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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
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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
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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”.
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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.
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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
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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
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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.
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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.
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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
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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.
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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
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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
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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 .
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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.
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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
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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.
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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
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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.
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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.
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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.
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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!!
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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
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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
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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.
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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
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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
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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).
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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.
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Six Sigma Fundamentals Process Map Exercise
Notes
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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.
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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?
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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
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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
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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
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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
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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
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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
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COPQ – Soft Savings • • • • •
Gaining Lost Sales Missed Opportunities Customer Loyalty Strategic Savings Preventing Regulatory Fines
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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
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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
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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
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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
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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
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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
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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.
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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
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Lean Six Sigma Black Belt Training
Define Phase Selecting Projects
Now we will continue in the Define Phase with the “Selecting Projects”.
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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.
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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
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Fre q u e n cy o f U p d a te
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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
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Here are some examples of the 80:20 Rule. Can you think of any other examples?
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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.
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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.
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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
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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
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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
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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.
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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
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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)
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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!!
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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.
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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.
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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
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Lean Six Sigma Black Belt Training
Define Phase Elements of Waste
Now we will continue in the Define Phase with “Elements of Waste”.
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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
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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.
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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.
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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
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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
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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
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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
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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
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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.
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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.
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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
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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
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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”.
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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
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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
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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
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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.
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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
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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.
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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
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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.
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Lean Six Sigma Black Belt Training
Measure Phase Process Discovery
Now we will continue in the Measure Phase with “Process Discovery”.
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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..
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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.
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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.
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Process Discovery Cause and Effect Diagram
Cause and Effect Diagram
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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
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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
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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.
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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.
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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!!
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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.
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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).
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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.
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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 ”.
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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
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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)
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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.
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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 ……!
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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)
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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.
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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!!
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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
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Lean Six Sigma Black Belt Training
Measure Phase Six Sigma Statistics
Now we will continue in the Measure Phase with “Six Sigma Statistics”.
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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
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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.
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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.
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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
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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?
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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
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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.
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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.
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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.
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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
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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
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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!!
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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?
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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:
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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?
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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.
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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.
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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
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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.
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What can you tell about the data expressed in a Box Plots?
Eat this – then check the Box Plot!!
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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.
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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
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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”.
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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?
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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.
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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
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Lean Six Sigma Black Belt Training
Measure Phase Measurement System Analysis
Now we will continue in the Measure Phase with “Measurements System Analysis”.
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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
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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.
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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.
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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.
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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
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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.
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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?
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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.
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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.
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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
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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?
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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.
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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?
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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.
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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
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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
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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.
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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
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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
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1 0 % o r g re a te r
Poor
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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
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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.
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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)”.
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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.
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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.
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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.
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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®.
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Measurement System Analysis Data Collection Sheet
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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.
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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
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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
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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
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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.
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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
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Measurement System Analysis Attribute Agreement Analysis
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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.
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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.
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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
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Lean Six Sigma Black Belt Training
Measure Phase Process Capability
Now we will continue in the Measure Phase with “Process Capability”.
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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.
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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
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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
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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.
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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
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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.
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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
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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
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Process Capability Z Scores
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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.
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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.
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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.
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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
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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.
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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
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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.
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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
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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
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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
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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.
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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
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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.
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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.
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“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.
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“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
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“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.
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“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
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#2 A m b ie n t Te m p
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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
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“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.
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W ednesday Die C ycle #3
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Between-Unit Encoding Comparing the averages from each die cycle is called Between Unit Variation.
Die C ycle #1
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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
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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
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Die C ycle #1
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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
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“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
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“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.
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“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.
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“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
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“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
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“X” Sifting Multi-Vari Exercise
Notes
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“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?
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“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.
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“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
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“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.
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“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.
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“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
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4 Granularity
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“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
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When a distribution is not symmetrical, then it’s Skewed. Generally a Skewed distribution longest tail points in the direction of the Skew.
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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
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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
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“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.
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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.
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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
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Spray
Off
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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
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“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
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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
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“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
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“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
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“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.
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“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
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“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
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“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
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Lean Six Sigma Black Belt Training
Analyze Phase Inferential Statistics
Now we will continue in the Analyze Phase with Inferential Statistics.
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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
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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
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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.
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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.
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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.
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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
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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.
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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
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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.
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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.
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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
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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.
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Inferential Statistics Standard Error
Standard Error
Standard Error approaches zero at about 30 samples.
0
5
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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.
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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
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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”.
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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.
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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.
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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.
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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
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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
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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.
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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
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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.
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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!!
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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.
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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
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– 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
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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
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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:
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Should we take some more samples just to be sure? No, not if you took the correct number of samples in the first place!
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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
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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.
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Introduction to Hypothesis Testing Hypothesis Testing Roadmap – Continuous Data
Hypothesis Testing Roadmap – Attribute Data
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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
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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
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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”.
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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.
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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!!
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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
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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.
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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.
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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.
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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.
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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
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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
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Hypothesis Testing Normal Data Part 1 1-Sample t Exercise
Notes
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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.
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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
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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.
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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.
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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?
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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.
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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…
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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…
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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
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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.
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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.
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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…
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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” .
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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
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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.
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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’
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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.
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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.
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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
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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.
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Hypothesis Testing Normal Data Part 1 Paired t-test Exercise: Solution
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Hypothesis Testing Normal Data Part 1 Continuous Data Roadmap
Notes
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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
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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”.
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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.
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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!!
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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
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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.
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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.
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Hypothesis Testing Normal Data Part 2 Normality Test – Follow the Roadmap Check for Normality.
According to the graph we have Normal data.
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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.
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Hypothesis Testing Normal Data Part 2 Normality Test
Test for Equal Variance (Normal Data)
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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.
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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.
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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.
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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.
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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.
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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.
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Hypothesis Testing Normal Data Part 2 Hypothesis Testing Roadmap
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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
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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
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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.
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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.
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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.
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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
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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.
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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?)
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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
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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’
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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.
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Hypothesis Testing Normal Data Part 2 ANOVA Exercise: Solution If the variances are unequal then use Welch’s ANOVA instead of One-Way ANOVA.
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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.
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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
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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”.
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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!!!
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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.
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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.
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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
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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.
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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.
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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……
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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.
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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.
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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
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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
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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.
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Hypothesis Testing Non-Normal Data Part 1 1 Sample Example: Solution
We disagree!!
Mann-Whitney Example
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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.
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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
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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.
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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.
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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
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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
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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…
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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.
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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.
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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.
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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.
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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
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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”.
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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
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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
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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!!
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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. • •
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Do you g et your a nnua l bonus? W as the sa mple siz e g ood enoug h?
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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?
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X 1680 pˆ = = = 0.84 n 2000
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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
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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
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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
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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.
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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.
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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
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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
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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
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Larry Curley Total 8 20 33 0.306 30 25 75 0.694 38 45 108
0.306*45 = 13.8
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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
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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
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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
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7
8
2 = 5.99 χcrit
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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.
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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
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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?!
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Per day?!
Per month?!
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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
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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.
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Improve Phase Process Modeling Regression
Now we will continue in the Improve Phase with “Process Modeling: Regression”.
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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
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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
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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
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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.
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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!!
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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
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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.
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Payton yards = -163.497 + 4.91622(250) = 1,065.6
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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
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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.)
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Process Modeling Regression Residuals (cont.)
These graphs are found on the “Mult Reg Residuals” sheet.
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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
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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
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Process Modeling Regression Modeling Y=f(x) Exercise
Modeling Y=f(x) Exercise: Question 1 Solution
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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!
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Process Modeling Regression Modeling Y=f(x) Exercise: Question 2 Solution (cont.)
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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.
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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
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Lean Six Sigma Black Belt Training
Improve Phase Advanced Process Modeling
Now we will continue with the Improve Phase “Advanced Process Modeling MLR”.
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Advanced Process Modeling Overview
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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
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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?
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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.
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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
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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)
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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.
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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.
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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
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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
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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
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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”.
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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
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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
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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
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Lean Six Sigma Black Belt Training
Improve Phase Designing Experiments
Now we are going to continue with the Improve Phase “Designing Experiments”.
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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
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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
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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 .
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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 )
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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 )
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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
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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.
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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
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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.
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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 .
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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
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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
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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?
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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?
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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
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Lean Six Sigma Black Belt Training
Improve Phase Experimental Methods
Now we will continue with the Improve Phase “Experimental Methods”.
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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Lean Six Sigma Black Belt Training
Improve Phase Full Factorial Experiments
Now we will continue in the Improve Phase with “Full Factorials”.
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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.
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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.
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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
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% Reacted
% Reacted 1
55 0 -1
Ct
0
-1 1
Cn
1 45
0 -1
T
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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.
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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
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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.
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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
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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 + .
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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.
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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.
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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)
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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.
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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
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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
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Full Factorial Experiments Panel Cleaning Example (cont.)
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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?!
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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
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Lean Six Sigma Black Belt Training
Improve Phase Fractional Factorial Experiments
Now we will continue with the Improve Phase “Fractional Factorial Designing Experiments”.
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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
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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.
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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
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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.
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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
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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
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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.
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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.
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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
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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
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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
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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
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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…..!
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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.
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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.
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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.
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Fractional Factorial Experiments Fractional Factorial Example (cont.)
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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…!
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Fractional Factorial Experiments Fractional Factorial Example (cont.)
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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…!!!
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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
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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
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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.
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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.
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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.
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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
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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
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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
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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.
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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
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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
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Lean Six Sigma Black Belt Training
Control Phase Advanced Experiments
Now we will continue in the Control Phase with “Advanced Experiments”.
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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.
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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.
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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?
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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.
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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
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Advanced Experiments Example of Projection Vector Method
Choosing the Step Size
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Advanced Experiments Other Factor Step Size
Work through each step to find the optimum result.
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Advanced Experiments Process Results from Steepest Ascent
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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
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Lean Six Sigma Black Belt Training
Control Phase Advanced Capability
Now we will continue in the Control Phase with “Advanced Capability”.
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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…
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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.
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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!
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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?
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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
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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.
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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.
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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
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Lean Six Sigma Black Belt Training
Control Phase Lean Controls
Now we will continue in the Control Phase with “Lean Controls”.
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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.
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Vision of Lean Supporting Vision of Lean Supporting Six Sig Six Sigma ma
Le Leaa nn CCoonntro trols ls
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Project Sustained Success Project Sustained Success
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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
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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
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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
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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
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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
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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
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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.
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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).
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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.
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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.
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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?
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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.
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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
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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 .
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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
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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
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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 .
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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
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Lean Six Sigma Black Belt Training
Control Phase Defect Controls
Now we will continue in the Control Phase with the “Defect Controls”.
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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
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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.
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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
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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 .
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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
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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?
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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
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Defect Controls 4 – 5 σ Process Interruption (cont.)
Ex a m p le : •
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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
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S ee ifi f you y ou can See can find find the the Pok a-‐ PokaY ok es!Yokes!!
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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 )
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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
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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 : •
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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
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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
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C h ild p ro o f ca p s o n m e d ica tio n s
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B u ta n e lig h te rs w ith s a fe ty b u tto n
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C o m p u te rs –
M o u s e in s e rtio n
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U S B ca b le co n n e ctio n
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B a tte ry in s e rtio n
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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
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A ir b a g s
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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
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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 –
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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.
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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.
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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
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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”.
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Statistical Process Control Overview
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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.
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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
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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.
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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
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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
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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
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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
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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.
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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.
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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 .
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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 .
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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.
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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
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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.
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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
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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.
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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
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Statistical Process Control Chart Selection Process
SigmaXL® includes a Control Chart Selection Tool to simplify the selection process. Notes
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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.
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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.
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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
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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.
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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
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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
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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
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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 )
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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.
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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.
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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
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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.
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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
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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
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Statistical Process Control Attribute SPC Example (cont.)
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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%
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Statistical Process Control Attribute SPC Example (cont.)
The chart has now been updated to include the new points.
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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…
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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.
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Statistical Process Control Attribute SPC Example (cont.)
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Statistical Process Control Attribute SPC Example (cont.)
Note: The Mean, UCL and LCL are unchanged when SigmaXL®’s Add Data button is used.
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Statistical Process Control Attribute SPC Example (cont.)
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Statistical Process Control SPC Chart Option in SigmaXL® for σ Levels
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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
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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”.
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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
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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
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Six Sigma Control Plans Cost Considerations
It’s all about the cash!!
Time Considerations
The clock’s ticking…!
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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
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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
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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.
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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
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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
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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!!
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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Six Sigma Control Plans Response Plan – Abnormality Report
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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
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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.
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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
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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 .
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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
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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
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Control Phase Wrap Up and Action Items
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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
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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
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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?
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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.
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Wrap Up and Action Items It’s a Wrap
Congratulations you have completed Lean Six Sigma Black Belt Training!!!
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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