far: v  Customer or business specification limits Ø  Business specification limits cannot be wider than the specification limits of a final product v  Nature of long term vs. short term data v  Mean and Standard Deviation of the process (for Continuous Data) v  The behavior and shape of the distribution of Continuous Data v  Procedure for determining Sigma level v  Relevance of data You may want to take a moment to review the key components of Capability taught in the Measure Phase. Here in the Control Phase Capability Studies are meaningful on stable processes. If random events are occurring frequently, then predictability will be less secure.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

564

Advanced Capability Components of Variation As in the Measure Phase, understanding whether you are dealing with long term or short term data is an important first step. If the process is stable, short term data provides a quick estimate of true process potential since special causes are minimal. Recall the difference between short and long term. The long term is the variation across the subgroups and within the subgroups. Think of it in terms of Population versus Sample. Subgroups or Lot represent Short Term; Overall represents Long term. You will have to slice and dice your data in respect to your business / process and determine what long term & short term are for your process.

Capability for the Control Phase Shown here is the roadmap for Capability within the Control Phase. Here we are going to teach you how to perform Capability Analyses on both Continuous and Attribute Data. Remember to always VALIDATE those spec limits!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

565

Advanced Capability Discrete Capability: Binomial

It’ll get ya there!! SigmaXL® does not include a tool for Binary Process Capability Analysis. However the above charts can be created using SigmaXL®'s P-Chart, Histogram and Scatter Plot tools. Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

566

Advanced Capability Example of Defectives

Here we are reporting the Capability relative to Late Reports. The subgroup size is varying as is the number of reports we analyze at each time frame for lateness. From the Summary Stats we see the following. The % Defective of the process is nearly 18%. Can you see that p bar is equal to 0.1756 PPM Def? This graph is a P-Chart which will be covered in more detail later. The red dot in this graph indicates a Special Cause showing the proportion of reports to be late to be excessively high and considered out of control.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

567

Advanced Capability Discrete Capability: Binomial Output

The upper left graph, is the plot of Proportion Defectives versus Sample Size. If this was widely varying and with a non-level slope, we might conclude our detection of late reports depends on the number of reports checked. The last graph in the lower right shows a histogram of the % defective or late in our example. You can see the target line of 10% and see that most if not all are above our target; the lower spec. The summary stats are there for our help although in this example, we have no question that our process is not capable with a target of less than 10% late reports. However, let’s consider the details of the summary stats box in the middle. The summary stats gives the % defective which was equal to the p bar shown in the upper left slide. Confidence intervals are given for the percent late. The ppm defective is just the p bar multiplied by a million. The process Z is determined from the percent defective and is shown with confidence intervals also. Remember if this data was long term, then the sigma level of the process would have a value added to this Z to obtain the sigma level. Do you remember what value is assumed that separates Z short term and Z long term? Remember when a process Z long term is used to estimate the Z short term, you add 1.5. In our example, assuming this data is from a long term capability analysis, the sigma level of the process would be 2.43 with an upper confidence interval of 2.49 and a lower confidence interval of 2.38. Remember that the summary stats do not indicate the percent of groups larger than the target but indicates the percent defective as a whole.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

568

Advanced Capability Discrete Capability: Poisson You can do a Capability Analysis using the Poisson Distribution in SigmaXL® if you are tracking the number of defective units.

Still works….!

More Capability Analysis This Capability Analysis for defects per unit is similar to the binomial Capability Analysis. However, there is no Z value stated for this Capability Analysis. Remember we had a desire for the process to have less than one defect per unit. If you look at the lower right graph, you can see the large majority of samples show less than 1.0 dpu. In this example even if the dpu never settled out at some value, it is clear the average dpu is much less than 1.0. In fact, we have 95% confidence that the upper confidence interval for the dpu is about 0.59.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

569

Advanced Capability Continuous Capability: Normal This should look familiar from the Measure Phase. Here we are treating the data as individual observations. Later we will re-analyze the data using Capability Combination Report (Subgroups) using “filler2” for Numeric Data Variable (Y) and “time” for Subgroup Column or Size.

Continuous Capability: Normal Output Review The black curve is the predicted Normal Distribution for all of the data using the Overall (Long Term) StDev. The StDev (Within, Short Term) is computed using the Individuals Chart MR-Bar/d2 estimate. This gives us our potential StDev, i.e. “entitlement”. If we had used Capability Combination Report (Subgroups), the StDev (Within, Short Term) would be computed using the X-Bar & R or X-Bar & S Control Chart methods for within subgroup variation.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

570

Advanced Capability Continuous Capability: Normal Output Review Note: Confidence Intervals for Process Capability Indices may be calculated using “SigmaXL>Basic Process Capability Templates>Proc ess Capability & Confidence Intervals”

Normal Capability Sixpack Notice the Capability Plot on the bottom right. This shows the overall and within variation relative to the placement and width in the specification limits.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

571

Advanced Capability Continuous Capability: Non-Normal Recall from the Measure Phase that you should always take a look at your data graphically; a picture is worth a 1000 words. You can almost always use SigmaXL® to help you identify what type of distribution you are dealing with and to create a graphical view of your data. Also, this is a great way to determine Process Capability without transforming data.

Individual Distribution Identification Output This is the output which you will use to determine your distribution. The P-values shown on each graph are used to evaluate if the distribution an appropriate predictor. Since most decisions require only an alpha risk of less than 5%, the P-values should be above 0.05. However, do not assume that a higher P-value means one distribution is better than another. There is just less error of that being the appropriate distribution to select.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

572

Advanced Capability Continuous Capability: Non-normal Now that you have the distribution identified run a Capability Analysis as shown here. In the Capability Combination Report (Individuals- Non-normal) select “Cycletime” as Numeric Data Variable (Y). Ensure “Weibull(2 Parameter)” is selected for “Specify Distribution”.

Technical note from SigmaXL®'s workbook: Z-Score Method (Default) The Z-Score method for computing process capability indices are obtained by using the inverse cdf of the normal distribution on the cdf of the Non-normal Distribution. Normal based capability indices are then applied to the transformed z-values. This approach offers two key advantages: the relationship between the capability indices and calculated defects per million is consistent across the normal and all Non-normal Distributions, and short term capability indices Cp and Cpk can be estimated using the standard deviation from control chart methods on the transformed zvalues. The Z-Score method was initially developed by Davis Bothe and expanded on by Andrew Sleeper. For further details, see Sleeper, Six Sigma Distribution Modeling. Percentile (ISO) Method The Percentile method to calculate process capability indices uses the following formulas: Ppu = (USL – 50th percentile)/(99.865 percentile – 50th percentile) Ppl = (50th percentile – LSL)/(50th percentile – 0.135 percentile) Ppk = min(Ppu, Ppl) Pp = (USL – LSL)/( 99.865 percentile – 0.135 percentile) References for Process Capability Indices: Bothe, D.R. (1997). Measuring Process Capability, McGraw-Hill, New York. Sleeper, A. (2006). Six Sigma Distribution Modeling, McGraw-Hill, New York. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

573

Advanced Capability Continuous Capability: Non-normal Output

Continuous Capability: Non-normal Output This should look a bit more familiar. Since the data was Long Term, the sigma level of the process would be adjusted by 1.5 and result in a sigma value of 1.48. Review the differential between observed performance and expected performance, what does this tell you?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

574

Advanced Capability Practical Capability for the Control Phase This is an example of using Process Capability differently than as presently in the Measure Phase. Process Capability within the Control Phase comes with the use of Control Charts as shown here. We will further explore this usage now since this is what allows us to make comparisons throughout the methodology.

Assess improved performance to establish the new baseline – don t try to predict anything. Just understand the relationship of the distribution to the spec limits and convert the observed failure rate to sigma level. Use a Control Chart to help understand the process behavior over time and identify unusual events. Details on these Control Charts are discussed later in the Control Phase.

Technical notes from SigmaXL®'s workbook: Individuals – Original Data The Individuals – Original Data chart displays the untransformed data with Control Limits calculated as: UCL = 99.865 percentile CL = 50th percentile LCL = 0.135 percentile The benefit of displaying this chart is that one can observe the original untransformed data. Since the Control Limits are based on percentiles, this represents the overall, long term variation rather than the typical short term variation. The limits will likely be non-symmetrical. Individuals/Moving Range – Normalized Data The Individuals/Moving Range – Normalized Data chart displays the transformed z-values with control limits calculated using the standard Shewhart formulas for Individuals and Moving Range charts. The benefit of using this chart is that tests for Special Causes can be applied and the control limits are based on short term variation. The disadvantage is that one is observing transformed data on the chart rather than the original data. SigmaXL®'s default setting is to display the three charts: Individuals – Original Data, Individuals & Moving Range – Normalized Data (with tests for Special Causes unchecked). LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

575

Advanced Capability Practical Sustainability in Control Phase Within the later phases of the methodology you can use Capability to identify Special Causes or Outliers as shown here. If you can minimize them over time then the Process Capability will improve!

Final Results of Control Phase By eliminating Outliers your variation will reduce and your Median could shift. It is even possible that you could Normalize your distribution.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

576

Advanced Capability Capability for the Control Phase In summary be sure to capture the correct information to, one, prove the improvement in your process and two, hand off the right information to the process owner for monitoring and measuring the improved process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

577

Advanced Capability At this point, you should be able to: §  Understand the importance of Capability Analysis as it is applied in the Control Phase §  Select the appropriate method for Capability Analysis based on the type of data distribution of your process §  Interpret the output of SigmaXL®’s Capability functions §  Understand how the use for Capability Analysis may alter through the DMAIC phases

You have now completed Control Phase – Advanced Capability.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

578

Lean Six Sigma Black Belt Training

Control Phase Lean Controls

Now we will continue in the Control Phase with “Lean Controls”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

579

Lean Controls Overview You can see in this section of the course we will look at the Vision of Lean, Lean Tools and Sustaining Project Success. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    CCoonntr trooll AA ddvvaa nnce cedd    Ex Ex ppeerim rim eennts ts AA ddvvaa nnce cedd    CCaa ppaa bbility ility

Vision  of  Lean  Supporting Vision  of  Lean  Supporting  Six  Sig  Six  Sigma ma

Le Leaa nn    CCoonntro trols ls

Lean  Tool  Hig Lean  Tool  Highlig hlights hts

D Deefe fect   ct  CCoonntro trols ls

Project  Sustained  Success Project  Sustained  Success

SSta ta tis tistica tica l  l  PPrrooce cessss    CCoonntr trool  l   (S (SPPCC)) SSix ix    SSig ig m m aa    CCoonntro trol  l  PPla la nnss W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Lean Controls You’ve begun the process of sustaining your project after finding the “vital few” X’s. In Advanced Process Capability, we discussed removing some of the Special Causes causing spread from Outliers in the process performance. This module gives more tools from the Lean toolbox to stabilize your process. Belts, after some practice, often consider this module’s set of tools a way to improve some processes that are totally “out of control” or of such poor Process Capability before applying the Six Sigma methodology. The tools we are going to review within this module can be used to help control a process. They can be utilized at any time in an improvement effort not just in Control. These Lean concepts can be applied to help reduce variation, effect outliers or clean up a process before, during or at the conclusion of a project.

Grab a tool and get busy!!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

580

Lean Controls The Vision of Lean Supporting Your Project Remember, the goal is to achieve and the SUSTAIN our improvements. We discussed 5S in the Define Phase but we are going to review it with a twist here in the Control Phase. K anban

Th e   C o n tin u o u s   G o a l … S u s ta in in g   R e s u lts

p

K a iz e n

W e   ca n n o t   s u s ta in   K a n b a n   w ith o u t   K a iz e n .

S ta n d a rd iz e d   W o rk p

V is u a l   Fa cto ry

p

p

W e   ca n n o t   s u s ta in   K a iz e n   (S ix   S ig m a )   w ith o u t   S ta n d a rd iz e d   W o rk .

W e   ca n n o t   s u s ta in   S ta n d a rd iz e d   W o rk   w ith o u t   a   V is u a l   Fa cto r y .    

W e   ca n n o t   s u s ta in   a   v is u a l   fa cto ry   w ith o u t   5 S .    

Le a n   to o ls   a d d   d is cip lin e   re q u ire d   to   fu rth e r   s u s ta in   g a in s   re a liz e d   w ith   S ix   S ig m a   B e lt   P ro je cts .

What is Waste (MUDA)? The first step toward waste elimination is waste identification which you did originally with your Project Charter and measured with your primary metric even if you didn’t use the term waste. All Belt projects focus efforts into one (or more) of these seven areas. W a s te   is   o fte n   th e   ro o t   o f   a n y   S ix   S ig m a   p ro je ct.     Th e   7   b a s ic   e le m e n ts   o f   w a s te   (m u d a   in   J a p a n e s e )   in clu d e : – M u d a   o f   C o r re ctio n – M u d a   o f   O v e rp ro d u ctio n – M u d a   o f   P ro ce s s in g – M u d a   o f   C o n v e y a n ce – M u d a   o f   In v e n to ry – M u d a   o f   M o tio n – M u d a   o f   W a itin g

Get   that   g arbag outta e   outta   hhere!! ere! Get that garbage

Th e   s p e cifics   o f   th e   M U D A   w e re   d is cu s s e d   in   th e   D e fin e   P h a s e : – Th e   re d u ctio n   o f   M U D A   ca n   re d u ce   y o u r   o u tlie rs   a n d   h e lp   w ith   d e fe ct   p re v e n tio n .     O u tlie rs   b e ca u s e   o f   d iffe rin g   w a s te   a m o n g   p ro ce d u re s ,   m a ch in e s ,   e tc. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

581

Lean Controls The Goal Remember that any project needs to be sustained. Muda (pronounced like mooo dah) are wastes than can reappear if the following Lean tools are not used. The goal is to have your Belts move onto other projects and not be used as firefighters.

D o n ’ t   fo rg e t   th e   g o a l   -­‐-­‐ S u s ta in in g   y o u r   P ro je ct   w h ich   e lim in a te s   MUDA ! W ith   th is   in   m in d ,   w e   w ill   in tro d u ce   a n d   re v ie w   s o m e   o f   th e   Le a n to o ls   u s e d   to   s u s ta in   y o u r   p ro je ct   s u cce s s .

5S - Workplace Organization The term “5S” derives from the • 5 S  means  the  workplace  is   Japanese words for five practices clean,  there  is  a  place  for   leading to a clean and everything  and  everything   manageable work area. The five is  in  its  place. “S” are: ‘Seiri' means to • 5 S  is  the  starting  point  for   separate needed tools, parts, and implementing   instructions from unneeded improvements  to  a  process.   materials and to remove the • To  ensure  your  g ains  are   latter. 'Seiton' means to neatly sustainable,  you  must  start   arrange and identify parts and with  a  firm  foundation.   tools for ease of use. 'Seiso' • Its  streng th  is  conting ent   means to conduct a cleanup upon  the  employees  and   campaign. 'Seiketsu' means to company  being  committed   conduct seiri, seiton, and seiso at to  maintaining  it. frequent, indeed daily, intervals to maintain a workplace in perfect condition. 'Shitsuke' means to form the habit of always following the first four S’s. On the next page we have translated the Japanese words to English words. Simply put, 5S means the workplace is clean, there is a place for everything and everything is in its place. The 5S will create a workplace that is suitable for and will stimulate high quality and high productivity work. It will make the workplace more comfortable and a place that you can be proud of. Developed in Japan, this method assumes no effective and quality job can be done without clean and safe environment and without behavioral rules. The 5S allow you to set up a well adapted and functional work environment, ruled by simple yet effective rules. 5S deployment is done in a logical and progressive way. The first three S’s are workplace actions, while the last two are sustaining and progress actions. It is recommended to start implementing 5S in a well chosen pilot workspace or pilot process and spread to the others step by step. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

582

Lean Controls 5S Translation - Workplace Organization

S te p                   J a p a n e s e

Lite ra l   Tra n s la tio n  

En g lis h

S te p   1 :

Seiri

C learing  Up

Sorting

S te p   2 :

Seiton

O rg aniz ing

Straig htening

S te p   3 :

Seiso

C leaning

Shining

S te p   4 :

Seketsu

Standardiz ing

Standardiz ing

S te p   5 :

Shitsuke

Training  &  Discipline

Sustaining

Fo cu s   o n   u s in g   th e   En g lis h   w o rd s ,   m u ch   e a s ie r   to   re m e m b e r.

The English translations are: Seiri = Sorting Eliminate everything not required for the current work, keeping only the bare essentials. Seiton = Straightening Arrange items in a way that they are easily visible and accessible. Seiso = Shining Clean everything and find ways to keep it clean. Make cleaning a part of your everyday work. Seketsu = Standardizing Create rules by which the first three S’s are maintained. Shitsuke = Sustaining Keep 5S activities from unraveling

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

583

Lean Controls SORTING - Decide what is needed. The first stage of 5S is to organize the work area, leaving only the tools and materials necessary to perform daily activities. When “sorting” is well implemented, communication between workers is improved and product quality and productivity are increased.

D e fin itio n :

– To  sort  out  necessary  and   unnecessary  items. – To  store  often  used  items  at   the  work  area,  infrequently   used  items  away  from  the   work  area  and  dispose  of   items  that  are  not  needed. W hy :

– – – –

Removes  waste. Safer  work  area. G ains  space. Easier  to  visualiz e  the   process.

Th Thininggss   to   to   re   remmeemmbbeer r

••Start  in  one  area,  then  sort   Start  in  one  area,  then  sort   throug through  everything h  everything. . ••Discuss  removal  of  items  with  all   Discuss  removal  of  items  with  all   persons  involved. persons  involved. ••Use  appropriate   Use  appropriate   decontamina decontamination,    environmenta tion,    environmental,  l,   and  safety  procedures. and  safety  procedures. ••Items  tha Items  that  ca t  cannot  be  removed   nnot  be  removed   immediately  should  be  tag immediately  should  be  taggged   ed   for  later  removal. for  later  removal. ••if  necessary,  use  movers  and   if  necessary,  use  movers  and   rig rigggers. ers.

A Method for Sorting 5S usually begins with a great initial cleaning, where sorting out the items is a highlight. For each item, it must be stated if it is useful, useless or undetermined. For some items, the statement may be touchy, as nobody seems to know if they are really useful or not, and what is their frequency of use.

Ite m

U s e fu l

Unk now n

U s e le s s

K e ep   &   M o n ito r K e ep   &   S to re

U s e fu l

S o rtin g

U s e les s

Always start with the A B C   easiest items to classify. S to ra g e Difficulty should be no excuse, go for it, starting with easiest: Sort each item according to three categories: 1. Useful 2. Useless 3. Unknown

D is p o s e

The two first categories are problem to sort as their status is clear. Dispose of immediately any useless items, because they just clutter the workspace, lead to loss of time, confusion and poor quality. For items in the unknown category or the frequency of use is unclear, keep them where they are for a predetermined period of time and if found that they are not used dispose of them. For items that are useful, there is also a method for determining how and where they should be stored to help you achieve a clean and orderly workplace. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

584

Lean Controls

Frequency of Use

A Method for Sorting

U s e   th is   g ra p h   a s   a   g e n e ra l   g u id e   fo r   d e cid in g   w h e re   to   s to re   ite m s   a lo n g   w ith   th e   ta b le   b e lo w .

A B

C

Distance Frequency of Utilization

Class

Keep within arms reach

Keep in local location

Keep in remote location

Daily or several times a day

A

YES

MAYBE

NO

Weekly

B

MAYBE

YES

NO

Monthly or quarterly

C

NO

NO

YES

After you have determined the usefulness of an item, set three classes for determining where to store an item based on the frequency of use and the distance to travel to get the item. “A” is for things which are to be kept close at hand, because the frequency of use is high. “B” is if the item is used infrequently but approximately on a weekly basis. Do no put it on your work surface, rather keep in easy walking distance, i.e. on a bookshelf or in a nearby cabinet, usually in the same room you are in. For “C” items it is acceptable to store in a somewhat remote place, meaning a few minutes walk away. By rigorously applying the sort action and the prescribed method, you will find that the remainder of the 5S items will be quite easy to accomplish. It is very difficult to order a large number of items in a given space and the amount of cleaning increases with the number of items. Your workplace should only contain those items needed on a daily to weekly basis to perform your job. STRAIGHTENING – Arranging Necessary Items The second stage of 5S involves the orderly arrangement of needed items so they are easy to use and accessible for “anyone” to find. Orderliness eliminates waste in production and clerical activities.

LSS Black Belt Manual XL v11

D e fin itio n :

– To  arrang e  all  necessary  items. – To  have  a  desig nated  place   for  everything . – A  place  for  everything  and   everything  in  its  place. – Easily  visible  and  accessible. W hy :

– Visually  shows  what  is  required   or  is  out  of  place. – More  efficient  to  find  items  and     documents  (silhouettes/ labels). – Saves  time  by  not  having  to   search  for  items. – Shorter  travel  distances.

Th Thininggss   to   to   re   remmeemmbbeer r

•• Thing Things  used  tog s  used  together   ether   should  be  kept  tog should  be  kept  together. ether. •• Use  labels,  tape,  floor   Use  labels,  tape,  floor   marking markings,  sig s,  signs,  and   ns,  and   shadow  outlines. shadow  outlines. •• SSharable  items  should  be   harable  items  should  be   kept  at  a  central  location   kept  at  a  central  location   (elimina (eliminated  excess). ted  excess).

© 2013 e-Careers Limited

585

Lean Controls SHINING – Cleaning the Workplace The third stage of 5S is keeping everything clean and swept. This maintains a safer work area and problem areas are quickly identified. An important part of “shining” is “Mess Prevention.” In other words, don’t allow litter, scrap, shavings, cuttings, etc., to land on the floor in the first place.

D e fin itio n :

– C lean  everything  and   find  ways  to  keep  it   clean. – Make  cleaning  a  part   of  your  everyday  work.

W hy :

– A  clean  workplace   indicates  a  quality   product  and  process. – Dust  and  dirt  cause   product  contamination   and  potential  health   haz ards. – A  clean  workplace   helps  identify  abnormal   conditions.

Th Thininggss   to   to   re   remmeemmbbeer r

•• “Everything “Everything  in  its  place”  in  its  place”frees  up   frees  up   time  for  cleaning time  for  cleaning. . •• Use  an  office  or  facility  layout  as  a Use  an  office  or  facility  layout  as  a     visual  aid  to  identify  individual   visual  aid  to  identify  individual   responsibilities  for  cleaning responsibilities  for  cleaning.  This   .  This   eliminates  “no  man’s  land.” eliminates  “no  man’s  land.” •• CClea leaning ning  the  work  area  is  like    the  work  area  is  like   bathing bathing.  It  relieves  stress  and  strain,   .  It  relieves  stress  and  strain,   removes  sweat  and  dirt,  and   removes  sweat  and  dirt,  and   prepares  the  body  for  the  next  da prepares  the  body  for  the  next  day.y.

STANDARDIZING – Creating Consistency The fourth stage of 5S involves creating a consistent approach for carrying out tasks and procedures. Orderliness is the core of “standardization” and is maintained by Visual Controls which might consist of: Signboards, Painted Lines, Colorcoding strategies and Standardizing “Best Methods” across the organization.

LSS Black Belt Manual XL v11

D e fin itio n :

– To  maintain  the  workplace   at  a  level  that  uncovers   problems  and  makes  them   obvious. – To  continuously  improve   your  office  or  facility  by   continuous  assessment  and   action. W hy :

– To  sustain  sorting ,  storag e   and  shining  activities  every   day.

Th Thininggss   to   to   r   reemmeemmbbeerr ••W e  must  keep  the  work  place  neat   W e  must  keep  the  work  place  neat   enoug enough  for  visual  identifiers  to  be   h  for  visual  identifiers  to  be   effective  in  uncovering effective  in  uncovering  hidden    hidden   problems. problems. ••Develop  a  system  tha Develop  a  system  that  ena t  enables   bles   everyone  in  the  workplace  to  see   everyone  in  the  workplace  to  see   problems  when  they  occur. problems  when  they  occur.

© 2013 e-Careers Limited

586

Lean Controls SUSTAINING – Maintaining the 5S This last stage of 5S is the discipline and D e fin itio n : commitment of all other stages. – To  maintain  our   Without discipline,  we  need  to   “sustaining”, your practice  and  repeat  until   workplace can easily it  becomes  a  way  of  life. revert back to being dirty and chaotic. Th Thininggss   to   to   R   Rem emem embbeer r That is why it is so •• Develop  schedules  and   W hy : Develop  schedules  and   crucial for your team check  lists. check  lists. – To  build  5 S  into  our   to be empowered to •• GGood  ha ood  habits  are  ha bits  are  hard   rd   everyday  process. improve and to  establish. to  establish. maintain their •• CCommitment  and  discipline   ommitment  and  discipline   toward  housekeeping workplace. Keeping toward  housekeeping  are    are   essentia a 5S program vital in essential  first  steps  toward   l  first  steps  toward   being being  world  class.  world  class. an organization creates a cleaner workplace, a safer workplace. It contributes to how we feel about our product, our process, our company and ourselves. It provides a customer showcase to promote your business and product quality will improve – especially by reducing contaminants. Efficiency will increase also. When employees take pride in their work and workplace it can lead to greater job satisfaction and higher productivity. The Visual Factory A visual factory can best be represented by a workplace where a recently hired supervisor can easily identify inventory levels, extra tools or supplies, scrap issues, downtime concerns or even issues with setups or changeovers.

The basis and foundation of a Visual Factory are the 5S Standards. A Visual Factory enables a process to manage its processes with clear indications of opportunities. Your team should ask the following questions if looking for a project: – Can we readily identify Downtime Issues? – Can we readily identify Scrap Issues? – Can we readily identify Changeover Problems? – Can we readily identify Line Balancing Opportunities? – Can we readily identify Excessive Inventory Levels? – Can we readily identify Extraneous Tools & Supplies? Exercise: – Can you come up with any opportunities for “VISUAL” aids in your project? – What visual aids exist to manage your process?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

587

Lean Controls What is Standardized Work? If the items are organized and orderly, then standardized work can be accomplished. –  Less Standard Deviation of results –  Visual factory demands framework of standardized work. The one best way to perform each operation has been identified and agreed upon through general consensus (not majority rules) –  This defines the Standard work procedure

We cannot sustain Standardized Work without 5S and the Visual Factory.

Affected employees should understand that once they together have defined the standard, they will be expected to perform the job according to that standard.

Standardized Work

Visual Factory

5S - Workplace Organization

Prerequisites for Standardized Work

Standardized work does not happen without the Visual Factory which can be further described with: Availability of required tools (5S). Operators cannot be expected to maintain standard work if required to locate needed tools Consistent flow of raw material. Operators cannot be expected to maintain standard work if they are searching for needed parts Visual alert of variation in the process (Visual Factory). Operators, material handlers, office staff all need visual signals to keep standard work a standard Identified and labeled in-process stock (5S). As inventory levels of inprocess stock decrease, a visual signal should be sent to the material handlers to replenish this stock

The steps in developing CTQ’s are identifying the customer, capturing the Voice of the Customer and finally validating the CTQ’s.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

588

Lean Controls What is Kaizen?

• 

• 

Definition*: The philosophy of continual improvement, that every process can and should be continually evaluated and improved in terms of time required, resources used, resultant quality and other aspects relevant to the process.

Kaikaku are breakthrough successes which are the first focus of Six Sigma projects.

* Note: Kaizen Definition from: All I Needed To Know About Manufacturing I Learned in Joe s Garage. Miller and Schenk, Bayrock Press, 1996. Page 75.

Kaizen

Standardized Work

Visual Factory

5S - Workplace Organization

A Kaizen event is very similar to a Six Sigma project. A Six Sigma project is actually a Kaizen. By involving your project team or other in an area to assist with implementing the lean control or concepts you will increase buy in of the team which will effect your projects sustainability. Prerequisites for Kaizen

Kaizens need the following cultural elements: Management Support. Consider the corporate support which is the reason why Six Sigma focus is a success in your organization Measurable Process. Without standardized work, we really wouldn t have a consistent process to measure. Cycle times would vary, assembly methods would vary, batches of materials would be mixed, etc… Analysis Tools. There are improvement projects in each organization which cannot be solved by an operator. This is why we teach the analysis tools in the breakthrough strategy of Six Sigma. Operator Support. The organization needs to understand that its future lies in the success of the value-adding employees. Our roles as Belts are to convince operators that we are here for them--they will then be there for us.

A Kaizen event can be small or large in scope. Kaizens are improvement with a purpose of constantly improving a process. Some Kaizens are very small changes like a new jig or placement of a product or more involved projects. Kaizens are Six Sigma projects with business impact. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

589

Lean Controls What is Kanban? Kanbans are the best control method of inventory which impacts some of the 7 elements of MUDA shown earlier. Kanban provides production, conveyance, and delivery Kanban information. In it s purest form the system will not allow any goods to be moved within the facility without an appropriate Kanban (or signal) attached to the goods. –  The Japanese word for a communication signal Kaizen or card--typically a signal to begin work –  Kanban is the technique Standardized Work used to pull products and material through and into the lean manufacturing system. –  The actual Kanban can be a physical signal such as an empty Visual Factory container or a small card.

5S - Workplace Organization This is a building block. A Kanban needs to be supported by the previous steps we have reviewed. If Kanbans are abused they will actually backfire and effect the process in a negative manner. Two Types of Kanban There are two categories of Kanbans, finished good Kanbans and incoming material Kanbans as depicted here.

There are two main categories of Kanbans: Ty p e   1 :     Fin is h e d   g o o d s   K a n b a n s

–

–

S ig n a l   K a n b a n : S h o u ld   b e   p o s te d   a t   th e   e n d   o f   th e   p r o ce s s in g   a r e a   to   s ig n a l   fo r   p r o d u ctio n   to   b e g in .   P .I.K   K a n b a n :     U s e d   fo r   a   m u ch   m o r e   r e fin e d   le v e l   o f   in v e n to r y   co n tr o l.     K a n b a n   is   p o s te d   a s   in v e n to r y   is   d e p le te d   th u s   in s u r in g   o n ly   th e   m in im u m   a llo w a b le   le v e l   o f   p r o d u ct   is   m a in ta in e d .  

Ty p e   2 :     In co m in g   M a te ria l   K a n b a n s

–

U s e d   to   p u r ch a s e   m a te r ia ls   fr o m   a   s u p p ly in g   d e p a r tm e n t   e ith e r   in te r n a l   o r   e x te r n a l   to   th e   o r g a n iz a tio n .     R e g u la te s   th e   a m o u n t   o f   W IP   in v e n to r y   lo ca te d   a t   a   p a r ticu la r   p r o ce s s .

LSS Black Belt Manual XL v11

In tr a -­‐ p r o ce s s P .I.K . Production   Instruction  Ka nba n

S ig n a l

W ith d r a w a l In te r -­‐ P ro ce s s Between  two   processes

S u p p lie r © 2013 e-Careers Limited

590

Lean Controls Prerequisites for a Successful Kanban System Kanbans should smooth out inventory and keep product flowing but use them cautiously. If you prematurely implement a Kanban it WILL backfire.

Th e s e   ite m s   s u p p o rt   s u cce s s fu l   K a n b a n s : •

Im p ro v e   ch a n g e o v e r   p ro ce d u re s .  

•

R e la tiv e ly   s ta b le   d e m a n d   cy cle .

•

N u m b e r   o f   p a rts   p e r   K a n b a n   (ca rd )   M U S T   b e   s ta n d a rd   a n d   S H O U LD   b e   k e p t   to   a s   fe w   a s   p o s s ib le   p a rts   p e r   ca rd .

•

S m a ll   a m o u n t   o f   v a ria tio n   (o r   d e fe cts ).

•

N e a r   z e ro   d e fe cts   s h o u ld   b e   s e n t   to   th e   a s s e m b ly   p ro ce s s   (R e s u lt   o f   e a rlie r   b e lt   p ro je cts ).

•

C o n s is te n t   cy cle   tim e s   d e fin e d   b y   S ta n d a rd iz e d   W o rk .

•

M a te ria l   h a n d le rs   m u s t   b e   tra in e d   in   th e   o rg a n iz a tio n   o f   th e   tra n s p o rta tio n   s y s te m .

Warnings Regarding Kanban

If you do NOT have 5S, Visual Factory, standardized work and ongoing Kaizens –

Kanbans cannot succeed! Kanban systems are not quick fixes to large inventory problems, workforce issues, poor product planning, fluctuating demand cycles, etc...

Don t forget that weakest Link thing!!

It is not possible to implement a viable Kanban system without a strong support structure made up of the prerequisites. One of the most difficult concepts for people to integrate is the simplicity of the Lean tools… and to keep the discipline. Benchmarks have organizations using up to seven years to implement a successful Kanban System all the way through supplier and customer supply chain. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

591

Lean Controls The Lean Tools and Sustained Project Success

Th e   Le a n   to o ls   h e lp   s u s ta in   p ro je ct   s u cce s s .     Th e   m a in   le s s o n s   y o u   s h o u ld   co n s id e r   a re : 1 . Th e   TEA M   s h o u ld   5 S   th e   p ro je ct   a re a   a n d   b e g in   in te g ra tin g   v is u a l fa cto r y   in d ica to r s . – In d ica tio n s   o f   th e   n e e d   fo r   5 S   a re : – O u tlie r s   in   y o u r   p ro je ct   m e tric – Lo s s   o f   in itia l   g a in s   fr o m   p r o je ct   fin d in g s 2 . Th e   TEA M   s h o u ld   d e v e lo p   S ta n d a rd iz e d   W o rk   In s tru ctio n s – Th e y   a re   r e q u ire d   to   s u s ta in   y o u r   s y s te m   b e n e fits . – H o w e v e r,   r e m e m b e r   w ith o u t   a n   o rg a n iz e d   w o rk   p la ce   w ith   5 S   s ta n d a rd iz e d   w o rk   in s tr u ctio n s   w o n ’ t   cre a te   co n s is te n cy 3 . K a iz e n ’ s   a n d   K a n b a n ’ s   ca n n o t   b e   a tte m p te d   w ith o u t   o r g a n iz e d   w o rk p la ce s   a n d   o r g a n iz e d   w o rk   in s tru ctio n s . – R e m e m b e r   th e   n e e d   fo r   5 S   a n d   S ta n d a rd iz e d   W o rk   In s tru ctio n s   to   s u p p o rt   o u r   p r o je cts . 4 . P ro je ct   S co p e   d icta te s   h o w   fa r   u p   th e   Le a n   to o ls   la d d e r   y o u   n e e d to   im p le m e n t   m e a s u re s   to   s u s ta in   a n y   p r o je ct   s u cce s s   fr o m   y o u r   D M A IC   e ffo rts . The 5 Lean concepts are an excellent method for Belts to sustain their project success. If you have outliers, declining benefits or dropping process capability, you need to consider the concepts presented in this module. Class Exercise

In   th e   b o u n d a rie s   fo r   y o u r   p ro je ct   s co p e ,   g iv e   s o m e   e x a m p le s   o f   Le a n   to o ls   in   o p e ra tio n .     – O th e rs   ca n   le a rn   fro m   th o s e   ite m s   y o u   co n s id e r   b a s ic. Lis t   o th e r   Le a n   to o ls   y o u   a re   m o s t   in te re s te d   in   a p p ly in g   to   s u s ta in   y o u r   p ro je ct   re s u lts . To   g e n e ra te   th e   Ex e rcis e   in fo rm a tio n   co n s id e r   w a lk in g   a ro u n d   y o u r   fa cility ,   e s p e cia lly   if   it   is   N O T   a   m a n u fa ctu rin g   o n e ,   a n d   co n s id e r   w h e re   a   v is u a l   fa cto ry   w o u ld   b e   u s e fu l   a lo n g   w ith   th e   o th e r   4   Le a n   co n ce p ts   re v ie w e d .

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

592

Lean Controls At this point, you should be able to: §  Describe some Lean tools §  Understand how these tools can help with project sustainability §  Understand how the Lean tools depends on each other §  Understand how tools must document the defect prevention created in the Control Phase

You have now completed Control Phase – Lean Controls.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

593

Lean Six Sigma Black Belt Training

Control Phase Defect Controls

Now we will continue in the Control Phase with the “Defect Controls”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

594

Defect Controls Overview

W W eelco lcom m ee    to to    CCoonntr trooll AA ddvvaa nnce cedd    Ex Ex ppeerim rim eennts ts AA ddvvaa nnce cedd    CCaa ppaa bbility ility Le Leaa nn    CCoonntro trols ls

Rea Realistic  Tolera listic  Tolerance  a nce  and  Six  Sig nd  Six  Sigma  Desig ma  Designn

D Deefe fect   ct  CCoonntro trols ls

Process  A Process  Automa utomation  or  Interruption tion  or  Interruption

SSta ta tis tistica tica l  l  PPrrooce cessss    CCoonntr trool  l   (S P C ) (S P C )

Poka Poka-­‐-­‐YYoke oke

SSix ix    SSig ig m m aa    CCoonntro trol  l  PPla la nnss W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

In an effort to put in place Defect Controls we will examine Tolerances, Process Automation and Poka-Yoke. We will examine the meaning of each of these and show you how to apply them. Purpose of Defect Prevention in Control Phase P ro ce s s   im p r o v e m e n t   e ffo rts   o fte n   fa lte r   d u rin g   im p le m e n ta tio n   o f   n e w   o p e ra tin g   m e th o d s   le a rn e d   in   th e   A n a ly z e   a n d   Im p ro v e   P h a s e s .   S u s ta in a b le   im p ro v e m e n ts   ca n   n o t   b e   a ch ie v e d   w ith o u t   co n tro l   ta ctics   to   g u a ra n te e   p e r m a n e n cy . D e fe ct   P r e v e n tio n   s e e k s   to   g a in   p e rm a n e n cy   b y   e lim in a tin g   o r   rig id ly   d e fin in g   h u m a n   in te rv e n tio n   in   a   p ro ce s s .

YYes es  ssir, ir,  wwe e  aare re  i in n  CCONTROL!! ONTR OL !

With Defect Prevention we want to ensure that the improvements created during the project stay in place. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

595

Defect Controls Sigma Level for Project Sustaining in Control

5-6σ: Six Sigma product and/or process design eliminates an error condition OR an automated system monitors the process and automatically adjust Critical X s to correct settings without human intervention to sustain process improvements

BEST

4-5σ: Automated mechanism shuts down the process and prevents further operation until a required action is performed 3-5σ: Mistake Proofing prevents a product/service from passing onto the next step 3-4σ: SPC on X s with the Special Causes are identified and acted upon by fully trained operators and staff who adhere to the rules 2-4σ: SPC on Y s 1-3σ: Development of SOPs and process audits 0-1σ: Training and awareness

WORST

Our objective is to achieve the highest sigma level at acceptable costs.

LSS Black Belt Manual XL v11

Copyright OpenSourceSixSigma.com © 2013 e-Careers Limited

596

Defect Controls Sigma Level for Project Sustaining in Control The best approach to Defect Prevention is to design Six Sigma right into the process.

Specification on Y

D e s ig n in g   p ro d u cts   a n d   p ro ce s s e s   s u ch   th a t   th e   o u tp u t   Y   m e e ts   o r e x ce e d s   th e   ta rg e t   ca p a b ility . 24

22

Distribution of Y

21 19

Relationship   Y  =  F(x)

17 10

11

12

13

14

15

16

17

18

19

20

Distribution of X

W hen  desig ning  the  part  or  process,  specifica tions  on  X  are  set   such  tha t  the   targ et  capability  on  Y  is  achieved.     Both  the  targ et  and  tolerance  of  the  X  must  be  addressed  in  the   spec  limits.

6s Product/Process Design

Upper   Prediction   Interval

Specification on Y

24

22

Distribution of Y

Relationship   Y  =  F(x)

21 19

17 10

11

12

13

14

15

16

17

18

19

Distribution of X

20

Lower   Prediction   Interval

If   th e   r e la tio n s h ip   b e tw e e n   X   a n d   Y   is   e m p irica lly   d e v e lo p e d   th ro u g h   re g re s s io n s   o r   D O E’ s   u n ce rta in ty   e x is ts .     A s   a   re s u lt,   co n fid e n ce   in te rv a ls   s h o u ld   b e   u s e d   w h e n   e s ta b lis h i n g   th e   s p e cifica tio n s   fo r   X .      

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

597

Defect Controls Product/Process Design Example

Usually we use the prediction band provided by SigmaXL®. This is controllable by manipulation of the confidence intervals. 90%, 05%, 99%, etc. Play with adjusting the prediction bands to see the effect it has.

Regression Plot Y = 2.32891 - 0.282622X R-Sq = 96.1 %

Output2

10

N o te :     H ig h   o u tp u t   s p e c   co n n e cts w ith   to p   lin e   in   b o th   ca s e s . 5

Regression

Regression Plot

95% PI

0

Y = 7.75434 + 5.81104X -30

-20

-10

R-Sq = 88.0 %

0

Input2

90 80 70

Output

60 50 40 30 20

Lo w e r   in p u t   s p e c

Regression

10

95% PI

0

0

5

10

Input

U s in g   to p   o u tp u t   s p e c   d e te rm in e s   h ig h   o r   lo w   to le ra n ce   fo r   in p u t d e p e n d in g   o n   s lo p e   o f   r e g re s s io n

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

598

Defect Controls Poor Regression Impacting Tolerancing

Mr. Correlation is poor!!

5 – 6 σ Full Automation Fu ll   A u to m a tio n : Systems  that  monitor  the  process  and  automatically   adjust  critical  X’s  to  correct  setting s   • A utomatic  g aug ing  and  system  adjustments   • A utomatic  detection  and  system  activation  systems   -­‐ landing  g ear   extension  based  on  aircraft  speed  and  power  setting • Systems  that  count  cycles  and  automatically  make  adjustments  based   on  an  optimum  number  of  cycles   • A utomated  temperature  controllers  for  controlling  heating  and  cooling   systems • A nti-­‐Lock  braking  systems • A utomatic  welder  control  units  for  volts,  amps  and  distance  traveled   on  each  weld  cycle

Automation can be an option as well which removes the human element and its inherent variation. Although use caution to automate a process, many time people jump into automation prematurely, if you automate a poor process what will that do for you?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

599

Defect Controls Full Automation Example

Don’t worry boss, it’s automated!!!

4 – 5 σ Process Interruption

P r o ce s s   In te rru p tio n : Mechanism  installed  that  shuts  down  the   process  and  prevents  further  operation  until  a  required  action  is   preformed: • G round  fault  circuit  breakers • C hild  proof  caps  on  medications • Software  routines  to  prevent  undesirable  commands • Safety  interlocks  on  equipment  such  as  lig ht  curtains,  dual  palm buttons,  ram  blocks • Transfer  system  g uides  or  fixtures  that  prevent  over  or  undersiz ed   parts  from  proceeding • Temperature  conveyor  interlocks  on  ovens • Missing  component  detection  that  stops  the  process  when  trig g ered

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

600

Defect Controls 4 – 5 σ Process Interruption (cont.)

Ex a m p le : •

•

A   B la ck   B e lt   is   w o rk in g   o n   la u n ch in g   a   n e w   e le ctric   d riv e   u n it   o n   a   tra n s fe r   s y s te m   – O n e   co m m o n   fa ilu re   m o d e   o f   th e   s y s te m   is   a   b e a rin g   fa ilu re   o n   th e   m a in   m o to r   s h a ft     – It   w a s   d e te r m in e d   th a t   a   h ig h   p re s s   fit   a t   b e a rin g   in s ta lla tio n   w a s   ca u s in g   th e s e   fa ilu re s     – Th e   ro o t   ca u s e   o f   th e   p ro b le m   tu rn e d   o u t   to   b e   u n d e rs iz e d   b e a rin g s   fro m   th e   s u p p lie r U n til   th e   s u p p lie r   co u ld   b e   b ro u g h t   in to   co n tro l   o r   re p la ce d ,   th e   te a m   im p le m e n te d   a   p re s s   lo a d   m o n ito r   a t   th e   b e a rin g   p re s s   w ith   a   in d ica to r – If   th e   m o n ito r   d e te cts   a   p re s s   lo a d   h ig h e r   th a n   th e   s e t   p o in t,   it   s h u ts   d o w n   th e   p re s s   a n d   w ill   n o t   a llo w   th e   u n it   to   b e   re m o v e d   fro m   p re s s   u n til   a n   in te rlo ck   k e y   is   tu rn e d   a n d   th e   ra m   re s e t   in   th e   m a n u a l   m o d e     – O n ly   th e   lin e   le a d   p e rs o n   a n d   th e   s u p e rv is o r   h a v e   k e y s   to   th e   in te rlo ck     – Th e   n o n -­‐co n fo rm in g   p a rt   is   a u to m a tica lly   m a rk e d   w ith   re d   dye

P ro ce s s   In te rru p tio n 3 – 5 σ Mistake Proofing Mistake Proofing is great because it is usually inexpensive and very effective. Consider the many everyday examples of Mistake Proofing. You can not fit the diesel gas hose into an unleaded vehicle gas tank. Pretty straightforward, right?

M is ta k e   P ro o fin g is  best  defined  as:     – Using  wisdom,  ing enuity,  or  serendipity  to  create  devices   allowing  a  1 0 0 %  defect  free  step  1 0 0 %  of  the  time Poka-­‐Y oke  is  the  Japanese  term  for  mistake  proofing  or  to  avoid   “yokeuro” inadvertent  errors  “poka”. 1

5

2

7

3

4

8

S ee  ifi f  you y ou  can   See can find find   the  the Pok a-­‐ PokaY ok es!Yokes!!

6

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

601

Defect Controls Traditional Quality vs. Mistake Proofing This clearly highlights the difference between the two approaches. What are the benefits to the Source Inspection method?

Tra d itio n a l   In s p e ctio n   R e s u lt W orker  or Machine  Error

Discover Error

Don’t  Do A nything

Sort A t  O ther Step

Defective

Take  A ction/ Feedback

N ext Step

No Defect

S o u rce   In s p e ctio n “ K EEP   ER R O R S   FR O M TU R N IN G   IN TO   D EFEC TS ”

Styles of Mistake Proofing

Th e re   a re   2   s ta te s   o f   a   d e fe ct   w h ich   a re   a d d re s s e d   w ith   m is ta k e   p ro o fin g . ER R O R   A B O U T   TO   O C C U R

ER R O R   H A S   O C C U R R ED

D EFEC T   A B O U T   TO   O C C U R (P re d ictio n )

D EFEC T   H A S   O C C U R R ED (D e te ctio n )

W A R N IN G   S IG N A L

W A R N IN G   S IG N A L

C O N TR O L   /   FEED B A C K

C O N TR O L   /   FEED B A C K

S H U TD O W N (S to p   O p e ra tio n )

S H U TD O W N (S to p   O p e ra tio n )

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

602

Defect Controls Mistake Proofing Devices Design

H in ts   to   h e lp   d e s ig n   a   m is ta k e   p ro o fin g   d e v ice : – – – – – –

S im p le In e x p e n s iv e G iv e   p ro m p t   fe e d b a ck G iv e   p ro m p t   a ctio n   (p r e v e n tio n ) Fo cu s e d   a p p lica tio n H a v e   th e   rig h t   p e o p le ’ s   in p u t

B ES T             ...makes  it  impossible  for  errors  to  occur B ETTER

… … allows  for  detection  while  error  is  being  made

G O O D           ...detects  defect  before  it  continues  to  the  next  operation The very best approaches make creating a defect impossible, recall the gas hose example, you can not put diesel fuel into an unleaded gas tank unless you really try hard or have a hammer.

Types of Mistake Proof Devices

C o n ta ct   M e th o d Guide Pins of – P h y s ica l   o r   e n e rg y   co n ta ct                              Different                     Siz        es                   w ith   p ro d u ct • Lim it   s w itch e s • P h o to -­‐e le ctric   b e a m s Error Detection Fix e d   V a lu e   M e th o d and Alarms – N u m b e r   o f   p a rts   to   b e                                                                                       a tta ch e d / a s s e m b le d   e tc.                                                                                   a re   co n s ta n t Limit Switches – N u m b e r   o f   s te p s   d o n e                                                                                         in   o p e ra tio n • Lim it   s w itch e s Counters M o tio n -­‐s te p   M e th o d – C h e ck s   fo r   co rre ct   s e q u e n cin g – C h e ck s   fo r   co rre ct   tim in g Checklists • P h o to -­‐e le ctric   s w itch e s                                                                                               a n d   tim e rs

1

2

3

4

5

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

603

Defect Controls Mistake Proofing Examples Let’s consider examples of mistake proofing or Poka-Yoke devices even in the home. Have a discussion about them in the work environment as well.

Ev e r y d a y   e x a m p le s   o f   m is ta k e -­‐p r o o fin g : •

– –

•

•

H om e A u to m a te d   s h u to ffs   o n   e le ctric   co ffe e   p o ts G ro u n d   fa u lt   circu it   b re a k e rs   fo r   b a th ro o m   in   o r   o u ts id e   e le ctric   circu its

–

P ilo tle s s   g a s   ra n g e s   a n d   h o t   w a te r   h e a te rs

–

C h ild   p ro o f   ca p s   o n   m e d ica tio n s

–

B u ta n e   lig h te rs   w ith   s a fe ty   b u tto n

•

•

C o m p u te rs –

M o u s e   in s e rtio n

–

U S B   ca b le   co n n e ctio n

–

B a tte ry   in s e rtio n

–

P o w e r   s a v e   fe a tu re  

A u to m o b ile –

S e a t   b elts

–

A ir   b a g s

–

C a r   e n g in e   w a r n in g   lig h ts

O ffice –

S p e ll   ch e ck   in   w o rd   p ro ce s s in g   s o ftw a re

–

Q u e s tio n in g   “ D o   y o u   w a n t   to   d e le te ” a fte r   d e p re s s in g   th e   “ D e le te ” b u tto n   o n   y o u r   co m p u te r

Fa cto ry –

•

D u a l   p a lm   b u tto n s   a n d   o th e r   g u a rd s   o n   m a ch in e ry

R e ta il –

Ta m p e r   p ro o f   p a ck a g in g

Advantages of Mistake Proofing as a Control Method M is ta k e   P ro o fin g   a d v a n ta g e s   in clu d e : – O n ly   s im p le   tr a in in g   p ro g ra m s   a re   r e q u ir e d – In s p e ctio n   o p e ra tio n s   a r e   e lim in a te d   a n d   th e   p ro ce s s   is   s im p lifi e d – R e lie v e s   o p e r a to rs   fro m   re p e titiv e   ta s k s   o f   ty p ica l   v is u a l   in s p e ctio n – P ro m o te s   cre a tiv ity   a n d   v a lu e   a d d in g   a ctiv itie s – R e s u lts   in   d e fe ct   fre e   w o rk – R e q u ire s   im m e d ia te   a ctio n   w h e n   p ro b le m s   a ris e – P ro v id e s   1 0 0 %   in s p e ctio n   in te r n a l   to   th e   o p e ra tio n Th e   b e s t   re s o u rce   fo r   p icto ria l   e x a m p le s   o f   M is ta k e   P ro o fin g   is :

P o k a -­‐Y o k e :   Im p ro v in g   P ro d u ct   Q u a lity   b y   P re v e n tin g   D e fe cts .     O v e rv ie w   b y   H iro y u k i   H ira n o .     P ro d u ctiv ity   P re s s ,   1 9 8 8 .) To see a much more in-depth review of improving the product or service quality by preventing defects you MUST review the book shown here. A comprehensive 240 Poka-Yoke examples are shown and can be applied to many industries. The Poka-Yoke’s are meant to address errors from processing, assembly, mounting, insertion, measurement, dimensional, labeling, inspection, painting, printing, misalignment and many other reasons.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

604

Defect Controls Defect Prevention Culture and Good Control Plans

All of the Defect Prevention methods used must be documented in your FMEA and the Control Plan discussed later in the Control Phase. Class Exercise

B re a k   in to   y o u r   g ro u p s   a n d   d is cu s s   m is ta k e   p ro o fin g   s y s te m s   cu rre n tly   a t   y o u r   fa cilitie s   Id e n tify   o n e   a u to m a tio n   e x a m p le   a n d   o n e   p ro ce s s   in te rru p tio n   e x a m p le   p e r   g ro u p     B e   p re p a re d   to   p re s e n t   b o th   e x a m p le s   to   th e   cla s s     A n s w e r   th e   fo llo w in g   q u e s tio n s   a s   p a rt   o f   th e   d is cu s s io n   a n d   p re s e n ta tio n : – H o w   w a s   th e   n e e d   fo r   th e   co n tro l   s y s te m   id e n tifie d ?     If   a   critica l   X   is   m is ta k e   p ro o fe d ,   h o w   w a s   it   id e n tifie d   a s   b e in g   critica l? – H o w   a re   th e y   m a in ta in e d ? – H o w   a re   th e y   v e rifie d   a s   w o rk in g   p ro p e rly ? – A re   th e y   e v e r   d is a b le d ? Y o u   h a v e   3 0   m in u te s ! Prepare a probable defect prevention method to apply to your project. List any potential barriers to implementation.

LSS Black Belt Manual XL v11

Tic toc…..! © 2013 e-Careers Limited

605

Defect Controls At this point, you should be able to: §  Describe some methods of Defect Prevention §  Understand how these techniques can help with project sustainability: - Including reducing those outliers as seen in the Advanced Process Capability section - If the vital X was identified, prevent the cause of defective Y §  Understand what tools must document the Defect Prevention created in the Control Phase

You have now completed Control Phase – Defect Controls.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

606

Lean Six Sigma Black Belt Training

Control Phase Statistical Process Control

We will now continue in the Control Phase with “Statistical Process Control or SPC”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

607

Statistical Process Control Overview

W W eelco lcom m ee    to to    CCoonntr trooll AA ddvvaa nnce cedd    Ex Ex ppeerim rim eennts ts AA ddvvaa nnce cedd    CCaa ppaa bbility ility Le Leaa nn    CCoonntro trols ls D Deefe fect   ct  CCoonntro trols ls SSta ta tis tistica tica l  l  PPrrooce cessss    CCoonntr trool  l   (S (SPPCC)) SSix ix    SSig ig m m aa    CCoonntro trol  l  PPla la nnss

Elements  and  Purpose Elements  and  Purpose Methodolog Methodologyy Special  C Special  Caause  Tests use  Tests Exa Examples mples

W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Statistical techniques can be used to monitor and manage process performance. Process performance, as we have learned, is determined by the behavior of the inputs acting upon it in the form of Y=f(X). As a result it must be well understood that we can only monitor the performance of a process output. Many people have applied Statistical Process Control (SPC) to only the process outputs. Because they were using SPC, their expectations were high regarding a new potential level of performance and control over their processes. However, because they only applied SPC to the outputs, they were soon disappointed. When you apply SPC techniques to outputs, it is appropriately called Statistical Process Monitoring or SPM. You of course know that you can only control an output by controlling the inputs that exert an influence on that output. This is not to say that applying SPC techniques to an output is bad, there are valid reasons for doing this. Six Sigma has helped us all to better understand where to apply such control techniques. In addition to controlling inputs and monitoring outputs, Control Charts are used to determine the Baseline performance of a process, evaluate measurement systems, compare multiple processes, compare processes before and after a change, etc. Control Charts can be used in many situations that relate to process characterization, analysis and performance. To better understand the role of SPC techniques in Six Sigma, we will first investigate some of the factors that influence processes, then review how simple probability makes SPC work and finally look at various approaches to monitoring and controlling a process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

608

Statistical Process Control SPC Overview: Collecting Data Control Charts are usually derived P o p u la tio n : from samples taken from the – A n  entire  g roup  of  objects  that  have  been  made  or  will  be   made  containing  a  cha racteristic  of  interest larger population. Sampling must S a m p le : be collected in such a way that it – A  sample  is  a  subset  of  the  population  of  interest does not bias or distort the – The  g roup  of  objects  actually  measured  in  a  statistical   interpretation of the Control Chart. study The process must be allowed to – Samples  are  used  to  estimate  the  true  population   operate normally when taking a parameters sample. If there is any special treatment or bias given to the P o p u la tio n process over the period the data is collected, the Control Chart interpretation will be invalid. The S a m p le frequency of sampling depends S a m p le on the volume of activity and the S a m p le ability to detect trends and patterns in the data. At the onset, you should error on the side of taking extra samples, and then, if the process demonstrates its ability to stay in control, you can reduce the sampling rate. Using rational subgroups is a common way to assure that this does not happen. A rational subgroup is a sample of a process characteristic in which all the items in the sample were produced under very similar conditions and in a relatively short time period. Rational subgroups are usually small in size, typically consisting of 3 to 5 units to make up the sample. It is important that rational subgroups consist of units that were produced as closely as possible to each other, especially if you want to detect patterns, shifts and drifts. If a machine is drilling 30 holes a minute and you wanted to collect a sample of hole sizes, a good rational subgroup would consist of 4 consecutively drilled holes. The selection of rational subgroups enables you to accurately distinguish Special Cause variation from Common Cause variation. Make sure that your samples are not biased in any way, meaning that they are randomly selected. For example, do not plot only the first shift’s data if you are running multiple shifts. Don’t look at only one vendor’s material if you want to know how the overall process is really running. Finally, don’t concentrate on a specific time to collect your samples; like just before the lunch break. If your process consists of multiple machines, operators or other process activities that produce streams of the same output characteristic you want to control, it would be best to use separate Control Charts for each of the output streams. If the process is stable and in control, the sample observations will be randomly distributed around the average. Observations will not show any trends or shifts and will not have any significant outliers from the random distribution around the average. This type of behavior is to be expected from a normally operating process and that is why it is called Common Cause variation. Unless you are intentionally trying to optimize the performance of a process to reduce variation or change the average, as in a typical Six Sigma project, you should not make any adjustments or alterations to the process if it is demonstrating only Common Cause variation. That can be a big time saver since it prevents “wild goose chases.” If Special Cause variation occurs, you must investigate what created it and find a way to prevent it from happening again. Some form of action is always required to make a correction and to prevent future occurrences. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

609

Statistical Process Control SPC Overview: I-MR Chart

Individuals (I) and Moving Range (MR) Charts are used when each measurement represents one batch. The subgroup size is equal to one when I-MR Charts are used. These charts are very simple to prepare and use. The graphic shows the Individuals Chart where the individual measurement values are plotted with the Center Line being the average of the individual measurements. The Moving Range Chart shows the range between two subsequent measurements. There are certain situations when opportunities to collect data are limited or when grouping the data into subgroups simply doesn't make practical sense. Perhaps the most obvious of these cases is when each individual measurement is already a rational subgroup. This might happen when each measurement represents one batch, when the measurements are widely spaced in time or when only one measurement is available in evaluating the process. Such situations include destructive testing, inventory turns, monthly revenue figures and chemical tests of a characteristic in a large container of material. All of these situations indicate a subgroup size of one. Because this chart is dealing with individual measurements it, is not as sensitive as the X-Bar Chart in detecting process changes.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

610

Statistical Process Control SPC Overview: Xbar-R Chart

An XBar-R Chart is used primarily to monitor and control the stability of the average value. The XBar Chart plots the average values of each of a number of small sampled subgroups. The averages of the process subgroups are collected in sequential, or chronological, order from the process. The XBar Chart, together with the R Chart shown, is a sensitive method to identify assignable causes of product and process variation and gives great insight into short-term variations. These charts are most effective when they are used together. Each chart individually shows only a portion of the information concerning the process characteristic. The upper chart shows how the process average (central tendency) changes. The lower chart shows how the variation of the process has changed. It is important to control both the process average and the variation separately because different corrective or improvement actions are usually required to effect a change in each of these two parameters. The R Chart must be in control in order to interpret the averages chart because the Control Limits are calculated considering both process variation and center. When the R Chart is not in control, the control limits on the averages chart will be inaccurate and may falsely indicate an out of control condition. In this case, the lack of control will be due to unstable variation rather than actual changes in the averages. XBar and RBar Charts are often more sensitive than I-MR, but are frequently done incorrectly. The most common error is failure to perform rational sub-grouping correctly. A rational subgroup is simply a group of items made under conditions that are as nearly identical as possible. Five consecutive items, made on the same machine, with the same setup, the same raw materials and the same operator, are a rational subgroup. Five items made at the same time on different machines are not a rational subgroup. Failure to form rational subgroups correctly will make your XBar-R Charts dangerously wrong. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

611

Statistical Process Control SPC Overview: U Chart

The U Chart plots defects per unit data collected from subgroups of equal or unequal sizes. The “U” in U Charts stands for defects per Unit. U Charts plot the proportion of defects that are occurring. The U Chart and the C Chart are very similar. They both are looking at defects but the U Chart does not need a constant sample size like the sample size like the C Chart. The Control Limits on the U Chart vary with the sample size and therefore they are not uniform, similar to the P Chart which we will describe next. Counting defects on forms is a common use for the U Chart. For example, defects on insurance claim forms are a problem for hospitals. Every claim form has to be checked and corrected before going to the insurance company. When completing a claim form, a particular hospital must fill in 13 fields to indicate the patient’s name, social security number, DRG codes and other pertinent data. A blank or incorrect field is a defect. A hospital measured their invoicing performance by calculating the number of defects per unit for each day’s processing of claims forms. The graph demonstrates their performance on a U Chart. The general procedure for U Charts is as follows: 1. Determine purpose of the chart 2. Select data collection point 3. Establish basis for sub-grouping 4. Establish sampling interval and determine sample size 5. Set up forms for recording and charting data and write specific instructions on use of the chart 6. Collect and record data. 7. Count the number of nonconformities for each of the subgroups 8. Input into Excel or other statistical software. 9. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

612

Statistical Process Control SPC Overview: P Chart

The P Chart plots the proportion of nonconforming units collected from subgroups of equal or unequal size (percent defective). The proportion of defective units observed is obtained by dividing the number of defective units observed in the sample by the number of units sampled. P Charts name comes from plotting the Proportion of defectives. When using samples of different sizes, the upper and lower Control Limits will not remain the same - they will look uneven as exhibited in the graphic. These varying Control Chart limits are effectively managed by Control Charting software. A common application of a P Chart is when the data is in the form of a percentage and the sample size for the percentage has the chance to be different from one sample to the next. An example would be the number of patients that arrive late each day for their dental appointments. Another example is the number of forms processed daily that had to be reworked due to defects. In both of these examples, the total quantity would vary from day to day. The general procedure for P Charts is as follows: 1. Determine purpose of the chart 2. Select data collection point 3. Establish basis for sub-grouping 4. Establish sampling interval and determine sample size 5. Set up forms for recording and charting data and write specific instructions on use of the chart 6. Collect and record data. It is recommended that at least 20 samples be used to calculate the Control Limits 7. Compute P, the proportion nonconforming for each of the subgroups 8. Load data into Excel or other statistical software 9. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

613

Statistical Process Control SPC Overview: Control Methods/Effectiveness Type 1 Corrective Action = Countermeasure: improvement made to the process which will eliminate the error condition from occurring. The defect will never be created. This is also referred to as a long-term corrective action in the form of mistake proofing or design changes. Type 2 Corrective Action = Flag: improvement made to the process which will detect when the error condition has occurred. This flag will shut down the equipment so that the defect will not move forward. SPC on X s or Y s with fully trained operators and staff who respect the rules. Once a chart signals a problem everyone understands the rules of SPC and agrees to shut down for Special Cause identification. (Cpk > certain level). Type 3 Corrective Action = Inspection: implementation of a short-term containment which is likely to detect the defect caused by the error condition. Containments are typically audits or 100% inspection. SPC on X s or Y s with fully trained operators. The operators have been trained and understand the rules of SPC, but management will not empower them to stop for investigation. S.O.P. is implemented to attempt to detect the defects. This action is not sustainable short-term or long-term. SPC on X s or Y s without proper usage = WALL PAPER.

The most effective form of control is called a type 1 corrective action. This is a control applied to the process which will eliminate the error condition from occurring. The defect can never happen. This is the “prevention” application of the Poka-Yoke method. The second most effective control is called a type 2 corrective action. This a control applied to the process which will detect when an error condition has occurred and will stop the process or shut down the equipment so that the defect will not move forward. This is the “detection” application of the Poka-Yoke method. The third most effective form of control is to use SPC on the X’s with appropriate monitoring on the Ys. To be effective, employees must be fully trained, they must respect the rules and management must empower the employees to take action. Once a chart signals a problem, everyone understands the rules of SPC and agrees to take emergency action for special cause identification and elimination. The fourth most effective correction action is the implementation of a short-term containment which is likely to detect the defect caused by the error condition. Containments are typically audits or 100% inspection. Finally you can prepare and implement an S.O.P. (standard operating procedure) to attempt to manage the process activities and to detect process defects. This action is not sustainable, either short-term or long-term. Do not do SPC for the sake of just saying that you do SPC. It will quickly deteriorate to a waste of time and a very valuable process tool will be rejected from future use by anyone who was associated with the improper use of SPC. Using the correct level of control for an improvement to a process will increase the acceptance of changes/solutions you may wish to make and it will sustain your improvement for the long-term. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

614

Statistical Process Control Purpose of Statistical Process Control

Causes of Variation are either: –  Common Cause: Reoccurring variability –  Special Cause: Unusual variability •  Assignable: Reason for detected Variability •  Pattern Change: Presence of trend or unusual pattern SPC is a basic tool to monitor variation in a process.

This is a special cause!!! SPC has its uses because it is known that every process has known variation called Special Cause and Common Cause variation. Special Cause variation is unnatural variability because of assignable causes or pattern changes. SPC is a powerful tool to monitor and improve the variation of a process. This powerful tool is often an aspect used in visual factories. If a supervisor or operator or staff is able to quickly monitor how its process is operating by looking at the key inputs or outputs of the process, this would exemplify a visual factory. SPC is used to detect Special Causes in order to have those operating the process find and remove the Special Cause. When a Special Cause has been detected, the process is considered to be “out of control”. SPC gives an ongoing look at the Process Capability. It is not a capability measurement but it is a visual indication of the continued Process Capability of your process.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

615

Statistical Process Control Elements of Control Charts

Use the “Orders” worksheet, column Avg. Orders Per Month 2. Control Charts were first developed by Dr. Shewhart in the early 20th century in the U.S. Control Charts are a graphical and visual plot of a process and is charted over time like a Time Series Chart. From a visual management aspect, a Time Plot is more powerful than knowledge of the last measurement. These charts are meant to indicate change in a process. All SPC charts have a Central Line and Control Limits to aid in Special Cause variation. Notice, again, we never discussed showing or considering specifications. We are advising you to never have specification limits on a Control Chart because of the confusion often generated. Remember we want to control and maintain the process improvements made during your project. These Control Charts and their limits are the Voice of the Process not the Voice of the Customer which are the specification limits.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

616

Statistical Process Control Understanding the Power of SPC C o n tro l   C h a rts   in d ica te   w h e n   a   p ro ce s s   is   “ o u t   o f   co n tro l” o r   e x h ib itin g   s p ecia l   ca u s e   v a ria tio n   b u t   N O T   w h y ! S P C   ch a rts   in co rp o ra te   u p p e r   a n d   lo w e r   co n tro l   lim its . –

Th e   lim its   a re   ty p ica lly   + / -­‐ 3   σ fro m   th e   ce n te rlin e .

–

Th e s e   lim its   rep re s e n t   9 9 .7 3 %   o f   n a tu ra l   v a ria b ility   fo r   n o rm a l   d is trib u tio n s .

S P C   ch a rts   a llo w   w o rk e rs   a n d   s u p e rv is io n   to   m a in ta in   im p ro v ed   p r o ce s s   p e rfo rm a n ce   fro m   S ix   S ig m a   p ro je cts . U s e   o f   S P C   ch a rts   ca n   b e   a p p lie d   w ith   a ll   p ro ces s e s . –

S e rv ice s ,   m a n u fa ctu rin g ,   a n d   re ta il   a re   ju s t   a   few   in d u s trie s   w i th   S P C   a p p lica tio n s .

–

C a u tio n   m u s t   b e   ta k e n   w ith   u s e   o f   S P C   fo r   n o n -­‐n o rm a l   p ro ce s s es .

C o n tro l   lim its   d es crib e   th e   p ro ce s s   v a ria b ility   a n d   a re   u n re la te d   to   cu s to m e r   s p e cifica tio n s .     (V o ice   o f   th e   P ro ce s s   in s tea d   o f   V o ice   o f   th e   C u s to m e r) –

A n   u n d e s ira b le   s itu a tio n   is   h a v in g   co n tro l   lim its   w id e r   th a n   cu s to m e r   s p e cifica tio n   lim its .     Th is   w ill   e x is t   fo r   p o o rly   p e rfo rm in g   p ro ces s es   w ith   a   C p   le s s   th a n   1 .0

M a n y   S P C   ch a rts   e x is t   a n d   s e lectio n   m u s t   b e   a p p ro p ria te   fo r   e ffe ctiv e n e s s .

The Control Chart Cookbook

General Steps for Constructing Control Charts 1.

Select characteristic (critical X or CTQ) to be charted.

2.

Determine the purpose of the chart.

3.

Select data-collection points.

4.

Establish the basis for sub-grouping (only for Y s).

5.

Select the type of Control Chart.

6.

Determine the measurement method/criteria.

7.

Establish the sampling interval/frequency.

8.

Determine the sample size.

9.

Establish the basis of calculating the Control Limits.

10. Set up the forms or software for charting data.

Stirred or Shaken?!

11. Set up the forms or software for collecting data. 12. Prepare written instructions for all phases. 13. Conduct the necessary training.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

617

Statistical Process Control Focus of Six Sigma and the Use of SPC This concept should be very familiar to you by now. If we understand the variation caused by the X’s, then we should be monitoring with SPC the X’s first. By this time in the methodology you should clearly understand the concept of Y=f(x). Using SPC we are attempting to control the Critical X’s in order to control the Y.

Y = F(x ) To  g et  results,  should  we  focus  our  behavior  on  the  Y  or  X? Y Dependent O utput Effect S ymptom Monitor

X 1 .  .  .  X N Independent Input C ause Problem C ontrol

If  we  find  the  “vital  few” X’s,  first  consider  using  S PC   on  the  X’s  to  achieve  a  desired  Y ?

Control Chart Anatomy Statistical Process Control (SPC) involves the use of statistical techniques, to interpret data, to control the variation in processes. SPC is used primarily to act on out of control processes, but it is also used to monitor the consistency of processes producing products and services. A primary SPC tool is the Control Chart - a graphical representation for specific quantitative measurements of a process input or output. In the Control Chart, these quantitative measurements are compared to decision rules calculated based on probabilities from the actual measurement of process performance. The comparison between the decision rules and the performance data detects any unusual variation in the process that could indicate a problem with the process. Several different descriptive statistics can be used in Control Charts. In addition, there are several different types of Control Charts that can test for different causes, such as how quickly major vs. minor shifts in process averages are detected. Control Charts are Time Series Charts of all the data points with one addition. The Standard Deviation for the data is calculated for the data and two additional lines are added. These lines are placed +/- 3 Standard Deviations away from the Mean and are called the Upper Control Limit (UCL) and the Lower Control Limit (LCL). Now the chart has three zones: (1) The zone between the UCL and the LCL which called the zone of Common Cause variation, (2) The zone above the UCL which a zone of Special Cause variation and (3) another zone of Special Cause variation below the LCL. Control Charts graphically highlight data points that do not fit the normal level of expected variation. This is mathematically defined as being more than +/- 3 Standard Deviations from the Mean. It’s all based off probabilities. We will now demonstrate how this is determined. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

618

Statistical Process Control Control and Out of Control

Control Charts provide you with two basic functions; one is to provide time based information on the performance of the process which makes it possible to track events affecting the process and the second is to alert you when Special Cause variation occurs. Control Charts graphically highlight data points that do not fit the normal level of variation expected. It is standard that the Common Cause variation level is defined as +/- 3 Standard Deviations from the Mean. This is also know as the UCL and LCL respectively. Recall the “area under the curve” discussion in the lesson on Basic Statistics, remembering that +/one Standard Deviation represented 68% of the distribution, +/- 2 was 95% and +/- 3 was 99.7%. You also learned from a probability perspective that you would expect the output of a process would have a 99.7% chance of being between +/- 3 Standard Deviations. You also learned that sum of all probability must equal 100%. There is only a 0.3% chance (100% - 99.7%) that a data point be beyond +/- 3 Standard Deviations. In fact, since we are talking about two zones; one zone above the + 3 Standard Deviations and one below it. We have to split 0.3% in two, meaning that there is only a 0.15% chance of being in one of the zones. There is only a .0015 (.15%) probability that a data point will either be above or below the UCL or LCL. That is a very small probability as compared to .997 (99.75%) probability the data point will be between the UCL and the LCL. What this means is there must have been something special happen to cause a data point to be that far from the Mean, like a change in vendor, a mistake, etc. This is why the term the term Special Cause or assignable cause variation applies. The probability that a data point was this far from the rest of the population is so low that something special or assignable happened. Outliers are just that, they have a low probability of occurring, meaning we have lost control of our process. This simple, quantitative approach using probability is the essence of all Control Charts.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

619

Statistical Process Control Size of Subgroups Typical  subg roup  siz es  are  3 -­‐1 2  for  variable  data: – If  difficulty  of  g athering  sample  or  expense  of  testing  exists,   the  siz e,  n,  is   smaller – 3 ,  5 ,  and  1 0  are  the  most  common  siz e  of  subg roups  because  of  ea se  of   calculations  when  SPC  is  done  without  computers. Siz e  of  subg roups  aid  in  detection  of  shifts  of  mean  indicating   special  cause   exists.  The  larg er  the  subg roup  siz e,  the  g reater  chance  of  detecting  a  special   cause.  Subg roup  siz e  for  A ttribute  Data  is  often  5 0   – 2 0 0 . Lot 1

Lot 5 Lot 3

Lot 2 Lot 4

Short-term studies

Long-term study

The Impact of Variation Remember the Control Limits are based on your PAST data and depending on what sources of variation you have included in your subgroups, the control limits which detect the Special Cause variation will be affected. You really want to have subgroups with only Common Cause variation so if other sources of variation are detected, the sources will be easily found instead of buried within your definition of subgroups.

Sources of Variation - Natural Process Variation as defined by subgroup selection

- Natural Process Variation - Different Operators

- Natural Process Variation - Different Operators - Supplier Source

-UCL -LCL

First, select a spread to declare as the Natural Process Variation so that whenever any point lands outside these Control Limits an alarm will sound

So, when a second source of variation appears, we will know!

And, of course, if two additional sources of variation arrive, we will detect that, too!

If you base your limits on all three sources of variation, what will sound the alarm?

Let’s consider if you were tracking delivery times for quotes on new business with an SPC chart. If you decided to not include averaging across product categories, you might find product categories are assignable causes but you might not find them as Special Causes since you have included them in the subgroups as part of your rationalization. You really want to have subgroups with only Common Cause variation so if other sources of variation are detected, the sources will be easily found instead of buried within your definition of subgroups. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

620

Statistical Process Control Frequency of Sampling Sampling Frequency is a balance between cost of sampling and testing versus cost of not detecting shifts in mean or variation. Process knowledge is an input to frequency of samples after the subgroup size has been decided. - If a process shifts but cannot be detected because of too infrequent sampling, the customer suffers - If choice is given of large subgroup samples infrequently or smaller subgroups more frequently, most choose to get information more frequently. - In some processes, with automated sampling and testing frequent sampling is easy. If undecided as to sample frequency, sample more frequently to confirm detection of process shifts and reduce frequency if process variation is still detectable. A rule of thumb also states “sample a process at least 10X more frequent than the frequency of ‘out of control’ conditions”. Sometimes it can be a struggle how often to sample your process when monitoring results. Unless the measurement is automated, inexpensive and recorded with computers and able to be charted with SPC software without operator involvement, then frequency of sampling is an issue. Let’s reemphasize some points. First, you do NOT want to under sample and not have the ability to find Special Cause variation easily. Second, do not be afraid to sample more frequently and then reduce the frequency if it is clear Special Causes are found frequently.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

621

Statistical Process Control SPC Selection Process The Control Charts you choose to use will always be based first on the type of data you have and then on the objective of the Control Chart. The first selection criteria will be whether you have Attribute or Continuous Data.

C h o o s e   A p p ro p ria te   C o n tro l   C h a rt

type of data

ATTRIBUTE

DEFECTS

type of attribute data

CONTINUOUS

subgroup size DEFECTIVES Sample size 1

type of defect

CONSTANT

type of subgroups VARIABLE

CONSTANT

I – MR Chart

2-5

10+

X–R Chart

X–S Chart

VARIABLE

Individuals Mean & Mean & Continuous SPC refers & Moving Range Std. Dev. Range to Control Charts that NP SPECIAL CASES C Chart U Chart P Chart display process input Chart or output Number of Incidences Number of Proportion Incidences per Unit Defectives Defectives CumSum EWMA characteristics based Chart Chart on Continuous Data Cumulative Exponentially data where decimal Sum Weighted Moving Average subdivisions have meaning. When these Control Charts are used to control the Critical X input characteristic it is called Statistical Process Control (SPC). These charts can also be used to monitor the CTQ’s, the important process outputs. When this is done it is referred to as Statistical Process Monitoring (SPM).

There are two categories of Control Charts for Continuous Data: charts for controlling the process average and charts for controlling the process variation. Generally, the two categories are combined. The principal types of Control Charts used in Six Sigma are: charts for Individual Values and Moving Ranges (I-MR), charts for Averages and Ranges (XBar-R), charts for Averages and Standard Deviations (XBar-S) and Exponentially Weighted Moving Average charts (EWMA). Although it is preferable to monitor and control products, services and supporting processes with Continuous Data, there will be times when Continuous Data is not available or there is a need to measure and control processes with higher level metrics, such as defects per unit. There are many examples where process measurements are in the form of Attribute Data. Fortunately, there are control tools that can be used to monitor these characteristics and to control the critical process inputs and outputs that are measured with Attribute Data. Attribute Data, also called discrete data, reflects only one of two conditions: conforming or nonconforming, pass or fail, go or no go. Four principal types of Control Charts are used to monitor and control characteristics measured in Attribute Data: the p (proportion nonconforming), np (number nonconforming), c (number of non-conformities), and u (non-conformities per unit) charts. Four principle types of Control Charts are used to monitor and control characteristics measured in Discrete Data: the p (proportion nonconforming), np (number nonconforming), c (number of non-conformities), and u (non-conformities per unit) charts. These charts are an aid for decision making. With Control Limits, they can help us filter out the probable noise by adequately reflecting the Voice of the Process. A defective is defined as an entire unit, whether it be a product or service, that fails to meet acceptance criteria, regardless of the number of defects in the unit. A defect is defined as the failure to meet any one of the many acceptance criteria. Any unit with at least one defect may be considered to be a defective. Sometimes more than one defect is allowed, up to some maximum number, before the product is considered to be defective. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

622

Statistical Process Control Chart Selection Process

SigmaXL® includes a Control Chart Selection Tool to simplify the selection process. Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

623

Statistical Process Control Understanding Variable Control Chart Selection

Ty p e   o f   C h a rt

W h e n   d o   y o u   n e e d   it?

A v e ra g e   &   u P ro d u ctio n   is   h ig h er   v o lu m e ;   a llo w s   p ro ce s s   m e a n   a n d   v a ria b ility R a n g e   o r   S to   b e   v ie w e d   a n d   a s s e s s e d   to g e th e r;   m o re   s a m p lin g   th a n   w ith   (X B a r a n d   R   o r   In d iv id u a ls   ch a rt   (I)   a n d   M o v in g   R a n g e   ch a rts   (M R )   b u t   w h en   X B a r a n d   S ) s u b g ro u p s   a re   d e s ire d .     O u tliers   ca n   ca u s e   is s u e s   w ith   R a n g e   (R ) ch a rts   s o   S ta n d a rd   D e v ia tio n   ch a rts   (S )   u s e d   in s te a d   if   co n ce rn e d .

M o s t   co m m o n In d iv id u a l   a n d M o v in g   R a n g e

P re -­‐C o n tro l

u P ro d u ctio n   is   lo w   v o lu m e   o r   cy cle   tim e   to   b u ild   p ro d u ct   is   lo n g   o r  

h o m o g e n eo u s   s a m p le   re p re s e n ts   e n tire   p ro d u ct   (b a tch   e tc.);   s a m p lin g   a n d   te s tin g   is   co s tly   s o   s u b g ro u p s   a re   n o t   d e s ire d .     C o n tro l   lim its   a re   w id e r   th a n   X B a r ch a rts .     U s e d   fo r   S P C   o n   m o s t   in p u ts .

u S e t-­‐u p   is   critica l,   o r   co s t   o f   s e tu p   s cra p   is   h ig h .     U s e   fo r   o u tp u ts

Ex p o n e n tia lly u S m a ll   s h ift   n e ed s   to   b e   d e te cte d ,   o ften   b e ca u s e   o f   a u to co rre la ti o n   W e ig h te d o f   th e   o u tp u t   res u lts .     U s e d   o n ly   fo r   in d iv id u a ls   o r   a v era g e s   o f M o v in g   A v e ra g e O u tp u ts .     In freq u e n tly   u s e d   b e ca u s e   o f   ca lcu la tio n   co m p le x ity . C u m u la tiv e   S u m u S a m e   re a s o n s   a s   EW M A   (Ex p o n en tia lly   W e ig h te d   M o v in g   R a n g e )   e x ce p t   th e   p a s t   d a ta   is   a s   im p o rta n t   a s   p re s e n t   d a ta .

Le s s   C o m m o n

Understanding Attribute Control Chart Selection

Ty p e   o f   C h a r t P nP

W h e n   d o   y o u   n e e d   it?

u N e e d     to   tra ck   th e   fra ctio n   o f   d e fe ctiv e

u n its ;   s a m p le   s iz e   is   v a r ia b le   a n d   u s u a lly   >   5 0

u W h e n   y o u   w a n t   to   tra ck   th e   n u m b e r   o f   d e fe ctiv e  

u n its   p e r   s u b g ro u p ;   s a m p le   s iz e   is   u s u a lly   co n s ta n t   a n d   u s u a lly   >   5 0

C

u W h e n   y o u   w a n t   to   tra ck   th e   n u m b e r   o f   d e fe cts  

U

u W h e n   y o u   w a n t   to   tra ck     th e   n u m b e r   o f  

p e r   s u b g r o u p   o f   u n its   p ro d u ce d ;   s a m p le   s iz e   is   co n s ta n t d e fe cts   p e r   u n it;   s a m p le   s iz e   is   v a r ia b le

The P Chart is the most common type of chart in understanding Attribute Control Charts.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

624

Statistical Process Control Detection of Assignable Causes or Patterns

C o n tro l   C h a rts   in d ica te   s p e cia l   ca u s e s   b e in g   e ith er   a s s ig n a b le   c a u s e s   o r   p a tte rn s . Th e   fo llo w in g   ru le s   a re   a p p lica b le   fo r   b o th   v a ria b le   a n d   A ttrib u te   D a ta   to   d ete ct   s p e cia l   ca u s es .     Th e s e   fo u r   ru le s   a re   th e   o n ly   a p p lica b le   tes ts   fo r   R a n g e   (R ),   M o v in g   R a n g e   (MR ),   o r   S ta n d a rd   D e v ia tio n   (S )   ch a rts . –

O n e   p o in t   m o re   th a n   3   S ta n d a rd   D e v ia tio n s   fro m   th e   ce n te r   lin e .

–

6   p o in ts   in   a   ro w   a ll   e ith e r   in cre a s in g   o r   a ll   d ecre a s in g .

–

1 4   p o in ts   in   a   ro w   a lte rn a tin g   u p   a n d   d o w n .

–

9   p o in ts   in   a   ro w   o n   th e   s a m e   s id e   o f   th e   ce n te r   lin e .

Th e s e   re m a in in g   fo u r   ru le s   a re   o n ly   fo r   v a ria b le   d a ta   to   d e tect   s p e cia l   ca u s e s . –

2   o u t   o f   3   p o in ts   g re a te r   th a n   2   S ta n d a rd   D e v ia tio n s   fro m   th e   ce n te r   lin e   o n   th e   s a m e   s id e .

–

4   o u t   o f   5   p o in ts   g re a te r   th a n   1   S ta n d a rd   D e v ia tio n   fro m   th e   ce n te r   lin e   o n   th e   s a m e   s id e .

–

1 5   p o in ts   in   a   ro w   a ll   w ith in   o n e   S ta n d a rd   D e v ia tio n   o f   e ith e r   s id e   o f   th e   ce n te r   lin e .

–

8   p o in ts   in   a   ro w   a ll   g re a te r   th a n   o n e   S ta n d a rd   D e v ia tio n   o f   e ith e r   s id e   o f   th e   ce n te r   lin e .

Remember Control Charts are used to monitor a process performance and to detect Special Causes due to assignable causes or patterns. The standardized rules of your organization may have some of the numbers slightly differing. For example, some organizations have 7 or 8 points in a row on the same side of the Center Line. We will soon show you how to find what your SigmaXL® version has for defaults for the Special Cause tests. There are typically 8 available tests for detecting Special Cause variation. Only 4 of the 8 Special Cause tests can only be used Range, Moving Range or Standard Deviation charts which are used to monitor “within” variation. Note, SigmaXL® V6 does not include tests for special causes on the Range, Moving Range or Standard Deviation charts. If you are unsure of what is meant by these specific rule definitions, do not worry. The next few slides will specifically explain how to interpret these rules.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

625

Statistical Process Control Recommended Special Cause Detection Rules •

If  implementing  SPC  manually  without  software  initially,  the  most  visually  obvious  violations  are   more  easily  detected.    SPC  on  manually  filled  charts  are  common   place  for  initial  use  of  defect   prevention  techniques.

•

These  3  rules  are  v is u a lly the  most  easily  detected  by  personnel.

•

–

O ne  point  more  than  3  Standard  Deviations  from  the  center  line.

–

6  points  in  a  row  all  either  increasing  or  all  decreasing .

–

1 5  points  in  a  row  all  within  one  Standard  Deviation  of  either  side  of  the  center  line.  

Dr.  Shewhart  that  worked  with  the  W estern  Electric  C o.  was  credited  with  the  following  4  rules   referred  to  as  W estern  Electric  Rules. –

O ne  point  more  than  3  Standard  Deviations  from  the  center  line.

–

8 points  in  a  row  on  the  same  side  of  the  center  line.

–

2  out  of  3  points  g reater  than  2  Standard  Deviations  from  the  center  line  on  the  same  side.

–

4  out  of  5  points  g reater  than  1  Standard  Deviation  from  the  center  line  on  the  same  side.

•

Y ou  mig ht  notice  the  W estern  Electric  rules  vary  slig htly.    The   importance  is  to  be  consistent  in   your  org aniz ation  and  decide  what  rules  you  will  use  to  detect  special  causes.

•

VERY  few  org aniz ations  use  all  8  rules  for  detecting  special  causes.

Special Cause Rule Default in SigmaXL®

When a Belt is using SigmaXL®, the default tests can be set when running SPC on the variable or Attribute Data. A Belt can always change which tests are selected. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

626

Statistical Process Control Special Cause Test Examples As promised, we will now closely review the definition of the Special Cause tests. The first test is one point more than 3 sigmas from the Center Line. The 3 sigma lines are added or subtracted from the Center Line. The sigma estimation for the short-term variation will be shown later in this module. If only one point is above the upper 3 sigma line or below the lower 3 sigma line, then a Special Cause is indicated. This does not mean you need to confirm if another point is also outside of the 3 sigma lines before action is to be taken. Don’t forget the methodology of using SPC.

If you want to see the SigmaXL® output on the left, execute the SigmaXL® command “Control Charts > ‘Tests for Special Causes’ Defaults”. Remember, your numbers may vary in the slide and those are set in the defaults as you were shown recently in this module. From now on, we will assume your rules are the same as shown in this module. If not, just adjust the conclusions.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

627

Statistical Process Control Special Cause Test Examples The second test for detecting Special Causes is nine points in a row on the same side of the Center Line. This literally means if nine consecutive points are above the Center Line, then a Special Cause is detected that would account for a potential Mean shift in the process. This rule would also be violated if nine consecutive points are below the Center Line. The amount away from the Center Line does not matter as long as the consecutive points are all on the same side of the Center Line. The third test looking for a Special Cause is six points in a row all increasing or all decreasing. This means if six consecutive times, the present point is higher than the previous point than the rule has been violated and the process is out of control. The rule is also violated if for six consecutive times the present point is lower than the previous point on the SPC chart. This rule obviously needs the time order when plotting on the SPC charts to be valid. Typically, these charts plot increasing time from left to right with the most recent point on the right hand side of the chart. Do not make the mistake of seeing six points in a line indicating an out of control condition. Note on the example shown on the right, a straight line shows 7 points but it takes that many in order to have six consecutive points increasing. This rule would be violated no matter what zone the points occur. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

628

Statistical Process Control Special Cause Test Examples (cont.) The fourth rule for a Special Cause indication is fourteen points in a row alternating up and down. In other words, if the first point increased from the last point and the second point decreased from the first point and the third point increased from the second point and so on for fourteen points, then the process is considered out of control or a Special Cause is indicated. This rule does not depend on the points being in any particular zone of the chart. Also note the process is not considered to be out of control until after the 14th point has followed the alternating up and down pattern.

The fifth Special Cause test looks for 2 out of 3 consecutive points more than 2 sigma away from the Center Line on the same side. The 2 sigma line is obviously 2/3 of the distance from the Center Line as the 3 sigma line. Please note it is not required that the points more than 2 sigma away be in consecutive order, they just have to be within a group of 3 consecutive points. Notice the example shown on the right does NOT have 2 consecutive points 2 sigma away from the Center Line but 2 out of the 3 consecutive are more than 2 sigma away. Notice this rule is not violated if the 2 points that are more than 2 sigma but NOT on the same side. Have you noticed that SigmaXL® will automatically place a number by the point that violates the Special Cause rule and that number tells you which of the Special Cause tests has been violated. In this example shown on the right, the Special Cause rule was violated two times. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

629

Statistical Process Control Special Cause Test Examples (cont.) The sixth Special Cause test looks for any four out of five points more than one sigma from the Center Line all on the same side. Only the 4 points that were more than one sigma need to be on the same side. If four of the five consecutive points are more than one sigma from the Center Line and on the same side, do NOT make the wrong assumption that the rule would not be violated if one of the four points was actually more than 2 sigma from the Center Line. The seventh Special Cause test looks for 15 points in a row all within one sigma from the Center Line. You might think this is a good thing and it certainly is. However, a you might want to find the Special Cause for this reduced variation so the improvement can be sustained in the future. The eighth and final test for Special Cause detection is having eight points in a row all more than one sigma from the Center Line. The eight consecutive points can be any number of sigma away from the Center Line. Do NOT make the wrong assumption this rule would not be violated if some of the points were more than 2 sigma away from the Center Line. If you reread the rule, it just states the points must be more than one sigma from the Center Line. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

630

Statistical Process Control SPC Center Line and Control Limit Calculations This is a reference in case you really want to get into the nitty-gritty. The formulas shown here are the basis for Control Charts. C a lcu la te   th e   p a ra m e te rs   o f   th e   In d iv id u a l   a n d   M R   C o n tro l   C h a rts w ith   th e   fo llo w in g :

C e n te rlin e X=

∑x

Where: Xbar: Xi: k: Ri :

C o n tro l   Lim its

k

k

i

MR =

i =1

k

∑R

i

i

k

UCL x = X + E 2 MR LCL x = X − E 2 MR

UCL MR = D 4 MR LCL MR = D 3 MR

>

Average of the individuals, becomes the centerline on the Individuals chart Individual data points Number of individual data points Moving range between individuals, generally calculated using the difference between each successive pair of readings MRbar: The average moving range, the centerline on the range chart UCLX: Upper control limit on individuals chart LCLX: Lower control limit on individuals chart UCLMR: Upper control limit on moving range LCLMR : Lower control limit on moving range (does not apply for sample sizes below 7) E2, D3, D4: Constants that vary according to the sample size used in obtaining the moving range

σ (st.  dev.  Estimate)          =

M R b a r (co m p u te d   a b o v e ) d2 (ta b le   o f   co n s ta n ts   fo r   s u b g ro u p   s iz e   n )

C a lcu la te   th e   p a ra m e te rs   o f   th e   X B a r   a n d   R   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e X=

∑x i =1

C o n tro l   Lim its k

k

i

R =

∑R i

i

UCL x = X + A 2 R LCL x = X − A 2 R

UCL R = D 4 R LCL R = D 3 R

>

k Where: k Xi: Average of the subgroup averages, it becomes the centerline of the control chart Xi: Average of each subgroup k: Number of subgroups Ri : Range of each subgroup (Maximum observation – Minimum observation) Rbar: The average range of the subgroups, the centerline on the range chart UCLX: Upper control limit on average chart LCLX: Lower control limit on average chart UCLR: Upper control limit on range chart LCLR : Lower control limit range chart A2, D3, D4: Constants that vary according to the subgroup sample size R b a r (co m p u te d   a b o v e ) σ (st.  dev.  Estimate)          = d2 (ta b le   o f   co n s ta n ts   fo r   s u b g ro u p   s iz e   n )

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

631

Statistical Process Control SPC Center Line and Control Limit Calculations (cont.) Yet another reference just in case anyone wants to do this stuff manually…have fun!!!! C a lcu la te   th e   p a ra m e te rs   o f   th e   X B a r   a n d   S   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e X=

C o n tro l   Lim its k

k

∑x i =1

k

i

S=

∑s

i

i =1

k

UCL x = X + A 3 S LCL x = X − A 3 S

UCLS = B4 S LCLS = B3 S

>

Where: Xi: Average of the subgroup averages, it becomes the centerline of the control chart Xi: Average of each subgroup k: Number of subgroups si : Standard deviation of each subgroup Sbar: The average s. d. of the subgroups, the centerline on the S chart UCLX: Upper control limit on average chart LCLX: Lower control limit on average chart UCLS: Upper control limit on S chart LCLS : Lower control limit S chart A3, B3, B4: Constants that vary according to the subgroup sample size S b a r (co m p u te d   a b o v e ) σ (st.  dev.  Estimate)          = c4         (ta b le   o f   co n s ta n ts   fo r   s u b g ro u p   s iz e   n )

We are now moving to the formula summaries for the Attribute SPC Charts. These formulas are fairly basic. The upper and lower Control Limits are equidistant from the Mean % defective unless you reach a natural limit of 100 or 0%. Remember the p Chart is for tracking the proportion or % defective. These formulas are a bit more elementary because they are for Attribute Control Charts. Recall p Charts track the proportion or % defective. C a lcu la te   th e   p a ra m e te rs   o f   th e   P   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C o n tro l   Lim its

C e n te rlin e p=

Total number of defective items Total number of items inspected

Where: p: ni: LCLp: UCLp:

p (1 − p ) ni p (1 − p ) LCL p = p − 3 ni UCL p = p + 3

Average proportion defective (0.0 – 1.0) Number inspected in each subgroup Lower control limit on p chart Upper control limit on p chart

S ince  the  C ontrol  Limits  are  a  function  of   sample  siz e,  they  will  vary  for  each  sample.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

632

Statistical Process Control SPC Center Line and Control Limit Calculations (cont.) The nP Chart’s formulas resemble the P Chart. This chart tracks the number of defective items in a subgroup.

C a lcu la te   th e   p a ra m e te rs   o f   th e   n P   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e np =

Total number of defective items Total number of subgroups

C o n tro l   Lim its UCL np = n i p + 3 ni p(1 − p) LCL np = n i p − 3 n i p(1 - p)

Where: np: ni: LCLnp: UCLnp:

Average number defective items per subgroup Number inspected in each subgroup Lower control limit on nP chart Upper control limit on nP chart

S ince  the  C ontrol  Limits  A N D  C enter  Line  are  a  function   of  sample  siz e,  they  will  vary  for  each  sample.

The U Chart is also basic in construction and is used to monitor the number of defects per unit.

C a lcu la te   th e   p a ra m e te rs   o f   th e   U   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e u=

Total number of defects Identified Total number of Units Inspected

Where: u: ni: LCLu: UCLu:

C o n tro l   Lim its UCL u = u + 3

u ni

LCL u = u − 3

u ni

Total number of defects divided by the total number of units inspected. Number inspected in each subgroup Lower control limit on u chart. Upper control limit on u chart.

S ince  the  C ontrol  Limits  are  a  function  of  sample   siz e,  they  will  vary  for  each  sample.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

633

Statistical Process Control SPC Center Line and Control Limit Calculations (cont.) The C Control Charts are a nice way of monitoring the number of defects in sampled subgroups.

C a lcu la te   th e   p a ra m e te rs   o f   th e   C   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e c=

C o n tro l   Lim its

Total number of defects Total number of subgroups

UCL c = c + 3 c LCLc = c − 3 c

W h e re : c: LCLc: UCLc:

Total number of defects divided by the total number of subgroups. Lower control limit on c chart. Upper control limit on c chart.

This EWMA can be considered a smoothing monitoring system with Control Limits. This is rarely used without computers or automated calculations. The items plotted are NOT the actual measurements but the weighted measurements. The exponentially weighted moving average is useful for considering past and historical data and is most commonly used for individual measurements although has been used for averages of subgroups.

C a lcu la te   th e   p a ra m e ters   o f   th e   EW M A   C o n tro l   C h a rts   w ith   th e   fo llo w in g :

C e n te rlin e

Zt = λ Xt + (1− λ) Zt −1 W h e re : Zt: Zt-1: λ: σ: Xt: UCL: LCL: n:

C o n tro l   Lim its UCL = X + 3

σ λ ( )[1 − (1 − λ) 2t ] 2 − λ n

LCL = X − 3

σ λ ( )[1 − (1 − λ) 2t ] n 2−λ

EWMA statistic plotted on control chart at time t EWMA statistic plotted on control chart at time t-1 The weighting factor between 0 and 1 – suggest using 0.2 Standard deviation of historical data (pooled standard deviation for subgroups – MRbar/d2 for individual observations) Individual data point or sample averages at time t Upper control limit on EWMA chart Lower control limit on EWMA chart Subgroup sample size

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

634

Statistical Process Control SPC Center Line and Control Limit Calculations (cont.)

C a lcu la te   th e   p a ra m e te rs   o f   th e   C U S U M   C o n tro l   C h a rts   w ith   M IN ITA B TM o r   o th e r   p ro g ra m   s in ce   th e   ca lcu la tio n s   a re   e v e n   m o re   co m p lica te d   th a n   th e   EW M A   ch a rts . B e ca u s e   o f   th is   co m p le x ity   o f   fo rm u la s ,   e x e cu tio n   o f   e ith e r   th is   o r   th e   EW M A   a re   n o t   d o n e   w ith o u t   a u to m a tio n   a n d   co m p u te r   a s s is ta n ce .

any body a  l aptop? Ah, Ah,   anybody got   gaot  laptop?!

The CUSUM is an even more difficult technique to handle with manual calculations. We aren’t even showing the math behind this rarely used chart. Following the Control Chart selection route shown earlier, we remember the CUSUM is used when historical information is as important as present data. Note, SigmaXL® V6 does not include CUSUM.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

635

Statistical Process Control Pre-Control Charts P r e -­‐C o n tr o l   C h a r ts use  limits  relative  to  the  specification  limits.    This  is  the  first   and  O N LY  chart  you  will  see  specification  limits  plotted  for  sta tistical  process   control.    This  is  the  most  basic  type  of  cha rt  and  unsophisticated  use  of  process   control.

0.0

RED

0.25

Yellow

LSL

0.5

0.75 1.0

GREEN

Yellow

Target

R e d   Z o n e s . Z one  outside  the   specification  limits.  Sig nals  the   process  is  out-­‐o f-­‐c ontrol  and   should  be  stopped Red

USL

Y e llo w   Z o n e s . Z one  between   the  PC    Lines  and  the   specification  limits,  indicates   caution  and  the  need  to  watch   the  process  closely G re e n   Z o n e . Z one  lies   between  the  PC  Lines,  sig nals  the   process  is  in  control

The Pre-Control Charts are often used for startups with high scrap cost or low production volumes between setups. Pre-Control Charts are like a stoplight are the easiest type of SPC to use by operators or staff. Remember Pre-Control Charts are to be used ONLY for outputs of a process. Another approach to using Pre-Control Charts is to use Process Capability to set the limits where yellow and red meet. SigmaXL® does not include Pre-Control. Process Setup and Restart with Pre-Control

Q u a lify in g   P r o ce s s • To  qualify  a  process,  five  consecutive  parts  must  fall  within  the  g reen  z one     • The  process  should  be  qualified  after  tool  cha ng es,  adjustments, new   operators,  material  cha ng es,  etc M o n ito r in g   O n g o in g   P r o ce s s • Sample  two  consecutive  parts  at  predetermined  frequency – If  either  part  is  in  the  red,  stop  production  and  find  reason  for  variation – W hen  one  part  falls  in  the  yellow  z one  inspect  the  other  and • If  the  second  part  falls  in  the  g reen  z one  then  continue • If  the  second  part  falls  in  the  yellow  z one  on  the  same  side,  ma ke  an   adjustment  to  the  process • If  second  part  falls  in  the  yellow  z one  on  the  opposite  side  or   in  the   red  z one,  the  process  is  out  of  control  and  should  be  stopped – If  any  part  falls  outside  the  specification  limits  or  in  the  red z one,  the   process  is  out  of  control  and  should  be  stopped

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

636

Statistical Process Control Responding to Out of Control Indications SPC is an exciting SPC power is to react to the Out of Control (OOC) indications tool but we must with an Out of Control Action Plan (OCAP). not get enamored with it. The power of SPC is not to Individual SPC chart for Response Time find the Center Line VIOLATION: 40 UCL=39.76 and Control Limits Special Cause is but to react to out 30 indicated of control _ 20 indications with an X=18.38 out of control action OCAP 10 plan. SPC for If response time is too effectiveness at 0 high, get additional LCL=-3.01 controlling and person on phone bank 1 4 7 10 13 16 19 22 25 28 31 reducing long-term Observation variation is to respond •  Requires immediate response to Special Cause. immediately to out of control or •  No reaction while process is within limits! Special Cause indications. SPC can be actually harmful if those operating the process respond to process variation with suboptimizing. A basic rule of SPC is if it is not out of control as indicated by the rules, then do not make any adjustments. There are studies where an operator that responds to off center measurements will actually produce worse variation than a process not altered at all. Remember, being off the Center Line is NOT a sign of out of control because Common Cause variation exists. Individual Value

1

Training is required to use and interpret the charts not to mention training for you as a Belt to properly create an SPC chart. Attribute SPC Example

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

637

Statistical Process Control Attribute SPC Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

638

Statistical Process Control Attribute SPC Example (cont.)

Now we must see if the next few weeks are showing Special Cause from the results. The sample size remained at 250 and the defective checks were 61, 64, 77.

No Special Causes were detected. Average % defective = 20.380%

UCL = 28.0%

LCL = 12.7%

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

639

Statistical Process Control Attribute SPC Example (cont.)

The chart has now been updated to include the new points.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

640

Statistical Process Control Attribute SPC Example (cont.) Because of the Special Cause, the process must refer to the OCAP or Out of Control Action Plan that states what Root Causes need to be investigated and what actions are taken to get the process back in Control. After the corrective actions were taken, wait until the next sample is taken to see if the process has changed to not show Special Cause actions. If still out of control, refer to the OCAP and take further action to improve the process. However, DO NOT make any more changes if the process shows back in control after the next reading. Also, even if the next reading seems higher than the Center Line don’t cause more variability. If process changes are documented after this project was closed, the Control Limits should be recalculated as in step 9 of the SPC methodology.

Special Cause

Activate

OCAP

Let’s walk through another example of using SPC within SigmaXL® but in this case it will be with Continuous Data. Open the worksheet called “hole diameter” and select the appropriate type of Control Chart and calculate the Center Line and Control Limits. Let’s try another one, this time variable…

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

641

Statistical Process Control Attribute SPC Example (cont.) The example has Continuous Data, subgroups and we have no interest in small changes in this small process output. The Xbar R Chart is selected because we are uninterested in the Xbar S Chart for this example.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

642

Statistical Process Control Attribute SPC Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

643

Statistical Process Control Attribute SPC Example (cont.)

Note: The Mean, UCL and LCL are unchanged when SigmaXL®’s Add Data button is used.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

644

Statistical Process Control Attribute SPC Example (cont.)

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

645

Statistical Process Control SPC Chart Option in SigmaXL® for σ Levels

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

646

Statistical Process Control At this point, you should be able to: §  Describe the elements of an SPC chart and the purposes of SPC §  Understand how SPC ranks in defect prevention §  Describe the 13 Step route or methodology of implementing a chart §  Design subgroups if needed for SPC usage §  Determine the frequency of sampling §  Understand the Control Chart selection methodology §  Be familiar with Control Chart parameter calculations such as UCL, LCL and the Center Line

You have now completed Control Phase – Statistical Process Control.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

647

Lean Six Sigma Black Belt Training

Control Phase Six Sigma Control Plans

Now we are going to continue in the Control Phase with “Six Sigma Control Plans”.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

648

Six Sigma Control Plans Overview The last physical result of the Control Phase is the Control Plan. This module will discuss a technique to selection various solutions you might want from all of your defect reduction techniques found earlier in this phase. We will also discuss elements of a Control Plan to aid you and your organization to sustain your project’s results. We will examine the meaning of each of these and show you how to apply them.

W W eelco lcom m ee    to to    CCoonntro troll AA ddvvaa nnce cedd    Ex Ex ppeerim rim eennts ts AA ddvvaa nnce cedd    CCaa ppaa bbility ility Le Leaa nn    CCoonntro trols ls DDeefe fect   ct  CCoonntro trols ls SSta ta tis tistica tica l  l  PPro roce cessss    CCoonntro trol  l   (S (SPPCC)) SSix ix    SSig ig m m aa    CCoonntro trol  l  PPla la nnss W W ra ra pp    U Upp    & &    AA ctio ctionn    Ite Item m ss

Solution  Selection Solution  Selection CC ontrol  Plan  Elements ontrol  Plan  Elements

End of Control: Your Objectives

We have discussed all of the tools to improve and sustain your project success. However, you might have many options or too many options to implement final monitoring or controls. This module will aid you in defect reduction selection. Another objective of this module is to understand the elements of a good Control Plan needed to sustain your gains. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

649

Six Sigma Control Plans Selecting Solutions

Selecting  improvements  to  implement: – Hig h-­‐level  objective  evaluation  of  all  potential  improvements • Impact  of  each  improvement • C ost  to  implement  each  improvement • Time  to  implement  each  improvement – Balance  desire  with  quantifiable  evaluation • Eng ineering  always  wants  the  g old  standard • Sales  always  wants  inventory • Production  always  wants  more  capacity The  tool  for  selecting  defect  prevention  methods  is  unnecessary   for  just  a   few  chang es  to  the  process. – Many  projects  with  smaller  scopes  have  few,  but  vital  control   methods  put  into  the  process. Selecting solutions comes down to a business decision. The impact, cost and timeliness of the improvement are all important. These improvement possibilities must be balanced against the business needs. A cost benefit analysis is always a good tool to use to assist in determining the priorities. Recall us talking about the progression of a Six Sigma project? Practical Problem – Statistical Problem – Statistical Solution – Practical Solution. Consider the Practical Solutions from a business decision point of view. Impact Considerations

Now that’s IMPACT!! LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

650

Six Sigma Control Plans Cost Considerations

It’s all about the cash!!

Time Considerations

The clock’s ticking…!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

651

Six Sigma Control Plans Improvement Selection Matrix

This should resemble the X-Y Matrix. This tool is of no use if you have one or two improvement efforts to consider. The outputs listed above in most cases resemble those of your original X-Y Matrix but you might have another business output added. The significance rating is the relative ranking of outputs. If one output is rated a 10 and it is twice the importance of a second output, the rating for the second output would be a 5. The improvements, usually impacting the X’s, are listed and the relative impact of each item on the left is rated against its impact to the output. The overall impact rating for one improvement is the sum of the individual impact ratings multiplied by their respective significant rating of the output impacted. Items on the left having more impacts on multiple outputs will have a higher overall impact rating. The cost and timing ratings are multiplied against the overall impact rating. The improvements listed with the highest overall ratings are the first to get consideration. The range of impact ratings can be zero to seven. An impact of zero means no impact. The cost and timing ratings are rated zero to seven. With zero being prohibitive in the cost or timing category. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

652

Six Sigma Control Plans Improvement Selection Matrix Project Outputs

Primary  and  Secondary  Metrics  of  your  Project. – List  each  of  the  Y ’s  across  the  horiz ontal  axis – Rate  the  importance  of  the  process  Y ’s  on  a  scale  of  1  to  1 0 • 1  is  not  very  important,  1 0  is  critical • The  Sig nificance  ranking s  must  match  your  updated  X-­‐Y  Matrix   ranking s Improvement Selection Matrix Just like when using the FMEA, your ratings may vary for the three Selection Matrix categories. Feel free to use whatever objective ratings you desire. These are some general guideline ratings, customize them to meet your business, just try to standardize whatever criteria you choose.

The recommended cost ratings from zero to seven are here. In many companies, expenditures that are not capitalized usually are desired because they are smaller and are merely expensed. Your business may have different strategies or need of cash so consider your business’ situation.

7 6 5 4 3 2 1 0

LSS Black Belt Manual XL v11

Cost to Implement Ratings Improvement Costs are minimal with upfront and ongoing expenses. Improvement Costs are low and can be expensed with no capital authorization and recurring expenses are low. Improvement Costs are low and can be expensed with no capital authorization and recurring expenses are higher. Medium capital priority because of relative ranking of return on investment. Low capital priority because of relative ranking of return on investment. High capital and ongoing expenses make a low priority for capital investment. High capital and/or expenses without acceptable return on investment. Significant capital and ongoing expenses without alignment with business priorities.

© 2013 e-Careers Limited

653

Six Sigma Control Plans Improvement Selection Matrix (cont.)

7 6 5 4 3 2 1 0

Time to Implement Ratings Less than a week to get in place and workable. 7 - 14 days to get in place and workable. 2 - 8 weeks to get the improvement in place and workable. 2 - 3 months to get the improvement in place and workable. 3 - 6 months to get the improvement in place and workable. 6 - 9 months to get the improvement in place and workable. 9 - 12 months to get the improvement in place and workable. Over a year to get the improvement in place and workable. All above times include time for approvals process.

These time ratings are ranked from zero to seven. You might wonder why something that would take a year or more we suggest gets a zero rating suggesting the improvement not be considered. Many businesses have cycle times of products less than a year so improvements that long are ill considered.

Mgmt visits/leaves ph #

3

Replace old coffee makers/coffee

4

Menus provided with nutrition info

5

Comp. gen. "quiet time" scheduled

6

Dietician approves menus

Food choices include "healthy choices"

Hotel staff monitors room

2

Plenty of bottled water available

1

Coffee is hot and rich tasting

Significance Rating

Potential Improvements

Outside noises do not interfer with speakers

Example of Completed Solution Selection Matrix

10 Impact Rating 2 2 0 0 6 0

9 Impact Rating 2 0 7 0 0 0

8 Impact Rating 6 4 0 0 0 0

9 Impact Rating 0 0 0 4 0 7

OVERALL IMPACT RATING

COST RATING

TIME RATING

OVERALL RATING

86 52 63 36 60 63

7 7 3 5 3 5

7 7 6 5 3 2

4214 2548 1134 900 540 630

Im p r o v e m e n t   S e le ctio n   M a tr ix   O u tp u t Improvements  with  the  hig her  overall  rating  should  be  g iven  first  priority. Keep  in  mind  that  long  time  frame  capital  investments,  etc.  should  have   parallel  efforts  to  keep  delays  from  further  occurring . This is just an example of a completed Selection Matrix. Remember that a cost or time rating of zero would eliminate the improvement from consideration by your project. Remember your ratings of the solutions should involved your whole team to get their knowledge and understanding of final priorities. Again, higher overall ratings are the improvements to be considered. Do NOT forget about the potential to run improvements in parallel. Running projects of complexity might need the experience of a trained project manager. Often projects need to be managed with gantt charts or timelines showing critical milestones. LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

654

Six Sigma Control Plans Implementing Solutions in Your Organization

Implementation  Plans  should  emphasiz e  the  need  to: – O rg aniz e  the  tasks  and  resources – Establish  realistic  time  frames  and  deadlines – Identify  actions  necessary  to  ensure  success C omponents  of  an  Implementation  Plan  include: – W ork  breakdown  structure – Influence  strateg y  for  priorities  and  resourcing – Risk  manag ement  plan – A udit  results  for  completion  and  risks. A ll  solutions  must  be  part  of  C ontrol  Plan  Document.

We We   havehave   a plan don’t we?! a  plan   don’t   we?

Once you’ve decided defect reduction solutions, you need to plan those solutions. A plan means more than the proverbial back of the envelope solution and should include timelines, critical milestones, project review dates and specific actions noted for success in your solution implementation. Many people use Excel or MS Project but many options exist to plan your project closing with these future sustaining plans.

What is a Control Plan?

A   C o n tr o l   P la n   is : • • • • • •

W ritte n   s u m m a ry   d e s cr ib in g   s y s te m s   u s e d   fo r   m o n ito rin g / co n tr o lli n g   p ro ce s s   o r   p ro d u ct   v a ria tio n D o cu m e n t   a llo w in g   te a m   to   fo rm a lly   d o cu m e n t   a ll   co n tr o l   m e th o d s   u s e d   to   m e e t   p ro je ct   g o a l Liv in g   d o cu m e n t   to   b e   u p d a te d   a s   n e w   m e a s u re m e n t   s y s te m s   a n d   co n tr o l   m e th o d s   a re   a d d e d   fo r   co n tin u o u s   im p ro v e m e n t O fte n   u s e d   to   cre a te   co n cis e   o p e ra to r   in s p e ctio n   s h e e t N O T   a   re p la ce m e n t   o f   in fo r m a tio n   co n ta in e d   in   d e ta ile d   o p e ra tin g ,   m a in te n a n ce ,   o r   d e s ig n   in s tr u ctio n s ES S EN TIA L   p o r tio n   o f   fin a l   p r o je ct   re p o rt – Fin a l   p r o je cts   a re   o r g a n iz a tio n a lly   d e p e n d e n t • In fo r m a l   o r   fo rm a l – File d   a s   p a rt   o f   p ro je ct   tra ck in g   m e ch a n is m   fo r   o rg a n iz a tio n • Tra ck   b e n e fits • R e fe re n ce   fo r   u n s u s ta in e d   r e s u lts

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

655

Six Sigma Control Plans WHO Should Create a Control Plan

The    team  working  on  the  project!!!! A N Y O N E  who  has  a  role  in  defining ,  executing  or  chang ing  the   process: – A ssociates – Technical  Experts – Supervisors – Manag ers – Site  Manag er – Human  Resources

We ddid We   id  it!! i t!!

WHY Do We Need a Control Plan?

Going for the distance, not the sprint!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

656

Six Sigma Control Plans Control Plan Elements The five elements of a Control Plan include the documentation, monitoring, response, training and aligning systems and structures.

Control Plan Information Control Plans use all of the information from the previous phases of your project and the defect prevention methods selected. Control Plans may not be exciting because you are not doing anything new to the process but stabilizing the process in the future with this document.

LSS Black Belt Manual XL v11

Th e   te a m   d e v e lo p s   th e   C o n tro l   P la n   b y   u tiliz in g   a ll   a v a ila b le   in fo rm a tio n   fro m   th e   fo llo w in g : – R e s u lts   fro m   th e   M e a s u re   a n d   A n a ly z e   P h a s e s – Le s s o n s   le a rn e d   fro m   s im ila r   p ro d u cts   a n d   p ro ces s es – Te a m ’ s   k n o w le d g e   o f   th e   p ro ces s – D es ig n   FM EA s – D es ig n   re v ie w s – D e fect   P re v e n tio n   M e th o d s   s e le cte d

D o cu m e n ta tio n   P la n

R e s p o n s e   P la n

A lig n in g   S y s te m s   &   S tr u ctu r e s

M o n ito r in g   P la n

Tr a in in g           P la n

© 2013 e-Careers Limited

657

Six Sigma Control Plans Training Plan

W h o / W h a t   o rg a n iz a tio n s   re q u ire   tra in in g ? – Those  impacted  by  the  improvements Tr a in in g • People  who  are  involved  in  the  process                                                     P la n impacted  by  the  improvement • People  who  support  the  process  impacted  by   the  improvement – Those  impacted  by  the  C ontrol  Plan • Process  owners/ manag ers • People  who  support  the  processes  involved  in  the  C ontrol  Plan • People  who  will  make  chang es  to  the  process  in  the  future W h o   w ill   co m p le te   th e   tr a in in g ? – Immediate  training • The  pla nning ,  development  a nd  execution  is  a Tr a in in g P la n responsibility  of  the  project  tea m • Typica lly  some  of  the  tra ining  is  conducted  by the  project  tea m – Q ualified  tra iners • Typica lly  owned  by  a  tra ining  depa rtment  or  process  owner • Those  who  a re  responsible  for  conducting  the  on-­‐g oing   tra ining  must  be  identified S pecific  tra ining  ma teria ls  need  developing . – PowerPoint,  O n  the  Job  checklist,  Exercises,  etc.

W hen  will  tra ining  be  conducted? W ha t  is  the  timeline  to  tra in  everyone on  the  new  process(es)?

Tr a in in g P la n

W ha t  will  trig g er  ong oing  tra ining ? – N ew  employee  orienta tion? – Refresher  tra ining ? – Pa rt  of  the  response  pla n  when  monitoring  shows   performa nce  deg ra ding ? LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

658

Six Sigma Control Plans Training Plan (cont.)

Tra in in g   P la n   O u tlin e Tr a in in g P la n

Training Module

Who Will Create Modules

Schedule for Training Modules Who Will be Completion Trained

Schedule for Training

Trainer(s)

Integration into Ongoing New Employee Training

Final Location of Employee Manuals

Documentation Plan

Documentation  is  necessary  to  ensure  that  what   has  been  learned  from  the  project  is  shared  and institutionaliz ed: – Used  to  aid  implementation  of  solutions – Used  for  on-­‐g oing  training

Documentation D o cu m e n ta tio n   Plan P la n

This  is  often  the  actual  Final  Report  some  org aniz ations  use.

D o cu m e n ta tio n   m u s t   b e   k e p t   cu r r e n t   to   b e   u s e fu l

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

659

Six Sigma Control Plans Documentation Plan (cont.)

Ite m s   to   b e   in clu d e d   in   th e   D o cu m e n ta tio n   P la n : – P ro ce s s   d o cu m e n ta tio n • U p d a te d   P ro ce s s   M a p s / flo w ch a rts • P ro ce d u r e s   (S O P ’ s ) • FM EA

D o cu m e n ta tio n   P la n

– C o n tro l   P la n   d o cu m e n ta tio n • Tra in in g   m a n u a ls • M o n ito rin g   p la n —p ro ce s s   m a n a g e m e n t   ch a rts ,     r e p o rts ,   sops • R e s p o n s e   p la n —FM EA • S y s te m s   a n d   s tru ctu re s —jo b   d e s crip tio n s ,   p e rfo rm a n ce   m a n a g e m e n t   o b je ctiv e s

A s s ig n in g   re s p o n s ib ility   fo r   D o cu m e n ta tio n   P la n : – Responsibility  at  implementation Documentation Plan • Black  Belt  ensures  all  documents  are  current                                         at  hand  off • Black  Belt  ensures  there  is  a  process  to  modify documentation  as  the  process  chang es  in  place • Black  Belt  ensures  there  is  a  process  in  place  to  review   documentation  on  reg ular  basis  for  currency/ accuracy – Responsibility  for  ong oing  process  (org aniz ationally  based) • Plan  must  outline  who  is  responsible  for  making   updates/ modifications  to  documentation  as  they  occur • Plan  must  outline  who  is  responsible  to  review  documents— ensuring  currency/ accuracy  of  documentation

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

660

Six Sigma Control Plans Documentation Plan (cont.)

D o cu m e n ta tio n   P la n   O u tlin e

Document

Items Necessary

Immediate Responsibility

D o cu m e n ta tio n   P la n

Update/ Review Modification Responsibility Responsibility

Monitoring Plan

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

661

Six Sigma Control Plans Monitoring Plan (cont.)

Knowledge Retention Tests –  When to Sample:

Monitoring Plan

•  After training •  Regular intervals •  Random intervals (often in auditing sense) –  How to Sample –  How to Measure

I knew I should have paid more attention!!

Statistical Process Control: –  Control Charts

Monitoring Plan

•  Posted in area where data collected •  Plot data points real time

–  Act on Out of Control Response with guidelines from the Out of Control Action Plan (OCAP). –  Record actions taken to achieve in-control results. •  Notes impacting performance on chart should be encouraged –  Establishing new limits •  Based on signals that process performance has changed

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

662

Six Sigma Control Plans Response Plan

FM EA   is   a   g re a t   to o l   to   u s e   fo r   th e   M o n ito rin g   P la n M o n ito r in g   P la n

#

Process Function (Step)

Potential Failure Modes (process defects)

Potential Failure Effects (Y's)

C S l E a V s

Potential Causes of Failure (X's)

O C C

Current Process Controls

D E T

R P N

Recommend Actions

Responsible Person & Target Date

Taken Actions

S O D E C E V C T

R P N

1 2 3 4 5 6

– A llo w s   p ro ce s s   m a n a g e r   a n d   th o s e   in v o lv e d   in   th e   p ro ce s s   to   s e e   th e   e n tire   p ro ce s s   a n d   h o w   e v e ry o n e   co n tr ib u te s   to   a   d e fe ct   fr e e   p ro d u ct/ s e rv ice . – P ro v id e s   th e   m e a n s   to   k e e p   th e   d o cu m e n t   cu rre n t— re a s s e s s in g   R P N s   a s   th e   p ro ce s s   ch a n g e s

Monitoring Plan

Check Lists/Matrices –  Key items to check –  Decision criteria; decision road map –  Multi-variable tables

Monitoring Plan

Visual Management –  Alerts or signals to trigger action. •  Empty bins being returned to when need stock replenished •  Red/yellow/green reports to signal process performance –  Can be audible also. –  5S is necessary for Visual Management

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

663

Six Sigma Control Plans Response Plan

R e s p o n s e   P la n R e s p o n s e   P la n s — outline  process(es)  to  follow  when there  is  a  defect  or  O ut  of  C ontrol  from  monitoring : – O ut  of  control  point  on  C ontrol  C hart – N on  random  behavior  within  C ontrol  Limits  in                                         C ontrol  C hart – C ondition/ variable  proven  to  produce  defects  present  in  process – C heck  sheet  failure – A utomation  failure

Response  to  poor  process  results  are  a  must  in  training .

R e s p o n s e   P la n s   a r e   liv in g   d o cu m e n ts   u p d a te d   w ith n e w   in fo r m a tio n   a s   it   b e co m e s   a v a ila b le .

C o m p o n e n ts   o f   R e s p o n s e   P la n :

R e s p o n s e   P la n

– The  trig g ers  for  a  response • W hat  are  the  failure  modes  to  check  for? • Usually  monitor  the  hig hest  risk  X's  in  the  process – The  recommended  response  for  the  failure  mode – The  responsibilities  for  responding  to  the  failure  mode – Documentation  of  Response  Plan  being  followed  in  a  failure  mode – Detailed  information  on  the  conditions  surrounding  the  failure   mode

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

664

Six Sigma Control Plans Response Plan – Abnormality Report

•

P ro v id e   a   m e th o d   fo r o n -­‐g o in g   co n tin u o u s im p ro v e m e n t. R e in fo rce   co m m itm e n t   to   e lim in a tin g   d e fe cts .

R e s p o n s e   P la n Process Metric Current Situation

•

D e ta ile d   d o cu m e n ta tio n w h e n   fa ilu re   m o d e s o ccu r.

Signal Situation Code Detailed Situation

Investigation of Cause

•

Date

Code of Cause

Corrective Action

Fits   w ith   IS O   9 0 0 0   s ta n d a rd   o f              Who       To     Be      Involved                                       h a v in g   a   C A R   o r   C o rre ctiv e     What To Be Done A ctio n   R e q u e s t.

•

M e th o d   to   co lle ct   fre q u e n cy   o f                                                                     Date for implementation of permanent prevention co rre ctiv e   a ctio n s .

Root Cause Analysis

•

Date for completion of analysis

Aligning Systems and Structures

Systems  and  structures  are  the  basis  for  allowing people  to  chang e  their  behaviors  permanently: – Performance  g oals/ objectives – Policies/ procedures – Job  descriptions – Incentive  compensation – Incentive  prog rams,  contests,  etc

A lig n in g   S y s te m s   &   S tr u ctu r e s

Th e r e   a r e   lo n g -­‐ a n d   s h o r t-­‐te r m   s tr a te g ie s   fo r   a lig n m e n t   o f   s y s te m s   a n d   s tr u ctu r e s .

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

665

Six Sigma Control Plans Aligning Systems and Structures (cont.)

• G et  rid  of  measurements  that  do  not  alig n  with                                     desired  behaviors A lig n in g  

• G et  rid  of  multiple  measures  for  the  same                                               desired  behaviors

S y s te m s   &   S tr u ctu r e s

• Implement  measures  that  alig n  with  desired  behaviors  currently  not   motivated  by  incentives • C hang e  manag ement  must  consider  your  process  chang es  and  how   the  process  will  respond? • A re  the  hourly  incentives  hurting  your  chance  of  success?

Project Sign Off

Best  method  to  assure  acceptance  of  C ontrol  Plan  is                           having  supervisors  and  manag ement  for  the  area                                     A lig n in g   involved. S y s te m s   – Meeting  for  a  summary  report &   S tr u ctu r e s – Specific  chang es  to  the  process  hig hlig hted – Information  where  C ontrol  Plan  is  filed

that’s   a  C ontrol  Plan!! Plan! NowNow   that’s a Control

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

666

Six Sigma Control Plans At this point, you should be able to: §  Identify all 5 phases of the Six Sigma methodology §  Identify at least 3 tools from each phase §  Show progress on your ongoing project Now for the last few questions to ask if you have been progressing on a real world project while taking this learning. First, has your project made success in the primary metric without compromising your secondary metrics? Second, have you been faithfully updating your metric charts and keeping your process owner and project champion updated on your team’s activities. If not, then start NOW. Remember a basic change management idea you learned in the Define Phase. If you get involvement of team members who work in the process and keep the project champion and process owner updated as to results, then you have the greatest chance of success.

You have now completed Control Phase – Six Sigma Control Plans.

Notes

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

667

Lean Six Sigma Black Belt Training

Control Phase Wrap Up and Action Items

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

668

Wrap Up and Action Items Control Phase Overview—The Goal

The goal of the Control Phase is to: •  Assess the final Process Capability. •  Revisit Lean with an eye for sustaining the project. •  Evaluate methods for Defect Prevention. •  Explore various methods to monitor process using SPC. •  Implement a Control Plan.

Gooooaaallllll!!!

Organizational Change

Ea ch   “ p la y e r ” in   th e   p r o ce s s   h a s   a   r o le   in   S U S TA IN IN G   p r o je ct   s u cce s s   a ch ie v e d . • • • • • • •

A ccept  responsibility Monitoring Responding Manag ing Embracing  chang e  &  continuous  learning Sharing  best  practices Potential  for  horiz ontal  replication  or  expansion  of  results

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

669

Wrap Up and Action Items Control Phase—The Roadblocks

Look  for  the  potential  roadblocks  and  plan  to  address  them   before  they  become  problems:   – Lack  of  project  sig n  off – Team  members  are  not  involved  in  C ontrol  Plan  desig n   – Manag ement  does  not  have  knowledg e  on  monitoring  and   reacting  needs – Financial  benefits  are  not  tracked  and  integ rated  into   business – Lack  of  buy  in  of  process  operators  or  staff

C hampion/ Process  O wner

DMAIC Roadmap

Identify  Problem  A rea

Define

Determine  A ppropria te  Project  Focus Estima te  C O PQ

Improve

A nalyz e

Measure

Establish  Tea m A ssess  Sta bility,  C apability,  a nd  Mea surement  Systems

Identify  a nd  Prioritiz e  A ll  X’s

Prove/ Disprove  Impact  X’s  Ha ve  O n  Problem

Identify,  Prioritiz e,  Select  Solutions  C ontrol  or  Eliminate  X’s  C a using  Problems  

C ontrol

Implement  Solutions  to  C ontrol  or  Eliminate  X’s  C a using  Problems  

Implement  C ontrol  Pla n  to  Ensure  Problem  Doesn’t  Return

Verify  Financia l  Impact

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

670

Wrap Up and Action Items Control Phase Improvement  S elected Develop  Training  Plan Implement  Training  Plan Develop  Documentation  Plan Implement  Documentation  Plan   Develop  Monitoring  Plan Implement  Monitoring  Plan Develop  Response  Plan Implement  Response  Plan Develop  Plan  to  A lig n  S ystems  and  S tructures A lig n  S ystems  and  S tructures Verify  Financial  Impact

G o  to  N ext  Project

Control Phase Checklist Control Questions Step One: Process Enhancement And Control Results • How do the results of the improvement(s) match the requirements of the business case and improvement goals? • What are the vital few X’s? • How will you control or redesign these X’s? • Is there a process control plan in place? • Has the control plan been handed off to the process owner? Step Two: Capability Analysis for X and Y Process Capability • How are you monitoring the Y’s? Step Three: Standardization And Continuous Improvement • How are you going to ensure that this problem does not return? • Is the learning transferable across the business? • What is the action plan for spreading the best practice? • Is there a project documentation file? • How is this referenced in process procedures and product drawings? • What is the mechanism to ensure this is not reinvented in the future? Step Four: Document what you have learned • Is there an updated FMEA? • Is the control plan fully documented and implemented ? • What are the financial implications? • Are there any spin-off projects? • What lessons have you learned? General Questions • Are there any issues/barriers preventing the completion of the project? • Do the Champion, the Belt and Finance all agree that this project is complete?

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

671

Wrap Up and Action Items Planning for Action

WHAT

WHO

W H EN

WHY

W H Y   N O T

HOW

Test  validation  plan  for  a  specific  time C alculate  benefits  for  breakthrough Implement  chang e  across  project  team Process  map  of  improved  process Finaliz e  Key  Input  Variables  (KPIV)  to  meet  g oal Prioritiz e  risks  of  output  failure C ontrol  plan  for  output C ontrol  plan  for  inputs C hart  a  plan  to  accomplish  the  desired  state  of  the  culture Mistake  proofing  plan  for  inputs  or  outputs Implementation  plan  for  effective  procedures Knowledg e  transfer  between  Belt,  PO ,  and  team  members Knowledg e  sharing  between  businesses  and  divisions Lean  project  control  plan Establish  continuous  or  attribute  metrics  for  C pk Identify  actual  versus  apparent  C pk Finaliz e  problem  solving  strateg y C omplete  RPN  assessment  with  revised  frequency  and  controls Show  improvement  in  RPN  through  action  items Repeat  same  process  for  secondary  metrics

Summary

A t   th is   p o in t,   y o u   s h o u ld : • Have  a  clear  understanding  of  the  specific  deliverables  to  complete   your  project. • Have  started  to  develop  a  project  plan  to  meet  the  deliverables. • Have  identified  ways  to  deal  with  potential  roadblocks. • Be  ready  to  apply  the  Six  Sig ma  method  on  your  N EXT  project.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

672

Wrap Up and Action Items It’s a Wrap

Congratulations you have completed Lean Six Sigma Black Belt Training!!!

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

673

Glossary Affinity Diagram - A technique for organizing individual pieces of information into groups or broader categories. ANOVA - Analysis of Variance – A statistical test for identifying significant differences between process or system treatments or conditions. It is done by comparing the variances around the means of the conditions being compared. Attribute Data - Data which on one of a set of discrete values such as pass or fail, yes or no. Average - Also called the mean, it is the arithmetic average of all of the sample values. It is calculated by adding all of the sample values together and dividing by the number of elements (n) in the sample. Bar Chart - A graphical method which depicts how data fall into different categories. Black Belt - An individual who receives approximately four weeks training in DMAIC, analytical problem solving, and change management methods. A Black Belt is a full time six sigma team leader solving problems under the direction of a Champion. Breakthrough Improvement - A rate of improvement at or near 70% over baseline performance of the as-is process characteristic. Capability - A comparison of the required operation width of a process or system to its actual performance width. Expressed as a percentage (yield), a defect rate (dpm, dpmo,), an index (Cp, Cpk, Pp, Ppk), or as a sigma score (Z). Cause and Effect Diagram - Fishbone Diagram - A pictorial diagram in the shape of a fishbone showing all possible variables that could affect a given process output measure. Central Tendency - A measure of the point about which a group of values is clustered; two measures of central tendency are the mean, and the median. Champion -A Champion recognizes, defines, assigns and supports the successful completion of six sigma projects; they are accountable for the results of the project and the business roadmap to achieve six sigma within their span of control. Characteristic - A process input or output which can be measured and monitored. Common Causes of Variation - Those sources of variability in a process which are truly random, i.e., inherent in the process itself. Complexity -The level of difficulty to build, solve or understand something based on the number of inputs, interactions and uncertainty involved. Control Chart - The most powerful tool of statistical process control. It consists of a run chart, together with statistically determined upper and lower control limits and a centerline. Control Limits - Upper and lower bounds in a control chart that are determined by the process itself. They can be used to detect special or common causes of variation. They are usually set at ±3 standard deviations from the central tendency. Correlation Coefficient - A measure of the linear relationship between two variables. Cost of Poor Quality (COPQ) - The costs associated with any activity that is not doing the right thing right the first time. It is the financial qualification any waste that is not integral to the product or service which your company provides.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

674

Glossary CP - A capability measure defined as the ratio of the specification width to short-term process performance width. CPk -. An adjusted short-term capability index that reduces the capability score in proportion to the offset of the process center from the specification target. Critical to Quality (CTQ) - Any characteristic that is critical to the perceived quality of the product, process or system. See Significant Y. Critical X - An input to a process or system that exerts a significant influence on any one or all of the key outputs of a process. Customer - Anyone who uses or consumes a product or service, whether internal or external to the providing organization or provider. Cycle Time - The total amount of elapsed time expended from the time a task, product or service is started until it is completed. Defect - An output of a process that does not meet a defined specification, requirement or desire such as time, length, color, finish, quantity, temperature etc. Defective - A unit of product or service that contains at least one defect. Deployment (Six Sigma) - The planning, launch, training and implementation management of a six sigma initiative within a company. Design of Experiments (DOE) - Generally, it is the discipline of using an efficient, structured, and proven approach to interrogating a process or system for the purpose of maximizing the gain in process or system knowledge. Design for Six Sigma (DFSS) - The use of six sigma thinking, tools and methods applied to the design of products and services to improve the initial release performance, ongoing reliability, and life-cycle cost. DMAIC - The acronym for core phases of the six sigma methodology used to solve process and business problems through data and analytical methods. See define, measure, analyze, improve and control. DPMO - Defects per million opportunities – The total number of defects observed divided by the total number of opportunities, expressed in parts per million. Sometimes called Defects per Million (DPM). DPU - Defects per unit - The total number of defects detected in some number of units divided by the total number of those units. Entitlement - The best demonstrated performance for an existing configuration of a process or system. It is an empirical demonstration of what level of improvement can potentially be reached. Epsilon ε - Greek symbol used to represent residual error. Experimental Design - See Design of Experiments. Failure Mode and Effects Analysis (FMEA) - A procedure used to identify, assess, and mitigate risks associated with potential product, system, or process failure modes. Finance Representative - An individual who provides an independent evaluation of a six sigma project in terms of hard and/or soft savings. They are a project support resource to both Champions and Project Leaders.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

675

Glossary Fishbone Diagram - See cause and effect diagram. Flowchart - A graphic model of the flow of activities, material, and/or information that occurs during a process. Gage R&R - Quantitative assessment of how much variation (repeatability and reproducibility) is in a measurement system compared to the total variation of the process or system. Green Belt - An individual who receives approximately two weeks of training in DMAIC, analytical problem solving, and change management methods. A Green Belt is a part time six sigma position that applies six sigma to their local area, doing smaller-scoped projects and providing support to Black Belt projects. Hidden Factory or Operation - Corrective and non-value-added work required to produce a unit of output that is generally not recognized as an unnecessary generator of waste in form of resources, materials and cost. Histogram - A bar chart that depicts the frequencies (by the height of the plotted bars) of numerical or measurement categories. Implementation Team - A cross-functional executive team representing various areas of the company . Its charter is to drive the implementation of six sigma by defining and documenting practices, methods and operating policies. Input - A resource consumed, utilized, or added to a process or system. Synonymous with X, characteristic, and input variable. Input-Process-Output (IPO) Diagram - A visual representation of a process or system where inputs are represented by input arrows to a box (representing the process or system) and outputs are shown using arrows emanating out of the box. lshikawa Diagram - See cause and effect diagram and fishbone diagram. Least Squares - A method of curve-fitting that defines the best fit as the one that minimizes the sum of the squared deviations of the data points from the fitted curve. Long-term Variation - The observed variation of an input or output characteristic which has had the opportunity to experience the majority of the variation effects that influence it. Lower Control Limit (LCL) - for control charts: the limit above which the subgroup statistics must remain for the process to be in control. Typically, 3 standard deviations below the central tendency. Lower Specification Limit (LSL) - The lowest value of a characteristic which is acceptable. Master Black Belt - An individual who has received training beyond a Black Belt. The technical, go-to expert regarding technical and project issues in six sigma. Master Black Belts teach and mentor other six sigma Belts, their projects and support Champions. Mean - See average. Measurement - The act of obtaining knowledge about an event or characteristic through measured quantification or assignment to categories. Measurement Accuracy - For a repeated measurement, it is a comparison of the average of the measurements compare to some known standard. Measurement Precision - For a repeated measurement, it is the amount of variation that exists in the measured values.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

676

Glossary Measurement Systems Analysis (MSA) - An assessment of the accuracy and precision of a method of obtaining measurements. See also Gage R&R. Median - The middle value of a data set when the values are arranged in either ascending or descending order. Metric - A measure that is considered to be a key indicator of performance. It should be linked to goals or objectives and carefully monitored. Natural Tolerances of a Process - See Control Limits. Nominal Group Technique - A structured method that a team can use to generate and rank a list of ideas or items. Non-Value Added (NVA) - Any activity performed in producing a product or delivering a service that does not add value, where value is defined as changing the form, fit or function of the product or service and is something for which the customer is willing to pay. Normal Distribution - The distribution characterized by the smooth, bell- shaped curve. Synonymous with Gaussian Distribution. Objective Statement - A succinct statement of the goals, timing and expectations of a six sigma improvement project. Opportunities - The number of characteristics, parameters or features of a product or service that can be classified as acceptable or unacceptable. Out of Control - A process is said to be out of control if it exhibits variations larger than its control limits or shows a pattern of variation. Output - A resource or item or characteristic that is the product of a process or system. See also Y, CTQ. Pareto Chart - A bar chart for attribute (or categorical) data categories are presented in descending order of frequency. Pareto Principle - The general principle originally proposed by Vilfredo Pareto (1848-1923) that the majority of influence on an outcome is exerted by a minority of input factors. Poka-Yoke - A translation of a Japanese term meaning to mistake-proof. Probability - The likelihood of an event or circumstance occurring. Problem Statement - A succinct statement of a business situation which is used to bound and describe the problem the six sigma project is attempting to solve. Process - A set of activities and material and/or information flow which transforms a set of inputs into outputs for the purpose of producing a product, providing a service or performing a task. Process Characterization - The act of thoroughly understanding a process, including the specific relationship(s) between its outputs and the inputs, and its performance and capability. Process Certification - Establishing documented evidence that a process will consistently produce required outcome or meet required specifications. Process Flow Diagram - See flowchart.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

677

Glossary Process Member - A individual who performs activities within a process to deliver a process output, a product or a service to a customer. Process Owner - Process Owners have responsibility for process performance and resources. They provide support, resources and functional expertise to six sigma projects. They are accountable for implementing developed six sigma solutions into their process. Quality Function Deployment (QFD) - A systematic process used to integrate customer requirements into every aspect of the design and delivery of products and services. Range - A measure of the variability in a data set. It is the difference between the largest and smallest values in a data set. Regression Analysis - A statistical technique for determining the mathematical relation between a measured quantity and the variables it depends on. Includes Simple and Multiple Linear Regression. Repeatability (of a Measurement) - The extent to which repeated measurements of a particular object with a particular instrument produce the same value. See also Gage R&R. Reproducibility (of a Measurement) - The extent to which repeated measurements of a particular object with a particular individual produce the same value. See also Gage R&R. Rework - Activity required to correct defects produced by a process. Risk Priority Number (RPN) - In Failure Mode Effects Analysis -- the aggregate score of a failure mode including its severity, frequency of occurrence, and ability to be detected. Rolled Throughput Yield (RTY) - The probability of a unit going through all process steps or system characteristics with zero defects. R.U.M.B.A. - An acronym used to describe a method to determine the validity of customer requirements. It stands for Reasonable, Understandable, Measurable, Believable, and Achievable. Run Chart - A basic graphical tool that charts a characteristic’s performance over time. Scatter Plot - A chart in which one variable is plotted against another to determine the relationship, if any, between the two. Screening Experiment - A type of experiment to identify the subset of significant factors from among a large group of potential factors. Short Term Variation - The amount of variation observed in a characteristic which has not had the opportunity to experience all the sources of variation from the inputs acting on it. Sigma Score (Z) - A commonly used measure of process capability that represents the number of short-term standard deviations between the center of a process and the closest specification limit. Sometimes referred to as sigma level, or simply Sigma. Significant Y - An output of a process that exerts a significant influence on the success of the process or the customer. Six Sigma Leader - An individual that leads the implementation of Six Sigma, coordinating all of the necessary activities, assures optimal results are obtained and keeps everyone informed of progress made.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

678

Glossary Six Sigma Project - A well defined effort that states a business problem in quantifiable terms and with known improvement expectations. Six Sigma (System) - A proven set of analytical tools, project management techniques, reporting methods and management techniques combined to form a powerful problem solving and business improvement methodology. Special Cause Variation - Those non-random causes of variation that can be detected by the use of control charts and good process documentation. Specification Limits - The bounds of acceptable performance for a characteristic. Stability (of a Process) - A process is said to be stable if it shows no recognizable pattern of change and no special causes of variation are present. Standard Deviation - One of the most common measures of variability in a data set or in a population. It is the square root of the variance. Statistical Problem - A problem that is addressed with facts and data analysis methods. Statistical Process Control (SPC) - The use of basic graphical and statistical methods for measuring, analyzing, and controlling the variation of a process for the purpose of continuously improving the process. A process is said to be in a state of statistical control when it exhibits only random variation. Statistical Solution - A data driven solution with known confidence/risk levels, as opposed to a qualitative, “I think” solution. Supplier - An individual or entity responsible for providing an input to a process in the form of resources or information. Trend - A gradual, systematic change over time or some other variable. TSSW - Thinking the six sigma way – A mental model for improvement which perceives outcomes through a cause and effect relationship combined with six sigma concepts to solve everyday and business problems. Two-Level Design - An experiment where all factors are set at one of two levels, denoted as low and high (-1 and + 1). Upper Control Limit (UCL) for Control Charts - The upper limit below which a process statistic must remain to be in control. Typically this value is 3 standard deviations above the central tendency. Upper Specification Limit (USL) - The highest value of a characteristic which is acceptable. Variability - A generic term that refers to the property of a characteristic, process or system to take on different values when it is repeated. Variables - Quantities which are subject to change or variability. Variable Data - Data which is continuous, which can be meaningfully subdivided, i.e. can have decimal subdivisions. Variance - A specifically defined mathematical measure of variability in a data set or population. It is the square of the standard deviation. Variation - See variability.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

679

Glossary VOB - Voice of the business – Represents the needs of the business and the key stakeholders of the business. It is usually items such as profitability, revenue, growth, market share, etc. VOC - Voice of the customer – Represents the expressed and non-expressed needs, wants and desires of the recipient of a process output, a product or a service. Its is usually expressed as specifications, requirements or expectations. VOP - Voice of the process – Represents the performance and capability of a process to achieve both business and customer needs. It is usually expressed in some form of an efficiency and/or effectiveness metric. Waste - Waste represents material, effort and time that does not add value in the eyes of key stakeholders (Customers, Employees, Investors). X - An input characteristic to a process or system. In six sigma it is usually used in the expression of Y=f(X), where the output (Y) is a function of the inputs (X). Y - An output characteristic of a process. In six sigma it is usually used in the expression of Y=f(X), where the output (Y) is a function of the inputs (X). Yellow Belt - An individual who receives approximately one week of training in problem solving and process optimization methods. Yellow Belts participate in Process Management activates, participate on Green and Black Belt projects and apply concepts to their work area and their job. Z Score – See Sigma Score.

LSS Black Belt Manual XL v11

© 2013 e-Careers Limited

A scientific approach to sustainably solving problems, reducing defects and getting results.

Lean Six Sigma is truly a remarkable problem-solving technology. First and foremost in gaining benefit from its use is your ability to see the possibilities. Part of this class is aimed at accomplishing this. You yourself know what issues and problems confront your everyday work experience. When you can see the power of Lean Six Sigma, you will be able to do something about these problems like you have never done before.

An e-Careers Limited Publication   10 Riverside Business Park Stony Common Road Stansted Mountfitchet Essex. CM24 8PL. United Kingdom Email: [email protected] (UK 0044) (0) 1279 799 444