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SIXSIGMA
INPRACTICE
A publication of: The Lean Six Sigma Company
Postal addresThe Lean Six Sigma CompanyP.O Box 132483004 HK ROTTERDAMThe netherlands
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Six Sigma in practice
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Authors
Rijk Schildmeijer
Master Black Belt and partner at The Lean Six Sigma
Company.
Paul Suijkerbuijk
Master Black Belt and partner at The Lean Six Sigma
Company
Editor
Mischa van Aalten
Special thanks to:
Kees Bultink, Master Black belt at The Lean Six Sigma Company
Cover:
Nick Heurter, Onlinemarketing.nl
Title: Six Sigma in practice
ISBN: 978-90-821026-4-2
4th edition, version October 2019
Published by The Lean Six Sigma Company. All rights reserved. Nothing in
this edition may be multiplied, stored in an automated data file and/or
published in form or manner, either electronically, mechanically, through
photocopies, recordings or in any other way without the prior written
permission by the publisher.
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Introduction Thank you for choosing a Lean Six Sigma training of The Lean Six Sigma
Company. Our ambition is to train and coach you as Black Belt or Green Belt
in such a way that you are able to independently guide organizations to a
higher level. We will help you with that. Our most important assets to do
this are our trainers, Master Black Belts with many years of experience in
commercial and non-commercial businesses. But also the way of training
and our training materials. Continuous improvement is the common theme
in all our trainings. We hoped this is also your ambition, and the reason to
sign up for the training. We will do anything to teach you the methods and
techniques to turn your ambition into solid result
Continuous improvement of course also applies to ourselves. We love to
hear from you how, when and where to improve our materials. Therewith
you help us improve. Continuous improvement is something to do together.
Good luck and a lot of fun with your trainings and I wish you fun and success
with applying everything in practice.
Mischa van Aalten
Managing Partner
The Lean Six Sigma Company
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Contents Introduction ................................................................................................ 3
CHAPTER 0: INTRODUCTION LEAN SIX SIGMA ............................................ 15
0.1 Introduction ............................................................................. 15
0.2 What is Six Sigma? .................................................................... 15
0.3 Origin of Six Sigma .................................................................... 17
0.4 Variation .................................................................................. 17
0.5 Standard deviation, a measurement for variation ..................... 19
0.6 Defects and Sigma level ............................................................ 20
0.7 Variation and defects in the process ......................................... 23
0.8 Six Sigma as an organization ..................................................... 27
0.9 The Six Sigma improvement structure ....................................... 30
0.10 Six Sigma in services and industry sectors ................................. 34
0.11 Implementing Lean Six Sigma .................................................... 34
0.12 Exercises .................................................................................. 38
PART 1 DEFINE .......................................................................................... 41
CHAPTER 1: PROJECT SELECTION AND SCOPE ............................................ 43
1.1 Introduction ............................................................................. 43
1.2 Selecting a project .................................................................... 43
1.3 Determining the scope ............................................................. 53
1.3.1 Voice of the Customer .............................................................. 53
1.3.2 Affinity diagram ........................................................................ 57
1.3.3 Kano Analysis ........................................................................... 58
1.4 Exercises .................................................................................. 60
CHAPTER 2: DEFINITION OF THE DEFECT .................................................... 63
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2.1 Introduction ............................................................................. 63
2.2 Critical to Quality ...................................................................... 63
2.2.1 Tree-diagram ............................................................................ 64
2.2.2 Quality Function Deployment ................................................... 65
2.3 The project charter ................................................................... 65
2.3.1 Project authorization ................................................................ 67
2.3.2 Project definition ...................................................................... 67
2.3.3 Process history ......................................................................... 69
2.3.4 Project team ............................................................................. 69
2.3.5 Stakeholders and stakeholder assessment ................................ 71
2.3.6 Project time line ....................................................................... 72
2.3.7 Benefits .................................................................................... 74
2.3.7.1 Economic Value Added ......................................................... 75
2.4 SIPOC: outline process description ............................................ 79
2.5 Value Stream Mapping ............................................................. 82
2.6 Exercises .................................................................................. 84
PART 2: MEASURE .................................................................................... 87
CHAPTER 3: DETERMINING ‘Y’ AND ANALYZING THE MEASURING SYSTEM 89
3.1 Introduction ............................................................................. 89
3.2 From CTQ to project Y .............................................................. 89
3.2.1 Tree-diagram ............................................................................ 90
3.2.2 Detailed process diagram ......................................................... 91
3.2.3 Pareto analysis ......................................................................... 92
3.2.4 Quality Function Deployment ................................................... 93
3.2.5 Scope and project Y .................................................................. 95
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3.3 Collecting data.......................................................................... 96
3.3.1 Data collection plan .................................................................. 97
3.3.1.1 Data collection plan: why are we measuring? ....................... 99
3.3.1.2 Data collection plan: What are we measuring? ................... 100
3.3.1.3 Data collection plan: how are we measuring? ..................... 104
3.3.1.4 Data collection plan: who is measuring? ............................. 108
3.4 Measurement System Analysis ............................................... 109
3.4.1 Resolution, accuracy, stability and linearity ............................. 111
3.4.2 Precision ................................................................................ 114
3.4.3 Gage R&R ............................................................................... 116
3.4.3.1 Gage R&R for continuous variables ..................................... 116
3.4.3.2 Gage R&R for discrete variables .......................................... 126
3.5 Exercises ................................................................................ 135
CHAPTER 4: BASELINE PERFORMANCE ..................................................... 139
4.1 Introduction ........................................................................... 139
4.2 Process Capability ................................................................... 139
4.2.1 Determining the performance standards ................................ 141
4.2.2 Determining Process Capability............................................... 142
4.3 Baseline performance ............................................................. 147
4.4 Exercises ................................................................................ 148
CHAPTER 5: OBJECTIVE GOAL ON BASELINE PERFORMANCE .................... 151
5.1 Introduction ........................................................................... 151
5.2 Determining the improvement goal ........................................ 151
5.3 Recalculation revenues ........................................................... 151
5.4 Exercises ................................................................................ 152
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PART 3: ANALYZE .................................................................................... 155
CHAPTER 6: POTENTIAL CAUSES OF VARIATION ...................................... 157
6.1 Introduction ........................................................................... 157
6.2 Potential causes (X’s) .............................................................. 158
6.2.1 Tools to determine potential causes ....................................... 159
6.2.2 Cause & Effect diagram........................................................... 159
6.2.3 Cause & Effect matrix ............................................................. 163
6.2.4 Failure Mode & Effects Analysis (FMEA) .................................. 165
6.2.5 Data collection X’s .................................................................. 171
6.2.6 Graphical data analysis ........................................................... 172
6.3 Use of instruments ................................................................. 176
6.4 Exercises ................................................................................ 178
CHAPER 7: DETERMINING THE ROOT CAUSES ......................................... 181
7.1 Introduction ........................................................................... 181
7.2 From potential causes to root causes ...................................... 181
7.3 Hypothesis Testing ................................................................. 183
7.3.1 Selecting the tests .................................................................. 183
7.3.2 Normality test ........................................................................ 184
7.3.3 1 Sample t-test ....................................................................... 186
7.3.4 2 sample t-test ....................................................................... 188
7.3.5 2-sample Standard Deviation test ........................................... 191
7.3.6 Paired t-test ........................................................................... 193
7.3.7 1-sample % defective test (1-Proportion test) ......................... 196
7.3.8 2-sample % defective test (2-proportions test) ........................ 199
7.3.9 Analysis of Variance (ANOVA) One Way .................................. 202
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7.3.10 Standard Deviations Test .................................................... 206
7.3.11 Analysis of Variance (ANOVA) Two Way .............................. 208
7.3.12 Kruskal-Wallis test .............................................................. 210
7.3.13 Chi-square test ................................................................... 214
7.3.14 Binary Fitted Line Plot ........................................................ 220
7.3.15 Correlation and regression ................................................. 224
7.3.15.1 Simple Regression .......................................................... 225
7.3.15.2 Multiple Regression........................................................ 227
7.4 The root causes ...................................................................... 230
7.5 Exercises ................................................................................ 230
PART 4: IMPROVE ................................................................................... 233
CHAPTER 8: DETERMINING THE OPTIMAL SOLUTION .............................. 235
8.1 Introduction ........................................................................... 235
8.2 Design of Experiments ............................................................ 236
8.2.1 Introduction DoE .................................................................... 236
8.2.2 DoE terminology ..................................................................... 237
8.2.3 The Design of Experiments approach ...................................... 238
8.3 Trial Experiments .................................................................... 277
8.3.1 Data collection ....................................................................... 277
8.3.2 Develop alternative solutions ................................................. 278
8.3.2.1 Brainstorming .................................................................... 279
8.3.2.2 Interviews .......................................................................... 281
8.3.2.3 Thought-inducing questions ............................................... 281
8.3.2.4 Mind Mapping .................................................................... 282
8.3.2.5 Six Thinking Hats technique ................................................ 283
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8.3.2.6 Building on ideas ................................................................ 287
8.3.2.7 Benchmarking .................................................................... 287
8.3.3 Assess the alternative solutions .............................................. 288
8.3.4 Risk assessment, FMEA ........................................................... 289
8.3.5 Select the best of the alternative solutions ............................. 290
8.3.5.1 Decision matrix .................................................................. 291
8.3.5.2 Pugh Matrix........................................................................ 291
8.3.5.3 AHP Matrix ......................................................................... 295
8.3.6 Conducting the trial experiment ............................................. 296
8.4 Exercises ................................................................................ 297
CHAPTER 9: TESTING THE SOLUTION ...................................................... 299
9.1 Introduction ........................................................................... 299
9.2 Executing a pilot ..................................................................... 299
9.3 Managing the pilot ................................................................. 300
9.4 Analyzing the pilot results ....................................................... 301
9.5 Practice tips for a successful pilot ........................................... 302
PART 5: CONTROL................................................................................... 305
CHAPTER 10: SECURING AND MEASUREMENT SYSTEM ANALYSIS ........... 307
10.1 Introduction ........................................................................... 307
10.2 Control plan ........................................................................... 308
10.3 Control Mechanisms ............................................................... 309
10.3.1 Mistake Proofing ................................................................ 310
10.3.2 Robust Process Design ........................................................ 314
10.3.3 Visual Management............................................................ 315
10.3.4 Procedures ......................................................................... 315
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10.3.5 Control Charts .................................................................... 317
10.4 Measurement System Analysis ............................................... 327
10.5 Exercises ................................................................................ 327
CHAPTER 11: IMPLEMENTATION AND CONFIRMATION OF THE
IMPROVEMENT ....................................................................................... 329
11.1 Introduction ........................................................................... 329
11.2 Implementation ...................................................................... 329
11.3 Confirming the improvement .................................................. 330
CHAPTER 12: PROJECT CLOSURE AND HAND-OVER ................................. 333
12.1 Introduction ........................................................................... 333
12.2 Hand-over to the sponsor ....................................................... 333
12.3 Project documentation ........................................................... 333
12.4 Lessons learned, suggestions for follow-up projects, striving for
perfection ........................................................................................... 334
12.5 Project audit ........................................................................... 335
APPENDIX 1: BASIC STATISTICS ................................................................ 337
A1.1 Introduction ................................................................................ 337
A1.2 Statistics ..................................................................................... 337
A1.3 Statistical values .......................................................................... 338
A1.3.1 The Mean (or Average) ............................................................. 339
A1.3.2 The Median .............................................................................. 340
A1.3.3 The Mode................................................................................. 341
A1.3.4 Range ....................................................................................... 341
A1.3.5 Quartiles .................................................................................. 341
A1.3.6 Inter Quartile Range (IQR) ........................................................ 342
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A1.3.7 Mean Deviation ........................................................................ 342
A1.3.8 Variance ................................................................................... 342
A1.3.9 Standard deviation ................................................................... 343
A1.4 Sample in relation to population ................................................. 344
A1.5 The distribution of data ............................................................... 345
A1.5.1 Distributions ............................................................................ 345
A1.5.2 Histogram ................................................................................ 346
A1.5.3 Normal distribution .................................................................. 349
A1.6 Exercises ..................................................................................... 353
APPENDIX 2: INTRODUCTION MINITAB .................................................... 355
A2.1 Introduction ................................................................................ 355
A2.2 Building and lay-out .................................................................... 355
A2.3 Minitab menus ............................................................................ 357
A2.4 Working with Minitab ................................................................. 364
A2.5 Saving the project ....................................................................... 382
APPENDIX 3: HYPOTHESIS TESTING .......................................................... 385
A3.1 Introduction ................................................................................ 385
A3.2 Confidence intervals .................................................................... 385
A3.3 Hypothesis Testing ...................................................................... 390
APPENDIX 4: ANSWERS TO EXERCISES ..................................................... 401
Appendix 5: Project charter ..................................................................... 409
Appendix 6: T-Table ................................................................................ 414
Appendix 7: Normal distribution .............................................................. 415
Appendix 8: standard Z Table .................................................................. 416
Appendix 9: Z to DPMO with shift ............................................................ 417
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Appendix 10: �� to P-value ..................................................................... 418
Appendix 11: abbreviations ..................................................................... 419
INDEX...................................................................................................... 420
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CHAPTER 0: INTRODUCTION LEAN SIX
SIGMA
0.1 Introduction The first chapter of this course provides a high-level overview of Six Sigma as
a philosophy and a method for process improvement. In this chapter, the
DMAIC structure, the Six Sigma organization, the roles of Six Sigma and its
application in industry and service are explained. Finally, we discuss the
implementation of Six Sigma within an organization.
0.2 What is Six Sigma? Six Sigma is related to quality. To answer the title above this paragraph, we
first need to answer the following question:
What is quality?
The Oxford English Dictionary gives us the following definition:
Qua-li-ty 1 (degree, esp. high degree of) goodness or worth 2 sth. That is
special in, or that distinguishes, a person or thing
When applied to companies with products and services, quality refers to the
extent to which the characteristics of a product or service meet the
requirements of the customer. All activities that a company executes to
transform input to a product or service, affect the quality of the result.
Together, we call these activities the process.
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There are two concepts that play a crucial role in processes:
Effectiveness: do our activities match the requirements of the customer
(doing the right things)
Efficiency: do we carry out our activities with a minimum of resources
(doing things right)
Six Sigma focuses both on effectiveness and efficiency.
In this course, we see Six Sigma as a method that can be used to bring the
quality of processes to a higher level. The aim of Six Sigma is to increase the
effectiveness and efficiency of processes.
The Six Sigma method consists of a number of steps, and each step has a
number of proven tools to move from a process problem to a solution that
is based on data. In the next chapters, the steps and tools are discussed in
detail.
Figure 0.0
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0.3 Origin of Six Sigma Six Sigma is a management strategy that was originally developed in 1986 by
Motorola in the USA and that has been applied in many business sectors. Six
Sigma tries to improve the quality of the results of business processes by
identifying and eliminating the causes of defects and errors and in doing so
reducing variation in the processes. It consists of a collection of quality
management methods and tools, including statistical tools and develops a
special infrastructure of people with the organization (“Black Belts”, “Green
Belts”, etc.) who are experts in using these methods. Every Six Sigma project
within an organization follows a predefined protocol and has quantifiable
financial objectives (cost reduction and/or profit increase).
The term “Six Sigma” has its origin in the terminology that was used in the
production industry, specific terms that are associated with the statistical
models or production processes. The maturity of a production process can
be described with a “sigma” process capability rating, which indicates the
performance, for instance as a percentage of flawless products being made.
A six sigma process is a process in which 99.99966% of all products is
flawless (3.4 defects per million). The aim of Motorola was to achieve “Six
Sigma” for all its production processes, and it became the nickname for all
the business and technical activities designed to realize that objective.
0.4 Variation Six Sigma focuses on a predictable result of a process, which matches
customer requirements. Unfortunately, the result of a process is not always
the same. The deviations in the results are known as variation. Variation
occurs in all processes. Some examples:
• The time it takes you to get from home to work and back; on some
days, it takes longer than on others
• The weight of the number of French fries per bag
• The time you need to wait at the supermarket check-out
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• The colour of different batches of the same paint
Variation occurs in the result of a process as well as within each step of the
process. Variation is no problem as long as the process has the desired
results, so when the variation is small compared to the specifications and
when it is stable over time.
Variation is a determining factor for the effectiveness and efficiency of a
process and as such for the quality of the process as well. Variation is
inevitable, but it becomes a problem in the following cases.
• The variation of the output of a process can lead to a situation where it
no longer matches the customer's requirements, which means that the
output (e.g. product or service) falls outside the customer's
specifications. This has a negative impact on the effectiveness and leads
to defects.
• When a process is divided into smaller steps, and the output of one step
serves as the input of another step, with its own specifications, some of
that input will not meet the specifications, which in Six Sigma is referred
to as defects. The result is that the input will have to be reworked
before the process can continue, or, in the worst case, an item is
scrapped. This causes delay and extra costs and has a negative impact
on the efficiency of the process.
The aim of Six Sigma is to reduce variation in processes, with the aim of
matching the customer's requirements regarding the product or service.
Within Six Sigma, customer specifications are a key concept. The
specifications are the measurable requirements of a product or service
(based on the customer's needs).
The importance of variation is illustrated by the following quote from quality
guru William Edwards Deming:
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“If I had to reduce my message to management to just a few words, I’d say it
all has to do with reducing variation”
Jack Welch, former CEO of General Electric, is the man who put Six Sigma on
the global map. He explained the importance of variation as follows:
“We have tended to use all our energy and Six Sigma science to “move the
mean”…The problem is, as has been said, ”the mean never happens” and
the customer is still seeing variances in when the deliveries actually occur-a
heroic 4-day delivery time on one order, with an awful 20-day delay on
another, and no real consistency…Variation is Evil.
0.5 Standard deviation, a measurement for
variation
In statistics, variation is expressed as a value called the standard deviation
(σ, sigma). As mentioned before, variation occurs in any process. By
measuring the critical characteristics (like size, weight, melting point, lead
time) of a product or service, we can determine whether or not it matches
the specifications. The outcome of these measurements will not always be
the same, it will vary.
The sum of the values divided by the number of measurements gives us the
mean. The specifications of the outcome of a characteristic have a Lower
Specifications Limit (LSL) and an Upper Specifications Limit (USL). In the
Gauss curve presented below, it is indicated how many of the
measurements fall within the specifications. In the chapter on statistics, we
will take a closer look at the Gauss curve (normal distribution).
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The standard deviation is the measure of variation. If there is little variation,
the values are closer to the mean (showing a narrow, high peak). When
there is a large variation, the curve will be lower and wider. This will be
discussed in greater detail in the chapter on statistics.
0.6 Defects and Sigma level When a measurement of a product or service characteristic falls outside of
the specifications, we call it a defect. The product is not approved and will
have to be reworked or, in the worst case, thrown away. The number of
defects in a process or at the end of a process is an indication of the
capability of the process. The smaller the variation (thus standard
deviation), the more space there is from the process mean to the
specification limits, and the smaller the likelihood of defects occurring.
The number of times that a standard deviation (σ) fits in the space between
the mean and the most nearby specification limit is an indication of the
process capability. We call this the sigma level, which is also known as Z.
When a process is at level Z=3, the process has a sigma level of 3.
Figure 0.1
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When a standard deviation fits 6 times between the mean and the closest
specification level, we call it a 6σ process or Z=6. By expressing the process
capability of a process in this way, we can compare different processes (and
even companies and industries). In many industries, like automotive, they
express this capability not with Z or sigma level, but with its predecessor,
Cpk. The value of Cpk is 1/3 of the sigma level, or in other words Z-level is
Cpk x 3. More about this Cpk measure for capability later, in chapter $4.2.2.
Concluding we can say that there are 2 measures which often lead to
misunderstandings:
• The standard deviation of a process, or Sigma. The numeric value
that describes the magnitude of the variation in the process.
• The Capability of a process, or Sigma Level, which is the number of
standard deviations that fit between the mean and the (nearest)
spec limit. This value is also called Z. Please note: for a Six Sigma
process, we need 12 standard deviations between the Lower Spec
Limit and the Upper Spec Limit, as you can see from Figure 0.1.
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The following terms are used as process capability metrics:
DPU: Defects per Unit, (average) number of defects per product
DPO: defects per opportunity (= Defect rate): number of actual defects
divided by the number of possible defects
DPMO: defects per million opportunities (in the case of 6σ, the number of
defects per million opportunities is 3.4 (carrying 1.5σ shift, which we will
explain later)).
Opportunities: number of possible defects per product (for instance, if a
form has 10 fields, it is possible to make 10 mistakes)
PPM: parts per million (number of units per million deviating from
specification, used with smaller quantities, e.g. when % errors as unit of
measure doesn’t work).
Figure 0.2
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0.7 Variation and defects in the process Why is the aim to reduce the percentage of defects and to maximize the
sigma level so important?
The answer lies in the consequences of the number of defects. A process
that matches the specifications in 99% of all cases may sound good, but the
potential consequences are:
• 200,000 wrong prescriptions per year
• 15 minutes of unsafe drinking water per day
• 7 hours without electricity per month
• your watch is off by 15 minutes each day
Defects not only have consequences for the output, but also create
additional internal actions and costs for companies. All the costs that are
made to identify or correct defects are called Cost of Poor Quality (COPQ).
These are also known as the hidden factory:
Figure 0.3
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Rolled Throughput Yield (RTY)
An important measurement within Six Sigma is the Rolled Throughput Yield,
which indicates to what extent consecutive steps in a process are completed
without defects. This is illustrated in Figure 0.4:
Only 95% * 95% * 95% = 85.7% ends up in the water reservoir. The rest is
spilled and mopped up in the hidden factory.
To illustrate the costs associated with poor quality:
A company sells product X at £1.000 apiece. Every quarter, a thousand
pieces are sold. Variable costs are £ 600 a piece, fixed costs are £ 350.000 in
total. The defect rate is 10% (in other words, 10% of all products are
substandard and are thrown out).
Figure 0.4
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If the cost of poor quality, in this case in the form of the defect rate, is not
included in the financial report, the company's profit and loss account looks
like this:
Turnover £1.000.000
Variable costs £600.000
Variable margin £400.000
Fixed costs £350.000,-
Profit £50.000,-
The costs of the hidden factory can be made visible as follows, which also
sheds light on potential cost savings.
With a 10% defect rate, in reality 1000/(1-10%) = 1111 products were
produced (111 were thrown out because of defects). This means that the
variable costs per product really are:
£ 600,000/1111 = £ 540 (instead of £ 600 per unit). The costs of poor quality
(COPQ) are: 111 * £ 540 = £ 59,946.
This results in the following profit and loss account (with the situation in
case of zero defects on the right):
Turnover £1.000.000,- Turnover £1.000.000,-
Variable costs £ 540.054,- Variable costs £ 540.054,-
Variable margin £ 459.946,- Variable
margin
£ 459.946,-
Fixed costs £ 350.000,- Fixed costs £ 350.000,-
£ 109.946,- £ 109.946,-
COPQ £ 59.946,- COPQ £ 0,-
Profit £ 50.000,- Profit £ 109.946,-
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In summary: the effect of poor quality has far-reaching consequences for
the company's profits. This means that a Six Sigma project that is used to
reduce the number of defects is a smart investment.
To indicate that this is easier said than done, see figure 0.5, which
represents the iceberg theory. We only see a part of the hidden costs. To
identify and eliminate all the hidden costs requires a methodical approach.
Figure 0.5
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0.8 Six Sigma as an organization In this paragraph, we discuss the Six Sigma program organization and the
roles within that organization. Figure 0.6 provides an overview:
Champion
The Champion is a trained manager, often a member of the management
team, who leads the roll-out of the Six Sigma initiative and ensures that
people can be trained in Six Sigma. Therefore, the Champion is often the
Deployment Leader. However, this can be a separate function, for instance
within the HR department. In addition, the Champion has the following
responsibilities:
• Providing the necessary resources for the roll-out phase
• Assure Project reviews are conducted
• Making sure that the recommendations of a project are
implemented,
• Making sure that the project savings are realized,
• Acceptance of the project results
• Assure that the sponsors (or process owners) have the realized
improvements institutionalized by the Green / Black Belt
Figure 0.6
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Master Black Belt (MBB)
At GE, there is typically one Master Black Belt per 50 Black Belts. An MBB is a
Six Sigma specialist and responsible for the Six Sigma strategy, the training
and supervision of Belts and the roll-out of the results of the Six Sigma
structure, including the following elements:
• Advanced statistical Six Sigma techniques,
• Coaching and supervising Black Belts,
• Supporting the roll-out of Six Sigma,
• Ensuring the quality of the training program,
• Providing assistance in solving Six Sigma problems,
• Leading complex projects,
• Providing support to project selection and definition,
• Providing the necessary expertise and knowledge as required for
the Black Belt projects.
Project sponsor
The Six Sigma sponsor is a process owner who is responsible for the Six
Sigma project results (of his process). In addition, he is responsible for
funding the process and, as such, for the benefits of the project results.
His/her tasks are:
• Support in solving bottlenecks,
• Providing support to project selection and definition,
• Providing suitable team members,
• Owner of the problem and, later, of the solution,
• Process owner,
• Owner of the financial results,
• Responsible for providing the means.
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Black Belt (BB)
A Black Belt is a trained Six Sigma expert who leads improvement-teams,
carries out projects and guides Green Belts. At GE there was typically 1 BB
per 100 employees. His/her tasks are:
• Accepting and validating the project mandate,
• Leading and completing improvement projects,
• Applying the Six Sigma method,
• Providing the statistical analyses,
• Assisting the Champion in identifying projects and preparing
project mandates,
• Transferring the project results to the process owner,
• Coaching and supervising Green Belts,
• Reporting to management regarding the progress and project
results.
Green Belt (GB)
A Green Belt is trained in Six Sigma and, in addition to his regular job, takes
part in Six Sigma project teams or carries out projects with a limited scope.
At GE there are typically 3-5 times as many GB’s as there are BB’s. The tasks
of a Green Belt include:
• Assisting the Champion in screening potential Six Sigma projects,
• Defining and leading small improvement projects,
• Assisting Black Belts in larger Six Sigma projects.
Yellow Belt (YB)
A Yellow Belt has had a basic training in Six Sigma. He/she understands the
concept of Six Sigma and speaks the Six Sigma language and often takes part
in improvement teams.
Other team members
Generally speaking, other team members are employees with specialist
knowledge of the process that needs to be improved. They contribute their
expertise to help solve the problem in the process.
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0.9 The Six Sigma improvement structure
DMAIC
The Six Sigma improvement structure consists of 5 main steps and 12 sub-
steps. The main steps are known as D-M-A-I-C:
Define Describe the problem and the value to the organization of
solving the problem. Organize the improvement team.
Measure Define the defect and collect baseline information about
the performance of the product or process. Set
improvement targets. Set up a suitable measuring system.
Analyze Determine which process parameters (inputs or x’s) have
the greatest effect on the critical process results (outputs
or Y’s)
Improve Identify potential improvements and present your
argument that the process objectives will be realized with
these improvements.
Control Implement the solutions that were selected and make
sure these are secured in the process and in the
organization. Share the solutions with other stakeholders
who (may) have a similar problem in their process.
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To go through the main steps in the process and realize the objectives with
every step, the Lean Six Sigma approach provides a toolbox filled with
methods and tools. See figure 0.7 for a schematic overview.
In the following chapters, the tools that can be used in the various steps are
discussed.
Figure 0.7
32
The twelve steps
The DMAIC main steps have been further refined in a 12-step program. To
realize improvements, the approach will increasingly focus on details. The
customer is at the heart of the approach:
What does the customer find important about our product or service? What
does the customer demand?
The Voice of the Customer (VOC), which is the starting point, will have to be
translated into requirements and process specifications. What are the
critical measurable quality aspects where the process needs to match
customer specifications (Critical to Quality; CTQ)? What are the process
outputs that determine whether or not we match these specifications and
how do we measure those outputs (Y)? What inputs (input X's) and process
variables (process X's) have the main impact on the value of Y? All these
questions are discussed systematically in the twelve-step plan. In a
schematic form, the Lean Six Sigma project looks as follows:
Figure 0.8
33
The 12-step plan consists of the following steps:
The 12 steps provide a guide for a Six Sigma project and, in the next
chapters, they will be explained one by one.
1 Determine project and scope
2 Definition of the defect
3 Determine project output (Y) and analyze the measurement system
4 Determine baseline performance
5 Set the improvement objective based on the baseline performance
6 Identify potential causes of variation
7 Determine root causes
8 Determine optimum solution
9 Test the solution
10 Secure and measure improvement
11 Implement and demonstrate improvement
12 Set up project documentation and organize hand-over
Figure 0.9
34
0.10 Six Sigma in services and industry sectors Six Sigma originates in industry, but it has also found its way into the service
sector. The main differences between industrial processes and service
processes are the following:
• Waste is less tangible in service processes,
• Historically, the service sector relies less on science and technology,
• The service sector is less process-oriented,
• There are fewer people with a process management background,
• The service sector focuses predominantly on financial process
indicators,
• There is less process data available in the service industry,
• In the industrial sector, terms like parts and semi-products are
used, while, in the service sector, people usually speak of
transactions (which can also be measured in the same way).
This does not mean that also in the service sector customers do expect a
reliable and consistent service.
0.11 Implementing Lean Six Sigma
A Lean Six Sigma organization is an organization which:
• Has insight into its processes and knows how it adds customer
value
• Has made the performance (and variation) of these processes
measurable
• Uses the performance and variation as a starting point for
continuous improvement through Lean Six Sigma
• Has created an awareness with regard to waste and customer value
at all levels
35
It is impossible for any organization to realize this ambition from one day to
another, which is why it is important to allow it to grow by demonstrating
the value of this method through the results. Start small and create
momentum. Train the organization in the Lean Six Sigma method in
accordance with the roles defined in paragraph 0.8. Make sure to start by
training Management (champions and sponsors) and then the Belts. Start
with pilot projects that are feasible and do not try to solve all problems at
once but start with clearly defined projects that allow you to realize a quick
result with a minor investment. Go for the low-hanging fruit and the fruit on
the ground first (which often can be done by executing Lean projects).
Choosing the right first project is critically important to the success of an
implementation.
Figure 0.10
36
The table below provides guidelines for a suitable Six Sigma project:
Suitable project Unsuitable project
• Focus on defects and
variation
• Aimed at reducing costs of
increasing efficiency
• Suitable for the application of
the DMAIC steps and the
tools
• Focus on low-hanging fruit
• Historical and actual data
available
• Has a high level of
complexity
• Has a broad scope
• Solution is already known
• Data is hard to obtain
• Requires high level of
investment
• Is not related to strategic
goals
Start the company-wide roll-out in the organization after the initial results
and select projects that are related to the strategic goals of the organization.
Aim for breakthrough projects. Lean Six Sigma does not solve every
problem. The following table provides as to when Lean Six Sigma should or
should not be used:
Use Do not use
• To reach a challenging goal or
solve a tricky problem
o Related to the business
strategy
o That has always existed
o The solution to which is not
known
• To involve the organization in
identifying and solving problems
• To realize a robust solution
• To generate creativity and team
spirit
• To create ownership with regard
to problems and solutions
• When there are no specific
problems that need to be
solved
• When the solution to the
problem already exists or is
really obvious
• When there is no
inconsistent process that
needs to be improved
37
Not all implementations of Lean Six Sigma have been successful. Over time,
the success factors and pitfalls have been mapped:
Success factors Pitfalls
• Support by top
management,
• Approach is top-down in
combination with bottom-
up,
• Money and resources are
available,
• Result-oriented (in terms of
costs and customer
satisfaction)
• Program related to strategy,
• Selection of the right
projects,
• Making the right people
available,
• Proper use of DMAIC and
tools.
• No recognition of Six Sigma,
• Six Sigma is an additional
goal,
• Not the right people have
been trained,
• Not enough time to
implement DMAIC correctly,
• Successful Belts are
perceived as a threat,
• Insufficient resources are
made available for Six Sigma
projects.
38
0.12 Exercises
Rolled Throughput Yield (RTY)
Suppose I have a 5-step process with an RTY of 59%. What is my average
fall-out rate per step?
Defects
Suppose one of the fields in the form to
the right is filled in incorrectly.
What is the DPO?
DMAIC
a. What are the Phases of the Six Sigma improvement structure?
b. What are the steps into which these 5 phases are subdivided?
Quality
a. With Six Sigma, the quality of the process is improved. What are the
two basic concepts of this quality?
b. What do these concepts mean?
Answer:
Form:
Name …………… age …….
Last name …………………….
Figure 0.11
39
Six Sigma origin
a. What is Sigma?
b. Why is it called “Six Sigma”?
Answer:
Six Sigma Roles
a. Which roles are there within a Six Sigma organization?
b. What are the ratios between these roles in terms of the number of
employees?
40
41
PART 1 DEFINE We discuss here the first step of the DMAIC approach. As discussed in the
previous chapter, the purpose of the Define phase is to:
Describe the problem that needs to be solved and the value of solving that
problem to the business. Organize the improvement team.
This concerns the following two steps from the 12-step program:
1 Project selection and scope
2 Definition of the defect
After finishing this section, you will be able to:
• Explain the role and importance of the Definition phase,
• Determine a project CTQ,
• Compose a Six Sigma project team,
• Set up a Six Sigma project charter.
After completing the Definition phase, the following items have to be
delivered:
• Voice of the Customer,
• Project CTQ and project Y,
• Project Charter & Kick-off,
• Process Map.
42
43
CHAPTER 1: PROJECT SELECTION AND
SCOPE
1.1 Introduction In this chapter, it is determined which problem to work on. This problem is
deducted from the customer requirements and translated into the output of
the process (Y). You are given techniques to transform a qualitative
requirement into a measurable process outcome. In addition, you learn to
translate the problem into a plan of approach, the project charter, which
serves as a guideline during the execution of the project.
1.2 Selecting a project Choosing the right Lean Six Sigma project is critical to its success. In this
paragraph, the selection of a Lean Six Sigma project is described in 5 steps:
1. Identify the value defining elements of the organization
2. Identify chances and opportunities
3. Examine the list of options
4. Scope and define projects
5. Prioritise the list of projects
44
This selection process leads to the choice of a (Lean) Six Sigma project. A
suitable project meets the following criteria:
• It has a challenging goal to be realized or a challenging problem to be
solved that has been around for a while of which the solution is not
known.
• There is capacity made available to solve the problem.
• The knowledge, skills and motivation of the people involved are
available to solve the problem.
• The solution has to be robust and support has to be created among the
people who will be working with the solution
.
Figure 1.0
45
A project is not suitable if:
• Problem is unclear,
• The solution and the path toward that solution are already known,
• The problem has no relation to a process improvement.
Figure 1.1. contains a schematic representation of the process of finding
suitable projects:
The process goes from diverging (from few to many) in translating ideas to
possible projects, to converging (from many to few) in selecting the critical
projects from the list of potential projects. In the next paragraphs, the 5
steps of this process are described in greater detail.
In the first step, we identify the elements that are of value to the
organization.
We look for the answer to the question: what is important to the
organization? The term that is used within Six Sigma is the “Voice of ...”
Figure 1.1
46
The figure below shows the various kinds of input used to determine what is
important:
The Voice of Business (VoB) represents the strategy of the organization. This
strategic focus can be focussed outward (customer, market) as well as
inward (financial: turnover, costs). The Voice of the Customer (VoC)
represents the customer/market approach.
Figure 1.2
47
Voice of the Business
Six Sigma projects can affect the profit and loss account and the balance
sheet. The different elements of the balance sheet can be the starting point
of the improvement. The Economic Value Added (EVA) is the basis for the
different elements. The EVA is described in greater detail in a later section of
this book. Figure 1.4 contains a schematic representation of this subdivision.
Figure 1.3
48
The following perspectives can be a driver for improvement:
• Revenue
• Operational costs
• Overhead
• Assets
• Working capital
Figure 1.4
49
Table 1.0 contains the opportunities for improvement that can be a reason
to start an improvement project:
Improvement
opportunities
related to revenue
• Service/product mix
• Customer mix
• Quality
• Warranty
• Sales effectiveness
• Brand name
• Distribution channel
• Product
rationalization
• Innovation
Improvement
opportunities
related to
operational costs
• Yield
• Purchasing costs
• Material costs
• Costs of raw
materials
• Standardization
• Overtime
• Automation
• Set-up times
• Productivity
• Design efficiency
• Span of control
• Outsourcing
• Process improvement
Improvement
opportunities
related to
overhead
• Time to market
• Project prioritisation
• Project skills
• Specifications
• Transactions
• Outsourcing
administration
• Shared services
• Productivity
Improvement
opportunities
related to assets
• Mean Time Between
Failure (MTBF)
• Mean Time To Repair
• Production capacity
• Outsourcing Lease
Contracts
Improvement
opportunities
related to working
capital
• Work in progress
• Inventory finished
product
• Inventory raw
materials
• Rework
• Production planning
• Forecasting
• Standardization
Consignment
• Outdated inventory
• Payment terms
• Transactions
• Technology
Table 1.0
50
Voice of the Customer
The Voice of the Customer provides insight into who our customers are and
what they want from us. Within a company, there are numerous sources of
information about what our customers think of our products and services.
Some examples:
• Customer satisfaction surveys,
• Warranty information,
• Information from the
customer service department,
• Market research,
• Benchmark research,
• Questions from Customers
• Customer complaints,
• Success rate of quotations,
• Requests for quotations,
• Market share development,
• Returned products,
• Requests for technical support.
All this information provides a picture of how we are doing and can be a
reason for improvement. As a part of the definition phase of the Six Sigma
project, the Voice of the Customer is discussed extensively.
Voice of the Process
When identifying the voice of the process, it is important to approach the
process across vertical or departmental boundaries. The list presented
below shows the differences between processes and departments:
Process
- Producing
- Processing customer orders
- Shipping the product
- Billing customers
- Selling the product
- Developing new products
- Hiring employees
Department
- Production
- Customer Service, Production
planning
- Production planning, warehouse,
distribution
- Administration
- Sales, Marketing, Production
- Engineering, R&D, HRM
51
We focus on processes, not on departments. When mapping the processes
with the people involved, the bottlenecks quickly become clear. These
bottlenecks can be used as input for a Lean Six Sigma project.
Often, steps 1 and 2 (see 1.2 selecting a project) in the selection of a project
take place consecutively in a session with the people involved. In the Voice
of the Business phase, a number of potential improvements have already
been identified. In the third step, the wheat is separated from the chaff as
far as opportunities for improvement are concerned. A useful tool for this
screening is the Benefit & Effort matrix in figure 1.5.
The potential benefits are set off against the estimated investments (effort),
taking the strategic objectives and potential risks into account.
Improvement opportunities with a high potential added value with relatively
little effort go on to the next step.
Figure 1.5
52
In step 4, the remaining opportunities for improvement are investigated and
further defined in an initial project definition. In a “Sixpack”, the project is
defined. In table 1.1., the elements of the “Sixpack” are described:
Impact on the Business
• Why should we do this, how
does it benefit us?
• What is the estimated financial
yield?
• How does the project fit within
the business strategy?
• What else do we need to think
of (projects creating enabling
conditions for risks, regulation
and legislation)?
Problem description
• What is going wrong, where is the
pain that we or our customers feel?
What is not working well?
• When did the problem begin?
• Where does the problem occur?
• What is the size of the problem?
• Why do we think that we can create
value as described in the business
impact?
Objective
• What is the objective of the
improvement? With what
percentage can we improve?
• What are we going to do and
what will the result be?
• How are we going to measure
the success of the project?
Project scope
• What are the boundaries of the
initiative or project (where does it
begin and when is it finished)?
• What authority does the team have
and who decides that?
• What is not included in the scope?
Project Plan
• How long will the entire project
last?
• When do we start and when is it
finished?
• What are the most important
milestones?
• What issues can we encounter?
Team selection
• Who will the team members be?
• What is their role?
• How much time will they spend on
the project?
Table 1.1
53
These project definitions create a more concrete insight into the
improvement potential of these projects. In the final step, the projects are
prioritized on the basis of the “Sixpack”.
In this prioritization, management, often together with the Black Belt(s), will
decide which project(s) will be started first, and which project will be led by
which Black Belt. In addition to financial and customer-related objectives,
strategic and policy objectives will also play a role in the prioritization. After
the projects and project leaders have been selected, the Black Belts proceed
with the definition phase of their project.
1.3 Determining the scope The quality of a service or product is determined by the value the customer
gives to it. This can be both an internal and an external customer. To
determine the scope of the improvement project and define the problem,
we start with the customer. Within Lean Six Sigma, this is referred to as the
Voice of the Customer (VOC).
1.3.1 Voice of the Customer Identifying the wishes and needs of the customer with regard to the service
or product is the first step in the Six Sigma approach to solving a process
problem. This problem is always related to the customer. This can be an
internal customer, or a different stakeholder within or outside the company
(for example legal or regulatory requirements). The Voice of the Customer
(VOC) describes the needs of the customer and his perception with regard
to the product or service. The VOC helps to provide direction for the
improvement project. After all, the customer decides what quality is.
The VOC is expressed in qualitative terms, often with regard to the following
factors:
54
Factor Explanation
Time and timeliness - Waiting times, timely deliveries
Completeness - Completeness of deliveries
Courtesy - Personal attention
Consistency - Knowing what you can expect
Accessibility - Easily obtainable
Accuracy - Works flawlessly
Response - Effective response in case of unexpected
situations
The Voice of the Customer also helps to determine the scope of the project.
What problem, from a customer point of view, are we going to tackle? In the
next chapter (chapter 2), this problem will be translated into quality
requirements for our process. Within Lean Six Sigma, these requirements
are called Critical to Quality. To determine the VOC and CTQ, the following
steps are carried out:
Figure 1.6
55
1 Identify the customers and determine what information you need (VOC)
2 Collect reactive data (from systems) and complete it with proactive data
(VOC)
3 Analyze the data and make a list of the critical requirements of the
customer (VOC)
4 Translate these customer requirements into CTQ’s
5 Set up the specifications for these CTQ's
In this chapter, we discuss steps 1 through 3, in the next chapter steps 4 and
5 are described.
1. Identify the customers and determine what information you need
There will be various customers buying your product or service. Often,
customers can be divided into market segments. Market segments differ
from each other because they have different requirements and wishes with
regard to the product or service. Prioritize customers and segments and
identify the most important ones to determine the Voice of the Customer.
2. Collect reactive system data and complete it with proactive data
We now know the customer group or market segment about which we need
to collect information. In the next step, customer data is collected that
provides insight into what the customer considers important. A distinction is
made between reactive and proactive data. Reactive data is data that came
through the customer's initiative, for example complaints, claims or service
calls. Proactive data is data that we collect ourselves from the customer, for
example in the form of interviews and market research. Collecting proactive
data is costly and time-consuming, which is why we prefer to start with
reactive data. If that does not yield enough information on the Voice of the
Customer, gathering further proactive data can be considered. Make sure
that it is collected on a structured and rational basis and that it contributes
to the project. When collecting customer data, use the following guidelines:
56
• Start with reactive data: easy to acquire and provides a basic
understanding of the customer's needs
• Analyze the data from reactive systems: try to discover patterns and
trends (for example in the customer complaints)
• Look at the customer's behaviour: many customer's do not give
feedback but just change the way they behave towards your company.
E.g. think about customer retention rates.
Examples of the Voice of the Customer:
• “We need reliable deliveries on the confirmed dates”
• “I want shorter lead times for special products”
• “I don't like it that delivery times are changing”
• “We need a quicker response to our questions”
• “Customer service was unable to answer my question”
• “Communication is critical, even when there are no problems”
• “You need to carry out certain procedures more quickly”
• “It would be good to acquire standard services more quickly”
• “It should be easier to place an order”
3. Analyze the data and make a list with critical customer requirements
The result of steps 1 and 2 (see Figure 1.6) is a broad selection of customer
data. In this third step, the data is translated into more detailed information
about the customer needs. This information serves as input for the next step
in the process: determining the Critical to Quality (CTQ), in other words the
requirements to the output of the process. To get the most important
information from the customer data, it is crucial to categorize the data into
themes or topics. Tools that can used are the “Affinity diagram” and the
“Kano Model”. On the next pages, we explain how these can be applied.
57
1.3.2 Affinity diagram
The affinity diagram is used when gathering large quantities of spoken or
written material (ideas, opinions, problems) and organizing them into
groups based on their natural interrelationships.
To construct an affinity diagram (using post-its on a board or brown paper):
• Collect remarks from the customers that you want to analyze
o One post-it per remark
o Place post-its on the wall
• Categorize the remarks that address general problems or themes
o Move the post-its to thematic groups
• Give each theme a name
o Name each theme as a problem or customer requirement
• Group the post-its by category.
Figure 1.7
58
1.3.3 Kano Analysis When determining what the customer considers important, there's a risk
that requirements that are self-evident to the customer are not mentioned,
because the customer implicitly assumes that they are present or fulfilled.
This is a real risk, because the customer will be very dissatisfied if that turns
out not to be the case (for example a car with no brakes).
The Kano analysis, invented by the Japanese Kano, maps the spoken and
unspoken requirements, which makes it a useful tool to get a better
understanding of the Voice of the Customer.
In the Kano diagram, these different wishes are divided into basic needs,
performance needs and excitement needs.
By using these categories, the Kano diagram helps us to work on the right
CTQ's.
Although it is possible to increase customer satisfaction by working on the
excitement needs, if you neglect the basic needs, you will lose customers
more quickly than you will gain them through the excitement needs.
59
. Figure 1.9
Figure 1.8
60
1.4 Exercises
Project selection
Which 5 steps does a good project selection consist of?
Voice of the…
a. There are different “Voices” that say something about a project. Name
three.
b. Which Voice is the most important?
VoC
To which three main categories can the Voice of the Customer be reduced?
Kano Model
The Kano model has a number of categories that say something about the
VOC with regard to the product or service. Categorize the products listed
below along the axes of the Kano model (see figure 1.8).
a. When the product is delivered more quickly, I am satisfied!
b. Thanks to new functionality, you can now use your telephone to turn on the air-
conditioning or heating in your car remotely.
c. There is toilet paper on the toilet.
d. After receiving the confirmation, you will be called for some questions.
e. Snacks are provided at breaks during the training course
f. The racks of the new dishwasher are painted grey
g. By training smaller groups, there is more time for individual attention
h. When we ordered a beer at the restaurant, they added a complementary snack
i. The paint meets all the European requirements
j. As of January 1, you no longer need a permit to cut down trees on your own
premises
Enthusiastic: Desirable:
Indifferent: Must:
61
62
63
CHAPTER 2: DEFINITION OF THE DEFECT
2.1 Introduction In this chapter, we zoom in further on the scope of the project and translate
the customer problem or wish into concrete requirements on the quality of
the process. In addition, a choice will be made as to which of these
requirements the improvement project will be worked out. In Lean Six
Sigma terms, the Voice of the Customer is translated into Critical to Quality.
2.2 Critical to Quality Critical to Quality (CTQ) is the term that is used for the most important
measurable characteristic of a product or process. The CTQ refers to the
performance standard that has to be met to satisfy the customer. It is the
link between the customer requirement and the critical problem that is the
subject of the improvement project. Usually, there are 1 or 2 CTQ's in a
project. Determining the CTQ's is seen as the first step in the DMAIC
approach and provides focus within the project. The CTQ has to be
expressed in an objective measurable way, though not necessarily numeric.
Sometimes, the VOC is already specific and not very different from the CTQ,
in which case we will not force an artificial difference.
4. Translate the customer requirements into CTQ’s
The customer requirement that has been determined in step 3 is now
translated into a project requirement. The central question in this
translation is: what requirements the process has to meet in order to solve
the customer's problem or meet his requirement.
64
For example:
Voice of the Customer Critical to Quality
Slow response time Answer questions quickly
Timely delivery Deliveries before or on the delivery date
Customer contacts are
confusing
Question has to be addressed in a
simple way
Candidate CTQ’s
Sometimes, there are several CTQ's that can contribute to the Voice of the
Customer. In that case, there are two frequently used tools to arrive at the
best CTQ.
2.2.1 Tree-diagram Tree diagram, also known as CTQ-Flowdown. In the Measure phase, this will
be discussed in greater detail. The tree diagram is constructed by putting
the Voice of the Customer at the highest level, and below anything that
contributes to that at a CTQ level. Next, the customer/sponsor and the
project leader select the CTQ to work on, based on where the highest need
for improvement lies. Normally this is where the greatest necessity or
greatest need is to improve. Later, in the Measure phase, if necessary,
the chosen CTQ is translated into a clear and measurable Project-Y.
Incidentally, sometimes as a Belt you have already received a project at
the level of a CTQ or even a specific Y. In that case, try to find out what
the real customer needs are and why your project is more important
than other possible projects that meet the same customer needs.
65
2.2.2 Quality Function Deployment
Another possible tool is QFD, which stands for Quality Function Deployment,
often also referred to as the House of Quality. This is a tool that can be used
to rank the potential CTQ's based on how much they contribute to the main
VOC(s) defined earlier. You will receive a digital article on how QFD can help
you define the CTQ.
5. Determine specifications for the CTQ’s
In the final step, specifications are determined for the CTQ to make the
result measurable.
CTQ Specified CTQ
Answer questions quickly Answer questions in < 45 minutes
Delivery before or on the delivery
date
Delivery on the delivery date
before 17:00
Question has to be addressed in a
simple way
Question is answered after one
phone call
We have seen that the Voice of the Customer can often be translated into
various CTQ's. To keep the Lean Six Sigma project manageable, one CTQ (or
two at the most) is tackled per project. This is the reason why the CTQ's
need to be prioritized, so the project can focus on the CTQ's that have the
greatest impact on the needs of the customer or organization. It is
preferable to involve the customer or a customer panel in prioritizing the
CTQ's. The tools mentioned earlier (tree diagram and QFD) can help to
determine which CTQ's contribute most to the VOC we want to work on.
2.3 The project charter Determining the CTQ's that will be tackled within the project creates focus
on what will be improved. To carry out this improvement in a structured
way and to keep the project manageable, a compact project plan is drawn
up. Within Lean Six Sigma, this is called the Project Charter. The Project
Charter creates clarity about the project objective and about the approach.
It provides direction to the team, keeps the team on course towards the
66
project objective and provides a road map for the execution of the project.
In addition, the Project Charter is the agreement between the client and the
Black Belt or Green Belt leading the project. Usually, the client is referred to
as the “Sponsor” and he is the owner of the problem at the beginning of the
project and of the solution at the end. The Sponsor is also the person who
provides the people and resources.
The Project Charter describes the following elements:
• The objective and the plan of the project
• Description of the problem (the defect)
• The scope of the project
• Description of the process that needs to be improved
• The objective of the improvement
• Estimation of the financial benefits
• The key players of the project and their roles
The Project Charter is a living document that is adjusted several times in the
course of the project.
Appendix 5 contains an example of the subjects included in a project
charter. In the following paragraphs, we discuss how to set up a project
charter.
67
2.3.1 Project authorization In the project authorization part of the Project Charter, the start of the
project is formalized. Based on a summary project description and a
description of the benefits of the project in terms of quality, delivery time,
costs and customer satisfaction, authorization is requested from the client(s)
and the main stakeholders. Although this part is located at the start of the
Charter, it is usually completed when the charter is finalized.
Appendix 5 contains an example of a Project Charter with tips
The goal of the formal authorization is to create commitment at the client
and to make sure that the resources are made available. Who needs to sign
depends on the authority structure of the organization and the placement of
Lean Six Sigma within the organization. As a rule, the following people are
the ones who authorize the project:
• Champion
• Master Black Belt
• CFO/Controller
• Process Owner/Sponsor
2.3.2 Project definition The project definition gives direction to the project and marks its
boundaries. The project is defined on the basis of the following elements:
• Problem definition
The problem definition provides a description of the current
situation. The description indicates what is going wrong, where and
when the problem emerged, the scope of the problem and how the
problem manifests itself. The Voice of the Customer provides
indications for the problem definition.
• Objective
The objective provides a description of the desired future situation,
after completion of the project. The performance improvement is
68
quantified as part of the objective. In the first version of the Project
Charter, the objective will be an estimation that is expressed in
terms of the CTQ's. As the project progresses and there is greater
insight into the data and opportunities, the objective will be
adjusted, and the project Y will be used. For the analysis phase, the
objective needs to be quantified on the basis of the baseline
performance (see paragraph 4.3). Express the objective on a
performance level and avoid including causes and solutions into the
objective.
• Project CTQ & Y
In this part, the quality requirements of the process in the form of
the CTQ are presented to provide direction to the project. In the
next phase, the CTQ is made concrete in a clear and measurable
project output: the project Y (see Chapter 3 Measure).
• Project Limits
The project limits indicate the boundaries of the project. It is
important to indicate what is and is not included in the project.
Think, for instance, in terms of customers, segments, departments,
locations and which elements of the process are and which are not
included.
• Project restrictions
Project restrictions refer to the limitations in terms of the space
you have to tackle the process problem. In this part, you often get
together with your sponsor, indicate the framework within which
the solution has to fit. Often, there are restrictions with regard to
the solution. Think for instance of existing procedures or legislation,
available technologies, or contractual obligations. In addition to
restrictions with regard to the solution, there may also be
restrictions with regard to the implementation of the solution, for
instance in terms of resistance to change of the organization's
culture.
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2.3.3 Process history The process history contains a brief description of the origin and
development of the process, placing the process in a historical context.
Insight into changes in the past can help with changes in the future.
In addition to the history, the Project Charter also contains a brief outline of
the process. The technique that is used to do that is the SIPOC, which is
discussed in the next paragraph (2.4).
In addition to providing insight into the process, it is also important to
provide insight into the performance of the process. This insight will not be
acquired until the Measure phase, step 4 Baseline performance.
2.3.4 Project team A Lean Six Sigma project is carried out with a team of process stakeholders
and process experts. The knowledge and answers are provided by the
organization through the Lean Six Sigma structure. When organizing the
project team, it is important to aim for diversity in expertise and opinions.
When the process that needs to be improved involves several departments,
there has to be at least one team member from each department. Usually, a
team consists of 4-6 members. Make sure that it is not always the same
people making up an improvement team. The knowledge and expertise that
is needed in the various phases of the project may differ. Adjust the team in
the course of the project but ensure that the core team remains intact. For
the entire project, the core team will be working on the project, so it's
crucial from an organizational perspective to ensure that the core team and
the other (temporary) team members are given time and space to make
their contribution to the project.
To make a good start with the team, it is recommended to organize a kick-
off to create a shared vision of the project, what the objective is and how
that objective will be realized. Below, a possible agenda for a kick-off:
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1. Introduction 15 min.
2. Explanation Lean Six Sigma 15 min.
3. Determining team mandate 15 min.
4. Determining meeting rules 10 min.
5. Determining roles and responsibilities 20 min.
6. Determining feedback and communication plan 10 min.
7. Wrap-up: determining actions and Benefits & Concerns 15 min.
In the first step, you explain who you are and why the team members have
been invited. In the second step, you explain in general terms what Lean Six
Sigma is. In the third step, you discuss the problem you all are going to try to
solve, as well as what you can and cannot influence (the mandate that you
have defined together with your sponsor).
In addition, you discuss the meeting rules and what the roles and
responsibilities of the team members and of yourself will be in the project
team.
Because a good communication from the team to the organization is
crucially important to the acceptance of the future result, it is decided
during the kick-off meeting how to organize the communication via the
communication plan.
Finally, you discuss the actions that you all agreed on and you conclude with
the Benefits and Concerns of the meeting.
In addition to the team, clients and immediate stakeholders in the
organization also play an important role in the success of the project. To
make clear agreements, the roles and responsibilities have to be clear as
well. A technique that can help with this is the RACI matrix.
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RACI stands for:
• Responsible: the person who will make sure a task or step is carried out
• Accountable: the person responsible for the end result of the task or
step
• Consulted: the person being consulted with regard to the task or step
before a decision is made
• Informed: the people who are informed about a decision regarding the
task or step after the decision has been made.
In the matrix, the people involved in the trajectory are indicated along the Y-
axis, and along the X-axis, the tasks, steps and deliverables are indicated. At
the intersections, the role of each of the people involved (R, A, C or I) is
indicated for each of the steps. This way, everyone knows what is expected
and who is responsible for what.
2.3.5 Stakeholders and stakeholder assessment Stakeholders are people with a vested interest in the execution and/or
results of the project. They are not involved in the project as such, but they
are affected by it. Often, this means that they, in turn, can influence the
course of the project. To respond to this adequately and make sure these
forces stay manageable, a stakeholder assessment is carried out in advance.
Figure 2.0
72
The purpose of the stakeholder assessment is to get a clear idea of whether
or not certain stakeholders require extra attention to motivate them or keep
them on board. An example of a stakeholder assessment is made available
digitally and can be used as basis for your own project.
The stakeholders that can influence the process are included in the project
charter. The stakeholder assessment, in which it is indicated how the various
stakeholders feel about the project (negative or positive, including a score),
is described in a separate document and does not belong to the Project
Charter. The Project Charter is a communication document aimed at the
various people involved. The stakeholder assessment, which is a subjective
assessment of possible resistance among stakeholders, does not belong to
the charter, but it is important information for the Black Belt or Green Belt,
so they can work on getting the results accepted.
2.3.6 Project time line
The project time line indicates the planning of the project on the basis of the
most important milestones. The project phases DMAIC are the fixed
milestones in the planning. At the start of the project, an initial planning is
made. The main uncertainty with regard to the timing occurs in the Improve
phase, during which the solution is implemented, because neither the
Figure 2.1
73
solution nor its implementation time are known at the beginning. Because,
in those phases, there is a lot of uncertainty about what has to happen and
how long it will take, we do not make the time line unnecessarily complex or
detailed. For a DMAIC project of 4-6 months, you could take roughly one
month per phase.
When using the DMAIC structure, it is customary to organize a Toll-gate
Review at the end of each phase. A Toll-gate Review is a formal meeting
between the project team and the sponsor (client).
The object of this review is to check whether the project is still on schedule
and whether the intended goal of the project will still be realized. The
review concludes with a go/no-go decision with regard to the start of the
next phase. During the Toll-gate Review, the following issues are discussed:
• Presentation of the project so far, with the main deliverables, results
and bottlenecks
• The project charter: the various themes in the Project Charter are once
again verified and, where necessary, adjusted, for example the
planning, the expected benefits and the objective.
• Outstanding questions and points of discussion
• Toll-gate decision (Go/No go)
• Actions and follow-up steps
Make notes of the Toll-gate Review and keep them as part of the project
documentation and make sure all of the people involved know where to find
the Toll-gate Reviews that have already taken place. Especially the
Champion will need this, to allow him to monitor the progress of all Lean Six
Sigma projects.
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2.3.7 Benefits
The last part of the Project Charter that is described is that of the expected
benefits, which can be divided into hard benefits and soft benefits. The
quantifiable financial benefits are seen as hard benefits. Examples of
potential soft benefits are increased customer satisfaction, costs being
avoided or improve morale. Mention these soft benefits in the Project
Charter. For the remainder of this paragraph, we focus on the hard benefits.
The financial benefits will become clearer in the course of the project
because the improvements that will be realized become clearer as well.
There are three formal moments when the financial benefits are assessed
and recorded in the project charter:
1. In the Define phase in step 2, when defining the defect: in the Define
phase, the financial benefits are an estimation based on the objective.
2. In the Measure phase, after step 4 baseline performance: there is now
insight into the performance of the process and the deviation compared
to the desired situation. The objectives can now be set more precisely in
terms of project Y. Based on this adjustment, it is possible to estimate
the benefits more accurately.
3. In the Improve phase after step 8: determining the solution(s): on the
basis of the solutions, it is possible to estimate the costs of
implementing the solution. This information can be used to make a
Business Case. What benefits are left after deduction of the costs? This
Business Case can play an important role in the Go/No go decision
regarding the implementation.
Making a good Business Case is a skill of its own. It is recommended to
involve the Financial Controller when making a Business Case.
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Examples of quantifiable benefits that are the direct result of the project:
• Direct cost savings
• Increased revenue
• Extra interest revenue
• Increased cash flow
Examples of implementation costs:
• New or modified equipment
• New or modified software
• New procedures
• Capacity loss during implementation
2.3.7.1 Economic Value Added
To determine the added value of the improvement project in financial
terms, the Economic Value Added (EVA) is used.
EVA: Annual profits after taxes and after reduction of the project-related
costs. Figure 2.2 shows how the EVA is determined:
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Terminology:
EBITDA: Earnings Before Interest,
Taxes, Depreciation,
Amortization
Measure for the gross profit
before deducting Taxes,
Depreciation, Amortization
NEBIT: Net Earnings Before Interest &
Taxes
Operational profits before
the deduction of taxes and
interest
NOPAT: Net Operating Profit After Tax Net operational profits after
deducting taxes
WACC: Weighted Average Cost of
Capital
Number that expresses the
costs a company incurs for
the capital with which the
company is financed (often
7-10%)
Figure 2.2
77
EVA Economic Value Added Annual profits after taxes
and after deducting the
project-related costs
VC: Value Creation Number to calculate the
long-term profits of a
project compared to current
value
Lean Six Sigma projects can have an effect both on a company's profits and
on its capital side. The EVA expresses the profits and capital usage, and in
doing so provides financial support for the (short-term) added value of a
project. To determine long-term value, Value Creation is used, in which the
future annual EVA's are translated into net cash. See the example in figure
2.3.
Figure 2.3
78
How can the EVA be influenced?
There are two pillars that affect the EVA: increasing profits and reducing
capital usage. In table 2.0, this is translated into CTQ that can be tackled
with a project:
EVA pillars Improvement
objectives
CTQ
Increasing
profits
Increasing revenue • Increasing customer
loyalty and retention
• Increasing profits per
customer
• Increasing number of
new customers
• Increasing service
speed
• Improving service
quality
Reducing costs • Increasing productivity
• Increasing production
yield
• Reducing lead time
Capital usage Reducing fixed assets • Making better use of
technology
• Making better use of
facilities
• Making better use of
capacity
Reducing working
capital • Reduce time between
paying and being paid
Table 2.0
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It is recommended to involve the controlling department in calculating the
financial benefits of the improvement project. For many multinational
companies, this is actually mandatory. When working out the benefits,
include the following items in the Project Charter:
• The period over which the current performance and costs of poor
quality have been calculated as a baseline for determining the savings.
• The assumptions on which the calculations are based, for example if
there is enough demand for the additional products/services that can
be produced as a result of this project.
2.4 SIPOC: outline process description A process description provides insight into the development of a product or
service and into the relationship between different departments. A process
is defined as follow:
A series of activities that use one or more inputs and turns them into
outputs that are of value to the customer.
A schematic representation of the outline of a process (process map):
• Helps the team understand the process
• Ensures that the team members all have the same perspective
• Validates the project scope
• Provides a focus for the team
• Helps to identify the areas that fall within (but also outside) your
control
• Is a communication tool to explain the process to others, both internally
and externally
• Creates a bridge between the project charter and later work
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When describing a high-level process map, the following starting points are
used:
• Symbols or geometric shapes are used to represent different types
of activities, for instance, actions, checks, decisions.
• Connecting lines or arrows are used to link activities and, in doing
so, indicated the order and flow of the process.
• The process represents the current situation (as is) and not the
desired future situation (to be).
• Usually, the High-level Process Map describes the process in 4-7
steps.
The method that we use to create a process map is SIPOC, which stands for:
S Supplier Supplier: a person or organization providing the input
to your process
I Input Materials, resources and data that are needed to carry
out your process (consist of nouns)
P Process A collection of activities that require one or more types
of input and that create an output that is of value to
the customer (consist of verbs)
O Output The tangible products or sometimes intangible services
that are the result of a process – which ought to satisfy
the customer's needs (consists of nouns).
C Customer A person or organization that receives the output of
your process. Can be internal or external.
Figure 2.4 contains a schematic representation of a SIPOC process. The
different types of input are indicated as X's, the different types of output as
Y's. In the following chapters, they will take a central position in the search
for improvement.
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Creating a SIPOC map:
1. Identify the start and finish of the process
2. Define the process steps between the start and finish (4-7 steps)
3. Identify the outputs of the process, based on the following questions:
- what product/service does this process make?
- at what point does the process end?
- what information does this process provide?
4. Identify the customer of every output (who uses the products, services
and information resulting from the process?)
5. Determine the main process inputs (what is the reason for starting the
process?)
6. Identify the main suppliers, based on the following questions:
- who are the suppliers?
- what do they supply?
- where do they influence the process flow?
- what effect do they have on the process and the outcome?
7. Validate the process map against the current situation. Are people
really working in accordance with the process map (does the process
map not divert from the formal procedures by using what happens in
practice?)
Figure 2.5 contains an example of a completed SIPOC-type process map.
Make sure that there is at least one customer for each output and one
supplier for each input.
Figure 2.4
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2.5 Value Stream Mapping Value Stream Mapping is a Lean technique that is used to analyze and
design the flow of materials and information that is needed to get a product
or service to the customer. The technique originated at Toyota (?) and is
known as “material and information flow mapping”. Value Stream Mapping
can be applied to virtually any value chain.
For more information on how to apply Value Stream Mapping, we refer you
to our textbook on Lean, based on “Learning to See” by Rother and Shook.
Figure 2.5
83
Example value stream map:
Figure 2.6
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2.6 Exercises Revenues
After determining the optimum solution, the project team settles on a
potential extra revenue of £ 1 million. A fantastic prospect, but it involves
necessary costs, which amount to £ 400,000. The tax level on profits is 20%.
The project team prepares itself for the Toll-gate review to determine
whether or not the project can go ahead. The information presented above
is collected to calculate the EVA. What will the EVA be?
o EVA £ 420.000
o EVA £ 480.000
o EVA £ 510.000
o EVA £ 560.000
EBITDA and EVA of costs reduction project
Project example:
“Reducing scrap of machine XYZ will reduce material costs”
Scrap of machine XYZ is £ 450,000 a month
40% of this is reused
This project reduces the remaining scrap by half (50%)
Tax rate is 25%
a. Calculate the EBITDA after the project per month
b. What is the EVA for the first year?
EVA of increased revenue
Project example:
“Reducing the lead time will increase revenue through additional demand”:
Current lead time is 9 business days
According to Sales, we lose 5 orders per month because we have a long
lead time. Apparently, others deliver within 3 business days
The average order size is £ 10K
The average profit margin on our products is 18%
Reducing lead time will yield 5 additional orders per month
Tax rate 25%
Q: What is the EVA in the first year?
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EVA from reduced working capital
Project example:
“Improving the uptime of a machine leads to a smaller necessary inventory
for that machine and thus reduces the working capital”:
Machine XYZ is less reliable and as a result it has an uptime of 63%.
Similar machines have an uptime of 75%
Inventory related to machine XYZ has a value of £ 540K, 80% of which is
located ahead of the machine.
Improving the reliability leads to a reduction of the necessary inventory
for the machine by 50%.
WACC is 10%
a. What is the value of the reduced inventory?
b. What is the EVA in the first year?
EVA from avoiding an investment
Project example:
“Increasing the production speed of a printing press means we do not have
to buy the budgeted new machine”
Current process speed is 10 meters/second
Sales are predicted to increase by 25% next year
Increasing the speed by 25% means we do not have to buy the
budgeted fifth machine
Current total output = 4 machines * 10m/sec/machine = 40m/sec
25% of the machine speed = 10m/sec on all 4 machine = 1 machine
1 machine costs £ 500K
WACC is 10%
What is the EVA in the first year?
SIPOC
Supplier Input Process Output Customer
Put the process data presented below in the correct columns of the SIPOC.
“copy, set machine to copying, employee, original, press start, put original
on glass plate, employee, paper, remove original from glass plate and copy
from print drawer, copier”
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87
PART 2: MEASURE In this second part, the second phase of the DMAIC approach is discussed.
The goals of the Measure phase are:
Define the defect and collect baseline information about the performance of
the product or process. Set improvement objectives. Use a suitable
measuring system.
Within the Measure phase, the following steps from the 12-step plan play a
central role:
3. Determining and analyzing measuring system Y
4. Baseline performance
5. Objective based on baseline performance
After this part, you will be able to:
• Define the Project Y measurable
• Explain the different data
• Define the measuring system
• Set up a data collection plan
• Calculate a baseline performance
• Determine the improvement objective
After completing the Measure phase, the following items have been
delivered:
• Project Y
• Data collection plan
• Analysis measuring system
• Baseline performance
• Improvement objective
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89
CHAPTER 3: DETERMINING ‘Y’ AND
ANALYZING THE MEASURING SYSTEM
3.1 Introduction In the last chapter, we have decided which problem we are going to tackle,
and which process result needs to be improved (the CTQ). In this first
chapter of the Measure phase, we are going to make this process result
measurable in an unequivocal way and determine which measuring system
we will use to measure the outcome of the process result.
3.2 From CTQ to project Y Project Y is the CTQ expressed as a measurable output of the process. The
Project Y is always quantitative, measurable, unequivocal and directly linked
to the process. In the following paragraphs, we discuss a number of
instruments that can be used to determine a suitable project Y for the
process:
• Tree diagram (CTQ flowdown)
• Detailed process description
• Pareto analysis
• QFD
The decision which instrument to use depends on the practical situation. For
instance, when it is decided to work on reducing the number of complaints,
and there is already a good complaint registration in place, PARETO is the
logical choice. If it is unclear what we will work on and which choice may
lead to a competitive advantage, the QFD is a good choice. When the
process is above all about improving the organization of the process, and
the steps are not logical or contain a lot of waste, it makes more sense to
use the detailed process description.
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3.2.1 Tree-diagram The tree diagram allows you to split the CTQ up into smaller parts and
concrete elements. This way, a generic objective or idea is worked out to a
specific sub-objective. The steps:
1. Create the right team
2. Write the CTQ at the top of the tree
3. Use brainstorming to define the main groups/sub-objectives
4. Work every main group out into greater detail
5. Stop detailing a level when the level is sufficiently detailed to
define a potential Y. Often, three levels are enough
6. Decide whether the complemented tree diagram has a logical
structure and is complete
Figure 3.0
91
3.2.2 Detailed process diagram In the define phase, we discussed a SIPOC: a process diagram with the main
outlines. Similar to the tree diagram, you work from generic to specific. To
make a good process diagram, you need the expertise of the people
involved in the process. The process diagram is a team effort. In addition to
the expertise and experience of the people involved, there are other kinds
of input that can be used, like manuals, product specifications or existing
process diagrams. Also, a Value Stream Map can be used to get to a suitable
Y; after all, a Value Stream Map is a detailed process diagram to which extra
information has been added.
Brainstorm with the team to create a detailed process diagram. Make sure
that the actual process is described; not the process that you think exists or
the process that should exist.
The detailed process diagram provides insight into the creation of the
product or service, and as such into the requirements in the form of the
CTQ. After creating the detailed process diagram, you consult with your
sponsor (together with the team). Together, you select a measurable unit
that, when improved, will lead to an improved process. This adds further
“scope” to the process, and usually focuses on the measurable output (for
example lead time) of one or a few steps in the process, which means that
the remaining steps fall outside of the scope.
Figure 3.1
92
3.2.3 Pareto analysis The Pareto analysis is used to order the factors based on their importance
(extent to which they occur). This provides insight into the factors that have
the greatest impact. In the analysis of causes and the separation between
possible causes and root causes in the Analysis phase, the Pareto analysis is
often used as well. A basic rule is that 20% of the causes is responsible for
80% of the results. This is known as the Pareto principle, often referred to as
the “80/20 rule”.
The Pareto analysis is expressed graphically in a Pareto diagram: this is a bar
diagram that runs from left to right in order of height. The Pareto contains
the contributing factors of a given output, ordered on the basis of their
impact on that output. This impact is expressed numerically on the Y-axis to
the left. On the Y-axis to the right, the cumulative percentage of the impact
factors is presented (from left to right), making it clear where the
intersection with, for instance, the 80% (cumulative) is located.
When the Pareto diagram has been completed, the analysis can commence.
Often, there are two or three factors that clearly have a larger impact than
the others and it is clear which factors need to be tackled. If it less clear,
follow the guidelines below:
• Look for the tipping point in the cumulative percentage line. The
factors below the steepest part are the most important ones.
• If there is no clear tipping point, look for the factors that represent
at least 60% of the problem.
• If the bars are all equal in size or more than half of all the
categories are needed to get to 60%, try to use a different category
division that has a better fit. Also, look at the different units you are
using in the Pareto. For instance, you can use quantities, as was
done in Figure 3.2, but also costs. Look for the unit that provides
the maximum information about your problem and try to remain
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close to the CTQ. When your CTQ is lead time, then also use lead
time in your Pareto diagram.
• For analysis of e.g. breakdowns it is for the same reason better to
display the time losses than the number of breakdowns per
category. This can easily be accomplished by multiplying the
frequencies with the average breakdown time for that category.
Figure 3.2 indicates how you can use a Pareto diagram about the CTQ
(reducing complaints) to get from the Voice of the Customer (improving
service) to a number of potential Y's.
3.2.4 Quality Function Deployment The last instrument we will discuss here to get from CTQ to Y is the Quality
Function Deployment (QFD). This technique can be applied throughout the
DMAIC cycle and helps to translate the Voice of the Customer to CTQ’s in
the Define phase, from CTQ’s to measurable process outputs (Y) in the
Total 962 505 350 127 97 83 101
Percent 43,2 22,7 15,7 5,7 4,4 3,7 4,5
Cum % 43,2 65,9 81,7 87,4 91,7 95,5 100,0
Complaint OtherTV receptionNoise after 11 pmWardrobeLightingToo coldCockroaches
2500
2000
1500
1000
500
0
100
80
60
40
20
0
Total
%
Pareto Chart of Complaint
Figure 3.2
94
Measure phase, from process outputs to the main influences on the outputs
(the X's) in the Analysis phase, and from process X's to process controls in
the Control phase. In the QFD, connections are made continually between
cause and effect of input and output. The degree of influence is quantified
on the basis of weighing factors.
The simplified version of the QFD is the priority matrix. In the Measure
phase, CTQ is translated into project Y's. Because it is possible to define
more than one Project Y per CTQ, it is important to prioritize, which can be
done with the help of the priority matrix (simplified QFD).
Construction of a priority matrix:
• Make a list of all the Project Y's (use, for example, the tree diagram
to map the Y's)
Figure 3.3
95
• Determine selection criteria to weigh the Y's
o Linked to CTQ
o Measurability, obtainability of data
o Impact on the organization
o Availability of people
o Costs of deviations (Cost of Poor Quality)
• Determine the weight criteria of the various Y's
For example, use a 1-3-5 scale to weigh the connection between
the Y and the selection criteria.
• Add the scores for each Y to arrive at a total score
• Order the Project Y's in descending order of importance to identify
the most suitable Y.
In Table 3.0, a priority matrix is applied to the reduction of fuel
consumption:
Project Y Directly
measure-
able
Ready in 6
months
Impact
organization
Related to
CTQ
Total
Weight car 5 1 1 5 12
Air resistance 1 1 1 5 8
Driving style 3 5 5 5 18
Friction 3 3 5 5 16
It turns out that driving style is the Y that needs to be tackled first.
Next to the priority matrix, there are other techniques that can be used to
order the different Y's, like the Pugh matrix and AHP (Analytic Hierarchy
Process). These techniques will be discussed in chapter 8.
3.2.5 Scope and project Y The techniques described above help you select the Project Y, which
determines the direction and scope of the project. It is important to choose
carefully, based on the following considerations:
Table 3.0
96
• Can the project be realized within a reasonable time frame (within
6 months)? If not, divide it into several projects.
• What expertise and resources are needed to come to a solution?
Are they available?
• Are there obstacles to the project?
• Are the resources, such as special equipment, machines and
facilities, available?
• Can the data be obtained to quantify Y?
All these facets determine the feasibility of the improvement project, given
a selected Y. In some cases, a second Y is included in the improvement
project. There should not be more two Y’s. If there are, it is recommended
to divide the project into several improvement projects to maintain focus
and keep the complexity manageable.
3.3 Collecting data Now that the Project Y has been defined, the next step is measuring the
current performance of Y. Lean Six Sigma is a fact-driven method. Data will
have to be collected to make decisions based on facts:
I think there is a problem ….
Becomes:
The data indicates that there is a problem ….
In this paragraph, we discuss the data collection. This has to be done in a
structured way, to make sure that the data is current, unambiguous and
accurate. The instrument that is used is the data collection plan.
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3.3.1 Data collection plan The data collection plan is a plan that determines what will be measured,
how it will be measured and by whom. The format of the data collection
plan can be used throughout the DMAIC cycle:
Measure: Collecting data about Project Y and stratification
factors to determine the baseline performance and the
entitlement
Analyze: To collect data about Project Y and potential X’s, to
identify the root causes that influence Project Y
Improve: To collect data about experiments and pilot projects,
to arrive at the best solution
Control: To collect data after the implementation of the
solution, to demonstrate there has been improvement
Data has to be collected for a reason and as accurately as possible: it is used
to justify critical decisions. Before starting with the data collection, it is
recommended to use the following checklist:
• Has the objective been described clearly?
• Who is responsible for the measurement and data collection?
• Have the people involved been informed, has it been explained
what it is about?
• Is there training necessary?
• Have all the potential data sources been identified?
• What kind of data will be collected?
• Have the data collection points been set up, so are the checklists,
etc. in place?
• What does the measuring system consist of and how reliable is it?
98
• Has a structure been created to organize, represent and summarize
the data?
Most of these points become clear in the data collection plan. Make
especially sure to explain everything well to the people involved, to prevent
them from becoming suspicious because of the data collection. For a
number of measurements, people will need to be trained, in many other
cases you will need to explain how the data should be collected, to prevent
people from collecting data in different ways.
Often, there are various sources that contain useful historical data. Always
start by identifying these sources to check whether the data is useful.
Possible historical sources:
• Interviews
• Studies
• “Work Order Travelers” (documents that travel along, like sales
orders, manufacturing information, etc.)
• Data sheets
• Check sheets
• Personal files
• Data files, reports from the ERP system
If additional data is needed to determine the current value of the Y process
output, a data collection plan is set up to actively collect new data. Below,
an example of such a data collection plan, which focuses on the following
questions:
• Why are the measurements taking place?
• What is being measured?
• How is it measured?
• Who is doing the measurements?
99
3.3.1.1 Data collection plan: why are we
measuring? In the data collection plan, briefly indicate what the goal of the
measurement is. Indicate for which Y the baseline performance is being
measured; to which process and inputs the measurement is related and
what the intended goal of the measurement is.
In the Measure phase, the goal is to measure the baseline performance of
the process that is related to the Y. This is the starting point for the
improvement. The baseline performance as a result of the measurement is
discussed in chapter 4. An additional goal can be to determine the best case
performance in the time frame being measured. Based on this best case, the
project objective can be refined and expressed in a target value for Y, also
known as the entitlement (Chapter 5).
Figure 3.4
100
3.3.1.2 Data collection plan: What are we
measuring? A data collection plan is created with an eye towards the future. Collecting
data can be costly and time-consuming. It is therefore important to collect
more data, not only for the Y. Possible influences on the Y, in the form of
input X's, process X's and stratification X's, can be included at this stage. The
tree diagram, the process diagram and the QFD can be used to this end. The
so-called Cause & Effect diagram is another technique that can be used to
identify X's. This technique is discussed in chapter 6.
In the data collection plan, there are 3 elements that together make up the
“what” of the data collection plan:
• The operational definition
• Type of measurement result
• Type of data
Operational definition
The operational definition gives a communicable meaning to a concept by
clearly indicating how that concept is measured and applied under certain
circumstances (Deming).
An operational definition contains the following elements:
1. Standard: the standard to which the result of a measurement is
compared
2. Procedure for measuring a characteristic
3. Decision: determination whether or not the characteristic of the
test result conforms to the standard.
Below, the concept of “quick service” for a pharmacy as an example:
101
Standard: medication is dispensed at a counter no longer than 10 minutes
after the prescription was handed in.
Test: The time needed to process a prescription and hand it over to the
customer, using a calibrated stopwatch.
Decision: when it takes less than 10 minutes to process the prescription, the
process meets the standard and the service can be described as being quick.
Type of measurement result
The measurement result can be related to the output Y, factors in the
process: the process X's, the inputs of the process: input X's or stratification
X's. The output has been discussed in this chapter. In the following chapters,
the X's will play a central role when we go looking for opportunities for
improvement. In this paragraph, we briefly discuss the stratification X's:
Stratification X's are factors that can identify subgroups that vary in terms of
their performance. For example, overall sales results in a given period can
be divided based on season. When you are selling ice skates or Christmas
decorations, this will be a stratification factor.
Stratification X's divide collected data into subgroups. Often, these are
factors that answer:
Which For example: type of complaints, type of defects, type
of problems
When For example: year, month, week, day
Where For example: country, region, town, work location
Who For example: business, department, individual
When dividing data into subgroups, it is important for the differences
between the groups to be as big as possible and the differences within the
groups to be as small as possible. The various factors of the groups have to
exclude each other and together form a whole, they are mutually exclusive
and collectively exhaustive.
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Stratification helps to look for differences in performance between groups
or periods, to determine the best case or explain a defect. In addition,
stratification provides insight into the process performance with regard to:
• Long term: long-term variation is not just about “time”. LT variation
is the variation of the entire process with all subgroups together.
Suppose the variation in lead time in the Netherlands could be
divided in five regions (north, east, south, west and center). If the
variation is smallest in the central region, that could be considered
the best (similar to “short-term”) performance. The variation of the
five regions combined would then be the overall
performance.(similar to the “long term” performance. (This overall
variation is always higher than the “within subgroup” or “short-
term” performance).
Figure 3.5
103
Types of data
In figure 3.6, the different types of data are presented schematically. From
bottom to top, the data types become richer in information. When
collecting data, continuous data is the most valuable. Sometimes “discrete”
data is referred to as “attribute”. Continuous data sometimes is called:
variable data.
Table 3.1 contains the most important characteristics per type.
Ma
in
cate
go
ry
Ty
pe
Inte
rva
l
Ord
er
Dif
fere
nce
/
rati
o
Me
an
Me
dia
n
Mo
de
Continuous Continuous Infinite � � � � �
Discrete Count Fixed,
equal
� � � � �
Discrete Ordinal � � � � � �
Discrete Nominal � � � � � �
Discrete Binary � � � � � �
Figure 3.6
Table 3.1
104
When formulating the central question to collect data, it is important to
think about how to formulate it. The question determines the value of the
information you are going to collect.
For example:
“Does the striker score during the season?” Or: “How often does the striker
score during the season?”
These two questions will result in different answers. The first answer (yes or
no) is binary; the second answer is a number and contains more
information. This answers the first question in three parts. The operational
definition, the type of measurement result and the type of data indicate
what is being measured according to the data collection plan.
3.3.1.3 Data collection plan: how are we
measuring? Now that we know what will be measured and what type of data we are
looking for, the next question is how to measure. The following elements
are important here:
• The instrument
• The resolution
• The sample (as part of the population)
Measuring instrument
Measuring instruments come in various types and sizes. A stopwatch to
measure time, observation to determine how many people are in a
supermarket check-out queue or a barcode scanner to determine how many
items of a product have been sold. The type of instrument depends very
much on what it is you want to measure. In the case of services, people
often count how often something occurs. In that case, the person doing the
counting is our “measuring instrument”. If we have a database where we get
105
our information through queries, you could call the query our measuring
instrument.
Resolution
The resolution is the accuracy with which the measurements are carried out.
To measure time during a marathon, minutes and seconds will be accurate
enough, while for the 100 meters sprint, even hundreds of a second may not
be accurate enough. The accuracy that is needed is linked to the goal of the
measurement. A basic rule that is used is that the instrument should be able
to divide the range you are measuring into at least 10 distinguishable
sections. This is called the “10 bucket rule”. In some organisations a rule of
20 is being used rather than 10.
Sample
To be able to draw conclusions from a measurement, it is not necessary to
measure the entire population. Often, a sample is enough to say something
about the population as a whole. The sample from a population is defined as
follows:
A subset or part that is representative of a larger population, that can be
studied with the aim of forming an opinion and making decisions based on
facts.
The reasons to use a sample and not the entire population can be diverse:
• It is often not practical to collect data from the entire population
(asking all 17 million people in the Netherlands a question may take
a long time).
• Some testing methods are destructive (for instance measuring the
number of decibels in firework – take better example, e.g. life
expectancy of a light bulb).
• It is too expensive to measure the entire population.
106
• It is simply not necessary to measure the entire population because
statistics can be used to make reliable statements.
A difference between the outcome of the measurement on the basis of the
sample and the entire population can be caused by:
Accidental mistake: there are too many extreme or atypical observations in
the sample, for example so-called outliers (in this case, use a larger sample
to reduce the effect of this).
Systematic error (or sample bias): the sample was not selected correctly. For
example, measuring the average height of male Dutchmen does not provide
an accurate insight into the average height of all the men on earth. A sample
has to be well thought out and planned to guarantee its reliability. In other
words, it has to be representative.
Sample frequency and sample size
To realize the objective of a measurement, determining the sample is
crucially important. When measuring a process, it is important to measure
often enough (frequency) to be able to detect a change from “good” to
“bad”. In addition, the period has to be long enough to see the long-term
process variation. If, for instance, it takes longer in the summer to receive a
quotation for a loan, it's important not to measure only in February and
March.
It is recommended to conduct various smaller samples at different points in
time. In case the process is unstable, samples have to be taken more often
than when the process is stable.
Table 3.2 provides a number of basic guidelines to determine the size of the
sample.
107
What do you want to know
about the population?
Minimal recommended sample
size
Mean value of a population 5
Standard deviation of a
population
25
Defective proportion (P) in a
population
30
Frequencies of values in different
categories (of histogram or
Pareto chart)
50
Relationship between variables
(like in a scatter diagram or
correlation)
25
Stability over time 25
To determine the size of a sample, Minitab, which will be discussed later,
can be used.
Sample planning
To select a reliable sample, every unit of the population has to have an
equal chance to be included in the sample. This is known as a-select (or
random) sampling. The table on the next page shows the possible types of
random sampling.
Table 3.2
108
Purely random
- Figuratively speaking: put the entire population
in a hat and select individual elements at
random by pulling them out of the hat
- Example: select 100 customer questions
randomly from the 5000 questions that were
asked this month.
Systematic
random - Select every nth individual of the population
(assuming that the population is not ordered in a
way that is related to the frequency in which you
are sampling).
- Example: select every 50th customer question
from the 5000 questions that were asked this
month.
Stratified
random - If the population has subgroups that are related
to what you are measuring, select a certain
amount at random from each subgroup; select
more from larger subgroups and less from
smaller ones.
- Example: because 35% of the questions are
related to software, 40% to hardware and 25%
to other issues, select 35 software-related
questions at random, 40 hardware-related
questions and 25 other questions.
3.3.1.4 Data collection plan: who is measuring? The what and how of the measurements have now been determined. The
last question that needs to be answered is: who will be measuring?
The purity of the measurement ultimately depends on who is conducting
the measurement. To make sure that the measurement is carried out
correctly, clear rules have to be established for the person doing the
measurement. They need in detail to be aware of the objective and
importance of the measurement and how it needs to be carried out.
Calibration of the measuring instruments is also critically important. The
Table 3.3
109
people conducting the measurement need to be aware of the instructions
regarding how and when to calibrate. In some cases, training will be needed
to make sure that the measurement is carried out in accordance with the
requirements.
In the next paragraph, we take a closer look at the measuring system used
to measure the Y. Because this is the output on which we base the
improvement project, having an accurate measuring system is important.
That can be determined by analyzing the measurement system.
3.4 Measurement System Analysis Before measuring the baseline performance of the chosen Y, we first take a
closer look at the variation of the measurement system. The process used to
determine the variation of the measuring system is called the Measurement
Systems Analysis or MSA. It is an analysis that answers two fundamental
questions.
• Is the variation of the measuring system too large to complete the
project successfully?
• What needs to be done to make sure that the measuring system is
adequate for the project?
Figure 3.7
110
A good measuring system is crucial to a successful project and one that
should not be taken for granted. Do not proceed with the project until you
are certain you have a capable measuring system. Within an industrial
environment, you may want to consider carrying out a separate project for a
good measurement, which by itself can lead to a significant process
improvement and makes it possible to carry out other improvement
projects that depend on this measurement.
The MSA contains the following steps:
1. Identifying potential sources of measurement variations
2. Choosing the right instrument to quantify the variation of the
measuring system
3. Comparing the size of the measurement variation to what is acceptable
for your project
4. If necessary, fixing the measuring system to reduce variation
In figure 3.8, the various types of variation are shown, which we will discuss
in greater detail in the next paragraphs.
Figure 3.8
111
The various types are analyzed step by step to determine whether or not the
measuring system you selected is acceptable for carrying out the measure-
ment. Figure 3.9 contains a schematic representation of this road map:
3.4.1 Resolution, accuracy, stability and linearity
Resolution
In 3.3.1.3, we discussed resolution. This is where the “10 bucket rule”
applies.
Accuracy
Accuracy indicates to what extent the measurement matches the real,
known standard value. Normally speaking, reality is determined by using the
most accurate available equipment or by using standard values. For
instance, the accuracy of a wristwatch can be compared to an atomic clock.
The deviation of the measurement from reality is called the bias (see left
part of figure 3.11 below).
Figure 3.9
112
This bias can be caused by the person operating the measuring instrument
or because the instrument shows a deviation in one direction. Accuracy is
Critical to Quality for the measuring instrument. The following procedure
can be used to test the accuracy:
1. Select at least 3 standard samples with known values in the range that
frequently occurs in practice
2. Apply the measuring instrument to get several measurements
3. Calculate the differences between the measurements and the real
values
4. Plot the differences (Y-axis) vs the “real” values (X-axis)
5. Determine the accuracy: when the measurement is accurate, the value
will be randomly distributed along the horizontal line (Y = 0).
Stability
The measuring instrument also has to be stable over time. A stable
measuring instrument provides consistent results over a longer period of
time. A measuring instrument that is used on moment 1 has to be equally
accurate on moment 2. In the case of the wristwatch, the deviation
compared to the atomic clock has to be same today and in a month from
now. With wristwatches, this is often not the case. For a measuring
instrument that is used to measure an improvement, stability is crucially
important, because the Y that is measured after the improvement is
compared to the baseline performance.
The following procedure can be used to test the stability:
1. Select a single standard sample that stays “stable” over time
2. Measure the sample every day for several days (preferably 30 days or
more)
3. Plot the measurements (Y-axis) against time (X-axis)
4. Determine the stability: the absence of clear trends or outliers in the
plot suggests that the measuring instruments is stable.
113
Linearity
A measuring system is linear when its accuracy is consistent across the
entire range of the potential values. In the case of an odometer (to measure
speed), this would mean that the deviation of the odometer is appr. 2
miles/h at 30 miles/h as well as at 140 miles/h. In practice, this is not the
case with odometers. If a measuring system is not linear, the results cannot
be compared properly for measurements that are different in size. Figure
3.10 provides a number of practical examples of accuracy versus scope.
For the sake of quality, a measuring system has to be linear. The following
procedure can be used to test the linearity:
1. Select “k” standard samples with “known” values across the range of
“typical” values
2. Conduct the measurement to determine the value for each sample
3. Calculate the difference between the measurements and the “real”
values
4. Plot the differences (Y-axis) against the “real” value (X-axis)
5. Determine the linearity: the absence of clear trends in the plot suggest
that the measurement is linear
Figure 3.10
114
Correcting the accuracy, stability and linearity of measuring instruments
Calibrating the measuring instrument is the method used to correct
accuracy, stability and linearity. When calibrating measuring instruments,
the bias is determined, by comparing with a reference or a calculated
model. The deviations are recorded in a so-called correction table. With
digital processing of the measurements, the measured values can be
automatically corrected to ensure that the measurements are accurate.
Alternatively, the measuring instrument can be adjusted to correct the
deviation. Based on the calibration, it can be determined whether or not the
measuring instrument still matches its specifications. In case standards are
used, they have to be of a certain quality to make sure that the adjustments
take place in a proper way.
3.4.2 Precision The final step in analyzing the measuring system is to determine the
precision of the instrument. In this step, the reproducibility and repeatability
(R&R) of the measurement play a central role.
A measurement is repeatable when the same sample carried out by the
same operator under the same circumstances during the second
measurement gives the same result as the first measurement.
A measurement is reproducible when a second person gets the same result
from a measurement as the first person.
A good measuring system is both reproducible and repeatable. The variation
that can be assigned to the precision can be calculated on the basis of the
variation caused by repeatability and reproducibility, as follows.
��&�� = ���� � � ��� + ������� � � ���
In figure 3.11, the difference between repeatability and accuracy is shown.
115
Better Repeatability Better Accuracy
Worse accuracy Worse Repeatability
A large variation in repeatability can have the following causes:
Equipment - Instrument requires maintenance
- Unstable instrument
Human - Environmental conditions (light, noise)
- physical conditions (eyes)
A bad reproducibility can have the following causes:
Procedure - Measurement procedure has not been clearly
defined
- The operational definition (how to measure) is not
clear (or unambiguous) (especially in the case of
transactional applications)
Human - Insufficient training in use and reading the
instrument
Figure 3.11
116
3.4.3 Gage R&R
Gage R&R is a statistical method designed to test the measuring system for
precision. The gage (or gauge) is the measuring instrument, while R&R refers
to Repeatability and Reproducibility. Variation in measurements can be
caused by human error or by a faulty measuring system. In preparation for
the Gage R&R, the instrument, if possible, is first calibrated to make sure
that it is accurate, linear and stable.
3.4.3.1 Gage R&R for continuous variables
A Gage R&R for continuous variables consists of the following steps:
1. Make a data collection plan to analyze your measuring system
2. Collect the data
3. Calculation and analysis
4. Correct the measuring system if necessary
1. Make a data collection plan to analyze your measuring system
Take the following steps to make a data collection plan:
• Select different items/parts that you will be measuring in the study
These items have to represent the typical range of the process
values (random sample). You need at least 5 items divided over the
entire range of values that is being encountered in practice Often
even 10 items are being used if available.
• Select at least two operators that will each conduct several
measurements for each item.
They have to be operators who normally carry out these
measurements. Preferably we include all operators, but at least
two.
117
• Determine how many repeat measurements each operator will
conduct. In addition, the following formula is used to determine the
number of measurements:
number of items * number of operators * number of repeats per
operator > 30
2. Collect the data
In the second step, the data is collected. Use Minitab to generate the data
collection worksheet for you (see below):
• Let the first operator measure all the items (or parts) once in
random order
• Make sure the other operators do not see the results of the first
operator
• Let the second operator measure all the items once in random
order
• Go on until all the operators have measured all the items: trial 1 is
complete
• Repeat the previous steps for all the repetitions (repeat at least
once)
• Make sure that the items are not recognizable to the operators
going from one to the next repetition.
3. Calculation and analysis
Create a worksheet in Minitab to enter the data obtained in the previous
step. The following column titles can be used:
• Item identification code
• Operator
• Trial
• Measurement result
118
Enter the data obtained in step 2 into the worksheet and carry out the
calculations in Minitab:
Minitab: Stat -> Quality Tools -> Gage R&R Study (Crossed)
Example
In the example, we want to measure a property Y of a given part that has a
specification of 20 to 100 units, with a target of 60. 10 items have been
selected that will be measured by 3 operators. Each operator has carried out
the measurements twice. The result is shown in the following worksheet
(figure 3.12).
Go to Minitab: Stat -> Quality Tools -> Gage R&R (Crossed)
Figure 3.12
119
The preferred method of analysis is ANOVA. Next, go to “Options”.
Figure 3.13
Figure 3.14
120
Fill in the upper and the lower spec. Leave the default ‘6’ at Study Variation
(this means that we want to include 99.7% of the measurement variation in
the study. If we prefer 99% of the variation we put the number to 5.15
standard deviations. (This used to be the default number in the past.)
Result:
Explanation of the results:
Term: Explanation:
Total Gage R&R This is the total variation due to
Repeatability and Reproducibility
Repeatability The variation due to Repeatability
Reproducibility The variation due to Reproducibility
Operator The variation due to differences between
operators
Part-To-Part Actual variation due to parts
Table 3.4
121
Total Variation The total observed variation in the entire
study (parts + measuring system)
VarComp The column expressing the Variation in
terms of Variance of the components
%Contribution (of
VarComp)
The percentage-wise contribution of the
above (variation compared to total
variation)
Study Variation The variation components, this time
expressed in terms of 6*Standard
deviations, not in variances
%Tolerance (SV/Toler) Study Variation divided by the indicated
tolerance
To determine whether or not the measuring system is good enough for the
measurement, the following additional criteria are used:
The number of distinct categories
The number of unique items that the measuring system can distinguish
across the measurement range. The higher this number is, the better.
% contribution
The percentage of the total variation in Y that can be attributed to the
measurement. The lower this percentage, the better the measuring system.
Captured in a formula:
������������ = � !"�� � �� #!��!�$ ���!% ��" �# & #!��!�$ × 100% = ��&��
�+� × 100%
122
% tolerance
The 6*sigma range of the measurement expressed as a percentage of the
specification range of Y (USL-LSL). This indicates how much of the range is
used by the variation in the measurement system. Here, too, a lower
percentage is better. Captured in a formula:
,�% �!�$ = -∗/0&01234323
The table presented below contains the basic guidelines to assess the
Figure 3.15
Figure 3.16
123
measuring system on the criteria discussed above. Assess the basic
guidelines within the context of your project and your process:
Traffic
light level
%
contribution % Tolerance
Number of
categories Proposed action
Red
Chemistry>
30%
Parts > 10%
>30% <5
Improve the
measuring system
before continuing
with the project
Yellow
Chemistry: 4-
30%
Parts: 4-10%
10-30% 5-10
Consider
improving the
system while
continuing with
the project
Green <4% <10% >10
Measuring system
is adequate.
Continue with the
project.
Because it is easier to make precise measurements of physical parts than of
continuous flows and chemical properties, and because the margin for error
is usually much smaller in the case of physical parts, a distinction is made
between measuring chemical processes and measuring parts.
About %Contribution and %Tolerance:
The %tolerance can be influenced artificially by a wide specification, or the
%tolerance can be unreasonably bad when the customer provides a too
narrow a specification in comparison to the capabilities of your measuring
device. The resulting %tolerance says more about the specification than it
does about the measuring instrument and its variation.
The %contribution can be influenced artificially, by choosing parts with a too
wide range (compared to what you normally make). In that case, the
%contribution (which is expressed as a percentage of the total, and also the
Part-to-Part variation) is relatively small, as a result of which your measuring
Table 3.5
124
instrument appears to be good. On the other hand, you can also choose
parts with a too narrow range, which will give the impression that your
measuring instrument is not good enough, because the contribution of the
measuring instrument to the variation is relatively large, due to the
narrowness of the range. This can be used to wake up the organization into
taking a critical look at the measuring instruments.
Interpreting the graphs
• Components of variation: the part-to-part variation has to be the
dominant component. Repeatability and reproducibility must not be the
dominant source of variation. Their total should be below 10% (parts) or
30% (chemical).
• R Chart by Operator: differences between the highest and lowest
measurement per part as measured by one operator. Large spread
indicates bad repeatability
Figure 3.17
125
• Xbar Chart by Operator: The Average value of the measurements per
part by one operator. Control limits need to be narrow compared to the
observations (parts need to be dominant source of variation).
• Measurement by PartID: there has to be a difference between the
parts. The points per part have to be closely grouped. There must be no
outliers. Helps to discover bad parts.
• Measurements by Operator: distribution of measurements per
operator. There has to be a similar pattern. Look for outliers.
• PartID * Operator Interaction: operator-part interaction trends have to
overlap. Clear distinction between operators indicates bad
reproducibility.
4. Correct the measuring system if necessary
If the results from step 3 require a correction to the measuring system, the
following guidelines will help you to take the appropriate corrective
measures, depending on the component causing the problem.
When repeatability is the dominant source of variation (the instrument), it is
recommended to replace or repair the instrument. When your supplier
informs you that the measuring instrument is state-of-the-art and works
properly, you can limit the lack of repeatability by conducting several
measurements and taking the mean.
When the operator is the dominant source of variation (reproducibility), you
can solve this through training and by improving the standard work
instructions. You could look at differences between the operators to get an
indication of where the problem lies (training, skills, instructions).
In case there are problems with the tolerance, always check the
specifications of the product with regard to their feasibility and
reasonability. If the capability of the measuring instrument is marginal (up to
126
30%) and the process operates on high capability (total variation much
smaller than the specifications for Y), the measuring instrument is unlikely to
cause much trouble and you continue using it.
Figure 3.18 shows the possible causes of variation with regard to the
measuring system. These can serve as a starting point of correction.
3.4.3.2 Gage R&R for discrete variables Most measurements depend on measuring instruments with scales or
equipment that show the value of the product characteristics directly. In
some cases, the measurements are obtained through subjective assessment
by people. Some examples:
• Assessing whether invoices are complete or incomplete
• Presence or absence of a certain characteristic in a product
Figure 3.18
127
• Taste of cheese (sweet, bitter, salty) on a scale from 1-5
• Registering complaints in 6 categories
These variables have qualities that are subjective. To determine whether the
classifications are consistent, we need to have various items assessed by
more than one person. The following principles apply:
• When there is insufficient agreement between the people doing
the assessments, the test cannot be used in that way. One option is
to reduce the number of testers.
• When the testers disagree most of the time, the assessment is only
useful to a limited extent
The attributive R&R helps to determine whether the subjective
classifications are consistent and correct, by looking at the scores for each
tester, between testers and compared to a standard.
The attributive data can have the following structures:
• Ordinal: categorical variables with 3 or more possible levels with a
natural order, like disagree, neutral, agree, or a numerical scale
from 1-5.
• Nominal: categorical variables with 2 or more possible values
without a logical order. For example, the taste of food: sweet, sour,
salty or bitter.
The steps that are taken to determine whether or not the measuring system
is suitable are the same as with continuous variables:
1. Make a data collection plan to analyze the measuring system
2. Collect the data
3. Calculate in Minitab and analyze the calculations
4. Correct the measuring system if necessary
128
Steps 1 and 2 are in accordance with the Gage R&R for continuous variables.
In the remainder of this paragraph, the focus is on the calculation, analysis
and correction of attribute Gage R&R.
In Minitab, the data can be analyzed for nominal and ordinal data via:
Minitab: Stat -> Quality Tools -> Attribute Agreement Analysis
For binary data: Minitab: Stat -> Quality Tools -> Attribute Gage Study:
Based on an example, we will discuss the analysis of the “Attribute
Agreement Analysis”.
Example
A development center is training five technicians in assessing the
smoothness of the remaining bottom half of an opened display box for
supermarket shelves. The extent to which the technicians are able to make a
correct assessment is tested. In the study, each technician assesses 15 items
on a 1-5 scale, whereby 1 is the worst result and 5 the best (ordinal data).
See figure 3.19.
Figure 3.19
129
The results of the technicians are shown in figure 3.20:
Minitab: Stat -> Quality Tools -> Attribute Agreement Analysis
Figure 3.20
Figure 3.21
130
Click on “results” and make the following selection:
Results:
In the graph, you can see the percent agreement of the appraisers
compared to the standard. In addition, there is also a confidence interval
around the indicated values, because this is just a sample and you need to
make a conclusion about what is going on in general, with the entire
population. This confidence interval is discussed in greater detail in the
Date of study:
Reported by:
Name of product:
Misc:
VerheijenVan den BergDe GrootBrouwerAdriaans
100
90
80
70
60
50
40
30
Appraiser
Perc
en
t
95,0% CI
Percent
Assessment Agreement
Appraiser vs Standard
Figure 3.22
Figure 3.23
131
Analysis module. The figures on which the graph is based are presented
below.
Attribute Agreement Analysis for Rating
Each Appraiser vs Standard
Addition to the assessment agreement: simple count that indicates to what
extent the results do or do not match the standard perfectly.
132
Explanation of Kappa: The Kappa statistic calculates the absolute agreement
between the assessments. Kappa statistics treats all differences in
classifications as “equally” seriously.
Kappa is the proportion of agreement after correcting for the agreement by
pure coincidence. When Kappa is equal to 1, there is perfect agreement.
When Kappa is equal to 0, the degree of agreement is as little as can be
expected by coincidence. The better the agreement, the higher the Kappa
value. Negative values can occur when there is less agreement than can be
expected due to pure coincidence (this rarely occurs). When Kappa is lower
than 0.7, this is an indication that the measuring instrument needs
improvement. Values above 0.9 are excellent.
Explanation Kendall's Coefficient: Kendall's coefficient does not treat all
differences in classifications as equally seriously. The consequences of
classifying a perfect item (rating = 5) as bad (rating = 1) are more serious
than if they were given a good score (rating = 4). Kendall's coefficient is used
to score the agreement between the appraisers when the scores are ordinal.
133
The degree of deviation is also included. The coefficient is also calculated to
determine the agreement with a standard. In that case, the value is between
0 and 1. Also for Kendall's coefficient, a value above 0.7 is acceptable and a
value above 0.9 is very good.
Between Appraisers
All Appraisers vs Standard
134
* NOTE * Single trial within each appraiser. No percentage of
assessment agreement within appraiser is plotted.
It is clear that, according to the Kappa statistic, there are a number of
appraisers who are not good enough (< 0.8,so less than 80% correct), but
when you take the relative deviation (Kendall’s) into account (having rated a
4 when it should have been a 5 is less serious than having rated a 1 when it
should have been a 5), the appraisers are all good enough (Kendall's
coefficient is > 0.8 for all the appraisers).
Finally:
There are two basic types of attributive data: nominal and ordinal, which
both have their own tool in Minitab. For a good analysis, it is important to
think about which MSA technique you will use even before collecting the
data. In this way, the data can be collected such that it matches a certain
attributive Gage R&R technique.
135
3.5 Exercises
Sample size
Determine the sample size for the following tests:
What do you want to know about the
population? Minimum recommend-
ded sample size Mean value of a population
Standard deviation of a population
Defective proportion (P) in a population
Frequencies of values in different categories
(from histogram to Pareto chart)
Relationship between variables (like in
scatter diagram or correlation)
Stability over time
Pareto
Make a Pareto chart of the following bar diagram:
X-ray occu
pied
patient n
ot ready
no surgery
room av
ail.
Not enough beds
Fire al
arm
No assis
tant a
vailab
le
No doctor a
vailable
60
50
40
30
20
10
0
occ
ure
nces
12
31
57
8
44
24
Causes for cancellation of surgery
136
Operational definition
Make an operational definition for the term:
“Rust-free”
Data types
Indicate in which categories the data types below fall:
A. right/wrong B. gender C. man/woman/child
D. sales price E. small/medium/large F. provinces in NL
G. salary scale 1 - 5 H. speed in km/hour I. whole/broken
J. complaint K. temperature L. month
Binary Continuous
Ordinal Nominal/category
Data collection: Post office case
Make a data collection plan for the post office by:
• Formulating the objective
• Writing down the operational definition
• Determining the stratification factors
• Determining the sample schedule, frequency and resolution
• Selecting a suitable measuring instrument
137
Reproducibility, repeatability & accuracy
Assess for each target (given the middle is the true value) the:
- Reproducibility (good+ or bad-)
- Repeatability (good+ or bad-)
- Accuracy (good+ or bad-)
Figure 3.24
138
139
CHAPTER 4: BASELINE PERFORMANCE
4.1 Introduction In the previous chapter, the process output Y has been defined in a
measurable way, the measurement method has been selected and the
reliability of the measuring instrument has been analyzed. We are ready to
start measuring! In the fourth step of the Lean Six Sigma project, we discuss
the baseline performance of the process: how well does the process perform
in the current situation? The performance of the process, expressed in a
value for Y, is called Process Capability. The value of the Process Capability in
the current situation is part of the Baseline Performance. In the next
paragraphs, these terms are explained in greater detail.
4.2 Process Capability The Process Capability of a process is important for the following reasons:
• Obtaining insight into the current performance of the process
compared to the process requirements
• Obtaining insight into the “best case” performance
• Identifying the factors that influence the process capability by:
- observing abnormal forms of distribution
- observing process instability over time
- observing outliers or abnormal output
140
There are various ways to determine the Process Capability. Descriptive
statistics and the following graphical analytical tools can be applied to
represent process behaviour on the basis of data that has been collected:
• Normal distribution
• Histogram
• Boxplot
• Run Chart
• Control chart
• Pareto diagram
In Appendix 1 and 2, these graphical tools are explained in detail. In
addition, it is explained how Minitab can be used for these graphical
analyses.
To determine the performance of a process, that performance needs to be
assessed against a standard or specification. These specifications can be
two-sided, for example the temperature of a swimming pool (not too cold
and not too hot) or one-sided (the sooner the better, but no longer than two
days). Within Six Sigma, the following terms are used:
• Lower Spec Limit (LSL)
• Upper Spec Limit (USL)
Depending on the process, you can either be dealing with both an LSL and a
USL, or only with an LSL or a USL. Figure 4.0 provides a graphical
representation of process behaviour versus specifications.
The specifications are not always available, then they will need to be
determined as part of the improvement project, sometimes in consultation
with the client.
141
4.2.1 Determining the performance standards To determine the Process Capability, performance standards are needed:
specifications. There are various sources that can be used to determine
these standards:
• Existing specifications: internally or imposed by the customer
• Results from internal pilots
• International standards, industrial or engineering standards (for
example ISO standards)
• Sales specifications, tolerances
• Government regulations
• Information from competitors
These sources can be the input for determining performance standards. A
performance standard has to be connected to the CTQ. If a standard is met,
in other words if all the values of Y are within the specification limits, that
means the process matches customer requirements: the CTQ.
Keep the following guidelines in mind when determining the performance
standards (the LSL and/or the USL):
1. Determine a standard that balances customer requirements, external
forces and internal requirements. For example: what does the
customer need, what is the competition doing, what does the
government require and what does the company feel is “right” to offer?
2. If a standard already exists: check its validity. Tests or experiments
among customers may be needed to determine what is really needed.
This can provide a broader standard (and perhaps the opportunity to
reduce prices) or a stricter standard, to prevent process-related
problems at the customer.
142
4.2.2 Determining Process Capability Now that the USL and/or LSL have been determined and the data collected,
the initial analysis of the data can take place. Use a histogram to check the
following:
Is the data distributed normally?
If the data is not normally distributed, look for an explanation. Check
whether a division into subgroups (via stratification factors) explains the
abnormal distribution. If the data within the subgroups is normally
distributed, that explains the abnormal distribution within the population as
a whole.
If this does not provide the desired explanation, special tools for non-
normally distributed populations can be used. In some cases, having a non-
normal distribution is acceptable (generally speaking, lead time is not-
normally distributed), or it may be possible to transform the data
mathematically into a normally distributed data set, for instance by taking
the square root of the log of the data (not recommended). Another option is
to simply determine the fraction “defect” and then apply the Sigma score
table to determine the associated sigma level.
Are there outliers?
First make sure that no measurement or registration errors have been made
and try to explain outliers. Turkey sales will not be distributed evenly
throughout the year. However, the outlier around Christmas is easy to
explain.
If fewer than 0.5% of all the data points are outliers, they can sometimes be
removed from the data set and kept aside (do not throw them away). The
remaining data can be used for the Process Capability.
The Process Capability is the extent to which the process output Y stays
within the performance standards that apply to the process, defined as the
LSL and/or USL. Any value of Y that lies outside the limits is seen as a defect.
143
In the case of continuous data, the normal distribution can be used. In the
case of discrete data, the Defects Per Million Opportunities (DPMO) is used
to determine the Sigma level, using the DMPO to Z conversion table (Z is
Sigma level).
Units to express Process Capability
There are various terms in which the performance of the process, the
Process Capability, can be expressed:
1. Z-score (or Sigma-level)
2. �
3. �5
These terms are dimensionless, which makes it possible to compare
different processes in terms of their performance. An administrative process
can be compared to a production process. Within organizations, this can be
used to set improvement goals, processes with the lowest scores are most in
need of improvement.
Z-score
The Z-score (or Sigma level) is related to the defect level and indicates how
many standard deviations fit between the mean of the data and the nearest
specification limit (the LSL or USL), based on a normal distribution.
Expressed in a formula (assuming LSL is the nearest limit):
6 = � !� − 898�
144
See figure 4.0 for a graphical explanation.
The higher the Z-score, the less chance of defects and the more stable the
process is.
The Z-score of all the data is seen as a long-term score (6��). All the
sources of variation are present in this. If the data can be divided into
rational subgroups via stratification factors, a new Z-score can be
determined for each subgroup. The subgroup with the highest Z-score
represents the best case performance of the process, without the additional
long-term variations (like different raw materials, different employee, wear
and tear, etc.).
Figure 4.0
145
This value is called the short-term Z-score (6:�). The difference between the
two indicates the improvement potential called 6:; <� . With many
companies, this difference is estimated to be 1.5 sigma, which is also the
background of the 1.5 sigma shift in the “DPMO to Z-score” table.
Process Capability � and �5
The unit for the performance of a process that is often used in industry is
the �. This is used when a process has to stay stable within two limits, an
LSL and a USL. The limits are expressed as the number of standard
deviations σ from the mean. In the case of the LSL, this number is negative.
The formula for �:
�= 1234323-/
The � value has a limitation. When the mean is not positioned exactly
between the USL and the LSL, the performance of the process is worse than
the � would have us believe. In extreme cases, all values can even be
outside of the specifications with � having an optimal value (see figure 4.2).
Figure 4.1
146
To exclude the limitation mentioned above, there is the �5 value. The �5
value relates the process behaviour to the process limit that is closest to the
mean (LSL or USL). Therefore, the formula for �5is:
�5= 1234>�?@/
�� �5= >�?4323@/
When the mean is located outside the specifications, the �5 value is below
zero. The difference between � and �5 is illustrated in figure 4.2:
Table 4.0 provides the � and �5 values for various process limits,
expressed in σ.
Figure 4.2
147
LSL, USL in σ 1 2 3 4 5 6
�5 0,33 0,67 1 1,33 1,67 2
4.3 Baseline performance
Based on the collected data, the current performance of the process has
been determined, expressed in a value for the process output Y. The value
of Y depends on what is being measured in accordance with the data
collection plan. Y can be expressed as temperature, time, speed or any other
unit. Depending on the type of data, there will be a standard deviation and a
mean of Y. In the previous paragraphs, three dimensionless entities were
discussed that measure the performance of the process: Z-score, �, �5.
The process capability can be expressed in these units. Make sure, in your
project charter, to include the current process capability, expressed in one
of these units.
For attribute (discrete) data, the capability can be expressed as “DPMO” or
percentage defect. Below an example for both continuous and for attribute
data:
Suppose your goal is to reduce the number of times customers have to wait
more than 2 minutes when calling the service department. To determine the
current process capability, you can measure, for example, 1000 calls over a
1-week period. You put these in Excel and calculate the mean and standard
deviation.
It turns out that the average waiting time is 90 seconds and the standard
deviation is 15 seconds.
This means that the Cpk value is (120-90)/(3*15) = 0.67.
The Z-score is the number of times that the standard deviation “fits”
between the mean and the outer limit, which is (120-90)/15 = 2.
Table 4.0
148
It is not possible to calculate a Cp, because there is only one outer limit.
If, however your project was to decrease the number of hang-ups, you
would have yes/no (attribute) data. In order to determine the capability,
you measure the number of hang-ups out of the total number of callers.
With that you calculate DPMO and/or Z-value as your capability.
Suppose there were 1000 calls, of which 200 did hang up before the phone
was picked up, the capability would be:
Defect percentage: 20%
DPMO: 200,000
Z-value (from DPMO to Z table) = 2.3
4.4 Exercises
Specification
What are the upper and lower limits of a customer specification called?
Process capability
To determine the Process Capability, we look at the performance of the
process (Y) compared to the relevant specification limit(s). A distinction is
made between continuous (or variable) data and discrete (or attribute) data.
What is that distinction?
Why is the performance of processes converted into process capability (Cp,
Cpk, Z-value)?
149
150
151
CHAPTER 5: OBJECTIVE GOAL ON BASELINE
PERFORMANCE
5.1 Introduction In the previous chapter, the current performance has been determined of
the process that we want to improve. Collecting and analyzing the data has
provided insight into the current values of Y (mean, standard deviation) and
the Process Capability. This insight can be used to work out the
improvement goal described in the Project Charter more concrete, which is
discussed in this chapter.
5.2 Determining the improvement goal When we have the baseline performance, we know the current
performance of the process. In this phase of the project, the improvement
has to be quantified. The goal has to be realistic. The following sources can
help to determine the improvement goal:
• Internal or external benchmark for a process
• Customer wishes or requirements
• The best case (in a subgroup)
The goal is expressed in a target value for Y. You can determine how realistic
this target value is by looking at the entitlement, the best performance of
the process in the past. Generally speaking, the target value is determined
together with the sponsor. The selected target value is also expressed in
terms of sigma value, DPMO (as a percentage of defects) and/or Cpk. This
objective is recorded in the Project Charter.
5.3 Recalculation revenues When the defect was first defined, and the Project Charter set up, the
benefits of the project were estimated on the basis of the information that
was available at that moment. After determining the Process Capability and
152
the quantified improvement goal, more insight is available into the potential
of the project. This may have consequences for the benefits that were
initially estimated.
Based on the improvement goal, which has now been defined more
precisely, the benefits will have to be recalculated (see 2.3.7) and recorded
in the updated version of the Project Charter. Discuss the benefits of the
project with the project sponsor. Because, as a result of the new insights,
the benefits may be considerably lower than originally estimated in the
Define phase, the priorities of the project need to be re-evaluated, and you
should not be afraid to abort the project if it turns out there is limited
potential for improvement compared to other potential improvement
projects.
5.4 Exercises
Improvement goal
Who ultimately determines the improvement goal?
153
154
155
PART 3: ANALYZE
In this third part, the third phase of the DMAIC approach is discussed. The
goal of the Analyze phase is:
Determine which process parameters (inputs or X’s) have the biggest impact
on the critical process results (outputs or Y)
Within the Analyze phase, the following two steps of the 12-step plan
occupy a central position:
6. Potential causes of variation
7. Determining the root causes
After completing this part, you will be able:
• To indicate which X's influence Y
• To order the X's based on their level of impact
• To demonstrate, based on statistics, which X's affect Y
• To explain which X's will be used to realize the improvement
objective
• To indicate what the costs(?) and benefits are based on the vital X's
After completing the Analyze phase, the following items have been
delivered:
• A list of potential X's
• A selection of the vital X's
156
157
CHAPTER 6: POTENTIAL CAUSES OF
VARIATION
6.1 Introduction In step 5 of the 12-step plan, the improvement objective has been
quantified and expressed in the new value for Y. Variation (and deviations)
are the reason that Y does not always has the desired value. In this chapter,
we look for potential causes of that. These potential causes are called the
X's. The aim of this chapter is to map the potential causes (also called the
“trivial many”). In the next chapter, we look for the X's that have the biggest
impact on the variation of Y (also called the “vital few”), which is what the
efforts will be focused on during the Improve phase.
Figure 6.0
158
6.2 Potential causes (X’s) The result of this first step in finding potential causes of variation is a list
with X's, not all of which contribute significantly. In addition to the question
whether the X's contribute significantly, it is important to know if they are
within our control. Are there knobs that can be turned? For instance,
although the weather is a major cause of traffic jams in the Netherlands, it is
hard to influence (although it can to some extent be predicted). The X's over
which we have no influence are referred to as “noise”. However, we also
include these X’s in our quest for influence factors. So, the quest for X's is
not limited to e.g. X's that represent the different configurations of
equipment, procedures or rules. X's can either be continuous or discrete.
X's that cannot be influenced are often included in this quest anyway; when
you know what influence the weather may have on your travel time and you
know what the weather will be today, you can take it into account and
adjust your departure time!
The procedure that will be followed in the next chapters to identify the root
causes is the same that is used to determine the CTQ and the Y:
• Map potential X's
• Prioritize the potential X's
• Select the root cause or root causes you are going to tackle
Mapping potential X's is the first step. The focus in this chapter is on
mapping possible X's that may contribute to Y.
159
6.2.1 Tools to determine potential causes
There are various tools that can be used to identify possible causes:
• Process diagram
• Cause-Effect diagram
• Cause-Effect matrix
• Failure Mode & Effects Analysis (FMEA)
In addition, when measuring the project Y, potential stratification factors or
other variables that can be potential X's have already been included, which
is why the following sources from the Measure phase are useful when it
comes to identifying causes:
• Data collection plan
• Graphical analysis of project Y
The process diagram was discussed in paragraphs 2.4 and 3.2.2. The process
diagram may provide insight into the steps and activities that cause
variation of the process output Y.
6.2.2 Cause & Effect diagram
A Cause & Effect diagram is a tool that helps to identify, sort and present all
potential causes of a specific problem or quality aspect. It provides a
graphical display of the relationship between a given outcome (Y) and all
factors (X) that influence that outcome. This type of diagram is also known
as Ishikawa diagram, after the man who invented it, Kaoru Ishikawa.
Figure 6.1 contains an example of an empty diagram. Often, Materials,
People, Methods, Machine, Measurements and Environment are used as
main axes to provide direction to the mapping process.
160
The Cause & Effect diagram is a very useful tool, for the following reasons:
The Cause & Effect diagram:
• helps to identify the root causes of a problem or quality aspect,
using a structured approach
• encourages group participation and uses the group knowledge of
the process
• uses a lay-out that is organized and easy to read to display the
cause and effect relationship
• indicates potential causes of process variations
• increases knowledge about the process by helping everyone to
learn more about the factors involved and how they are
interrelated
• indicates areas where data needs to be collected for further
investigation.
Figure 6.1
161
Building a Cause & Effect diagram
The steps presented below provide guidelines for building a Cause & Effect
diagram:
1. Clearly identify and define the effect that is being analyzed:
• effects are described as quality aspects, problems that are the
result of work. To determine the variation of Y, Y is the effect,
usually Y being too high or too low.
• use the operational definition of the Y (see data collection
plan) to makes sure that the meaning of the effect is clearly
understood.
2. Make sure that everyone can take part and that everyone can see the
diagram. Draw the diagram and the effect block (for example on a
whiteboard or piece of brown paper).
3. Identify the categories of causes that contribute to the effect being
studied:
• methods, materials, man, machines, measurement,
environment
• 4P’s: policies, procedure, people, plant
4. For each main branch, determine different factors that may be the
cause of the effect:
• Look for as many potential causes or factors as possible and
attach them to the sub-branches of the main branch (with a
team, it is good to use post-its and markers).
5. Identify increasingly more detailed levels of causes and organize them
based on related causes or categories:
• From the causes already mentioned, ask the why question a
number of times, to reach a deeper level of detail.
6. Analyze the diagram. This will help you to identify the causes that
require further investigation:
• Look at the “balance” of your diagram, check similar levels of
detail for most categories:
- A thick cluster of items in one area can indicate that
further research is needed
162
- A main category with only a few specific causes may
indicate that more causes need to be identified
- If there are several branches that only have a few sub
branches, it may make sense to combine them into a
single category.
• Look for causes that occur several times. They may be root
causes.
• Look for what you can measure with each cause, so that you
can quantify the effects of every change you carry out.
The Cause & Effect diagram can be made in Minitab via:
Stat -> Quality Tools -> Cause & Effect
Figure 6.2 contains an example of a Cause & Effect diagram that has been
filled in.
Figure 6.2
163
6.2.3 Cause & Effect matrix The Cause & Effect matrix establishes the correlation between several
effects (Y1, Y2, ….) and underlying causes (X1, X2, ….). In addition, the
correlation is given a score, so that relationships are prioritized immediately.
If one effect has a greater weight than the others, the effects are weighted.
This weight factor is multiplied by the correlation score, to determine the
total score per cause.
This matrix is often used after the cause and effect diagram (fishbone) in
order to make a first shift between more and less likely potential causes.
Apart from discussing in the team whether or not there is a correlation, the
team also scores the strength of the correlation. For this score, the numbers
0,1,3,6,9 are mostly used, for respectively no correlation, weak correlation,
medium correlation, strong correlation and very strong correlation.
If for some reason one effect (Y1) is more important to the project than
another effect (Y2, possibly a do not harm Y) the effects will get a different
weight factor. This weight factor, multiplied by the correlation score
(0,1,3,6,9), determines the total score for this cause. The numbers 0,1,3,6,9
are used to generate more differences between outcomes than when
0,1,2,3,4 would have been used. The outcome of the Cause & Effect matrix
can be presented graphically in a Pareto diagram. (See figures 6.3 and 6.4),
in order to apply the 80/20 rule to determine with which (potential) causes
to continue with and/or start collecting data on. This is especially useful if
there are (too) many potential X’s to collect data on them all. This first
selection is based on the common knowledge of the project team. If the
remaining causes are all very obvious to have an effect, it is possible to
continue with these causes directly to the improve phase. But only in Green
Belt projects. Black Belt (certification-) projects have to use data and Black
Belts will have to do analyses on the data to show the significant effect of X
on Y. Green Belt projects therefore have a risk of focussing on some X’s that
seemed obvious but were not significantly influencing the Y. Black Belt
projects do not have this risk with the data driven approach.
164
Count 126 117 95 66 60 48 39 33
Percent 21,6 20,0 16,3 11,3 10,3 8,2 6,7 5,7
Cum % 21,6 41,6 57,9 69,2 79,5 87,7 94,3 100,0
Cause
educ
atio
nal L
evel
# reso
urces
# signa
ture
s
amount
reque
sted
# of r
equest
s
avail.
of m
arke
t int
e r. %
avail.
of appr
oval m
gt.
# def
ects
per
reque
st
600
500
400
300
200
100
0
100
80
60
40
20
0
Cou
nt
Perc
en
t
Pareto Chart of Cause
Figure 6.3
Figure 6.4
165
Therefore, the Cause & Effect diagram and the Cause & Effect matrix can be
combined to determine the most likely causes of variation, after which data
can be collected on these most likely causes to be analyzed in the Analyze
phase to determine whether or not they are the actual causes (this is called
the step from “Trivial Many” to “Vital Few” X’s).
In this case, the Cause & Effect diagram serves as a filter between the
diagram,(a brainstorm result, which often contains 50 or more potential X's),
and the measurement of those X's. In many cases, 50 X's are too many to
collect data from, so this first selection method is needed. If it is possible to
collect data on 50 X's, (possibly with a query from a database) then of
course that is to be preferred.
In some Green Belt projects, or projects where the causes are sufficiently
clear without a hard analysis, the Cause & Effect diagram may lead to
tackling those so-called “Obvious” X's. In the other cases, further analysis
has to be carried out, which means data needs to be collected on those X's
and the associated Y for further analysis in the Analyze phase.
6.2.4 Failure Mode & Effects Analysis (FMEA) A powerful instrument to identify and prioritize causes is the Failure Mode &
Effects Analysis, which is used to map the potential failure of a product or
process, and its effect, in a systematic way before the failures occur. Based
on this insight, the action is determined to prevent the potential failure (or
severity of the effect). The relevant questions here are: What can go wrong?
How? Why? What can we do to avoid it?
For each step in the process, a team looks for potential failure factors,
defects and the effect of the failure. Also, they assess the severity of the
effect, the extent to which the cause of the defect occurs and the possibility
to detect the cause systematically before it occurs are scored. These scores
are multiplied to reach a total score: The Risk Priority Number (RPN), which
indicates the priority of the factors that need to be worked on to reduce the
risk (likelihood or effect). The FMEA can be applied in different phases to
166
establish and rank relationships, for example CTQ in relation to VOC, Y in
relation to CTQ or X in relation to Y.
Figure 6.5 contains an example of an FMEA template with the columns that
need to be filled.
Making an FMEA is a team effort that requires preparation to be successful.
The following instruments can be used in that preparation:
• The process diagram
• Cause & Effect diagram
• Cause & Effect matrix
• Process history
• Process technical procedures
As indicated, the result of an FMEA depends on the goal for which and the
phase in which it is applied. The outcome will be:
FMEA - Failure Mode and Effects Analysis (Product and Process FMEA)
Project: Process or Product Name: FMEA Date (Orig)
Project Leader: Responsible: FMEA Date (Review)
Date: Prepared by:
Process Step
/ Input
Potential
Failure
Mode
Potential
Failure
Effects
S
E
V
E
R
I
T
Y
Potential
Causes
O
C
C
U
R
R
E
N
C
E
Current
Controls
D
E
T
E
C
T
I
O
N
R
P
N
Resp.Actions
Taken
S
E
V
E
R
I
T
Y
O
C
C
U
R
R
E
N
C
E
D
E
T
E
C
T
I
O
N
R
P
N
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
Actions
Recommended
Figure 6.5
167
• A prioritized list of CTQ's (Define phase) and Y's (Measure phase)
• A prioritized list of X's (Analyze phase)
• List of actions to avoid failure modes (Improve phase)
• History of past actions and future activities (Control phase)
The central elements of the FMEA are:
• Mode: different circumstances under which the process step or a
component can fail
• Effect: the consequence when the process step or component fails
• Severity: the severity of the effect of the system failure
These elements are worked out in a team session. The following guidelines
can be used to build an FMEA
1. Write down the different process steps of inputs that could fail in
the first column. (“Process step/input”).
2. Determine the potential failure in the “potential failure mode”
column
3. Write the effect of the failure down in the “potential failure
effects” column
The effects have to be related to the CTQ's from the Define phase
and noticeable by the (internal) customer
4. Determine the severity of the defect in the “SEV” column
The severity is expressed in a score, which is determined by the
team. Table 6.0 can be used to score the severity:
168
Severity Description Score
High Does not meet customer requirements at
all; defect makes process highly inefficient;
causes major problems and delay
5
Medium Can cause customer dissatisfaction; defect
makes process a little less efficient; can
cause problems and delays
3
Low Affects the customer a little bit or not at all;
defect has little or no impact on efficiency
and hardly causes any delay
2
None Has no impact on customer or process 1
5. Write the potential causes of the failure down in the “potential causes”
column. Describe the cause of the failure in terms of something that can
be checked or corrected. Note that one failure may have several causes
6. Determine the frequency with which a failure cause is likely to occur,
the occurrence in the “OCC” column. The frequency is also expressed in
a score. Based on table 6.1, it is can be estimated how often a failure
occurs.
Frequency Estimation of how often a failure cause
occurs compared to how often the
process step is carried out.
Score
Very often 30% 5
Often 5% 4
Sometimes 0,5% 3
Rarely 0,01% 2
Never <0,01% 1
7. Write the existing control mechanisms down in the “current controls”
column
Table 6.0
Table 6.1
169
Give a brief description of the existing controls that have been installed
to prevent or detect the specific failure cause.
8. Assign the detection level in the “DET” column
The detection level is given a score, the guidelines for which are
presented in table 6.2:
Likelihood of the cause being
detected, qualitative
Likelihood of the cause
being detected,
quantitative
Score
There are no checks, no detection Likelihood 0-20% 5
Detection is possible, but unlikely Likelihood 20-40% 4
On average, half of the causes are
detected
Likelihood 40-60% 3
Generally speaking, this cause is
detected
Likelihood 60-90% 2
Causes are nearly always detected Likelihood>90% 1
9. Calculate the Risk Priority Number and write it down in the “RPN”
column
The RPN is calculated as follows: SEV * OCC * DET
10. Rank the RPN column from high to low to order the causes
This generates a prioritized list of X's
11. Generate corrective actions and put them in the “actions
recommended” column
The team needs to generate actions that are aimed at:
- increasing the likelihood of detection
- reducing the frequency
- limiting the severity of failure
Start with the causes at the top of the list. Any corrective action to
remedy those causes will have the biggest impact. When you use a 1-5
scale to score severity, occurrence and detection, the maximum score is
125. A guideline that in most cases was used in the past was that any
Table 6.2
170
scores above 100 needed to be dealt with, while it was also very
desirable to tackle all scores above 80. These days, scores of 10 are
often used, which means that the maximum score is 1000, and 800 and
600, respectively, could be used as guidelines.
12. Assign the action to a person who will be responsible in the “Resp.”
column
In addition, make a plan together to carry out the action.
13. Record which actions have been carried out in the “actions taken”
column of the FMEA
14. Recalculate the RPN after the actions have been carried out. Any action
will always cause one of the three scores (severity, occurrence,
detection) to go down, and in some cases even two of the three.
The FMEA is a living document and a list of priorities for the actions that
need to be carried out to improve a process. After an action has been
carried out, the team will determine the likelihood of detection, the
occurrence and the severity again, the RPN will be recalculated and the list
prioritized again. The cause in question will go down in the ranking and a
different cause will be at the top of the list.
The FMEA is designed to take action before failure occurs and not after a
failure occurred. To make a successful FMEA, representatives of the
departments involved in the process need to take part. Sometimes, experts
on specific subjects need to be involved to make a correct estimate. The
FMEA is a living document that needs to be revised with the team after
every action (or after a series of actions) to set new priorities.
In this phase of the improvement project, the FMEA is an instrument to map
and prioritize causes of variations in Y. The actions that are carried out to
remedy the situation will be discussed in the Improve phase.
171
6.2.5 Data collection X’s In the previous paragraph, we discussed the tools that help map and
prioritize potential causes of variation. The X's were prioritized on the basis
of scores and estimates by the process experts. To gain greater insight into
the X's that cause variation, data will have to be collected wherever possible
with regard to these X's. Part of this data may already have been included in
the Measure phase, where, in addition to Y, stratification X's and possible
input and process X's have also been collected. When there is no data
available yet, the same data collection procedure is used that was used to
collect data on Y. As discussed in paragraph 3.3.1, extend the data collection
plan with a list of prioritized X's you want to examine more closely. The data
you collect can be used to find connections between X and Y in the graphical
analysis.
Sometimes an X is very difficult to measure. Think for instance about the
level of experience of operators. One could try to express this in another
factor, like years working in this role, or the degree of training a person has
had, in order to quantify experience. There is a risk however, since years in a
role and level of training are not the same as experience. In such a case, one
can use the different operators as a (stratification) X. If there appears to be a
clear difference between operators on the process outcome, one can go a
level deeper to investigate what is causing this difference. And if there is no
difference between the operators on the outcome, one can leave this X out
of the project.
172
6.2.6 Graphical data analysis
In determining the Process Capability, an initial analysis was carried out of
the project X data, which may already provide insight into the X's that play a
role in the variation of Y. The following graphical tools can provide clues for
further identifying causes:
Histogram Y data for continuous data
• Several peaks in the histogram can provide indications for subgroups
• When the mean is far removed from the target, this may be a reason to
look for a root cause (X)
• Distribution is too broad for the specifications (low Cp, Cpk) is a reason
to investigate cause
• An abnormal distribution where a normal distribution is expected may
be a reason to examine potential causes in the area of Input or
Stratification X's.
604,8603,2601,6600,0598,4596,8
80
70
60
50
40
30
20
10
0
Mean 600,0
StDev 1,402
N 300
Freq
uen
cy
Histogram of Dimension
Figure 6.6
173
Boxplot
The boxplot provides a quick insight into outliers in our samples. Make sure
no errors have been made in the measurement. There may be a cause X
behind it, from which you can learn what to avoid or why the result was
actually extremely good.
To determine whether discrete stratification X's affect the output of a
continuous Y, the boxplot is also very useful. It visualizes the difference
between groups.
Figure 6.7
174
I-MR chart
An I-MR Chart displays the data of Y in time against the control limits for Y,
revealing the stability of the process. In addition, the I-MR Chart monitors
the variation and displays in red a warning when the data shows a
remarkable trend (for instance, 5 times a measured value that is below
mean or values outside of the control limits).
Remarkable trends, quick fluctuations in the value of Y or shifts of the mean
are reasons to take a closer look and see what is a specific underlying X.
9181716151413121111
605
600
595
Observation
Indiv
idual V
alu
e
_X=600,23
UCL=605,34
LCL=595,12
9181716151413121111
6
4
2
0
Observation
Movin
g R
ange
__MR=1,923
UCL=6,284
LCL=0
6
6
22
22
22
6
1
222
2
2
I-MR Chart of Supplier 2
Figure 6.8
175
Multi vari chart
If you want to map several X's at once for one Y, and it is also possible that
the X's influence each other, the Multi-vary Chart is the most suitable. A
Multi-Vari Chart is not always easy to interpret. One should realize that 2 (or
more) factors are varied simultaneously, 1 on the x-axis (packaging in this
case) and 1 in the legend (region in this case). The symbols represent the
means. The red line connects the means of sales for different types of
packaging. The blue lines with symbols represent the means of Sales per
region, for a given packaging.
Above, we show an example (figure 6.9) with 2 different X's, which, in
Minitab, can be found under “stat>quality tools”.
point of saleplaincolor
1100
1000
900
800
700
600
500
400
packaging
sale
s
1
2
3
region
Multi-Vari Chart for sales by region - packaging
Figure 6.9
176
Pareto chart
The Pareto chart can be used to visualize the most important defects.
Usually, the most important category points to an underlying X. This graph
can also be found in Minitab under quality tools, so not under the graphs!
6.3 Use of instruments The Black Belt or Green Belt leading the project decides which of the
instruments discussed in 6.2 to use. Not every instrument has to be used to
determine the causes. The availability of historical data or the type of
process (administrative or technical) can determine the choice of which
instruments to use. In this phase, a combination of the detailed process
map, the Cause & Effect diagram and Cause and Effect matrix is the most
common.
The detailed process map (or Value Stream Map) is suitable for a process
analysis of almost any administrative or transactional process. The Cause
Count 834 550 337 99
Percent 45,8 30,2 18,5 5,4
Cum % 45,8 76,0 94,6 100,0
Defects Not CompleteWrong Form UsedLateSent to wrong address
2000
1500
1000
500
0
100
80
60
40
20
0
Co
un
t
Perc
en
t
Pareto Chart of Defects
Figure 6.10
177
and Effect diagram can be used for many project types, even if there is no
logical following sequence of steps. (like the different causes for a machine
to have downtime.) In transactional processes the Cause and effect Diagram
is often combined with a detailed process map. The FMEA is mostly used for
a thorough analysis of technical processes and highly automated processes.
This last-mentioned tool is often used in “incident driven” problems, even
apart from Six Sigma project. It is a mandatory part of an 8D problem solving
analysis. And also with rarely occurring problems, where the use of
statistical methods, as described in the following chapters, cannot be used
due to a lack of data.
If it is not possible to achieve the desired result (list with potential X's) with
these instruments, additional instruments can be used. The initial analysis
may indicate that insufficient data has been collected to be able to map the
(root) causes. In that case, additional data needs to be collected and we
return to the Measure phase.
178
6.4 Exercises
Cause & Effect diagram
Make a Cause & Effect Diagram in Minitab for at least 8 X's that potentially
contribute to the Y (of your project).
Make sure to use at least 4 of the following categories:
(People, Material, Machines, Method, Measurement and Environment)
Fill in the Y and X's in Minitab and present the diagram to the class.
Cause & Effect matrix
In teams of 2, make a Cause & Effect Matrix in Excel for the X's and Y of the
previous exercise.
Use the Cause & Effect template you have received digitally
179
Graphs
What are the graphs presented below called and what is their purpose?
# Name Purpose
A
B
C
D
E
180
181
CHAPER 7: DETERMINING THE ROOT
CAUSES
7.1 Introduction In chapter 6, we mapped the potential causes of the variation in output Y. In
this chapter, we identify the root causes, based on the data we collected. In
preparation for this chapter, we recommend that you first read appendix 3
about Hypothesis testing.
In the following paragraphs, we discuss the procedure to identify the root
causes in greater detail. In addition, we provide guidelines for using the
correct statistical tests. The result of this step is to determine which of the
potential X’s are the vital x’s that will be tackled in the remainder of the
project. Also, it determines which trivial X’s will not be tackled.
7.2 From potential causes to root causes Figure 7.0 shows the procedure that is followed to reduce the list with
potential causes to the root causes.
182
Figure 7.00
183
In this chapter, the focus is on selecting and executing the right test to verify
your hypotheses.
7.3 Hypothesis Testing
7.3.1 Selecting the tests Statistical tests are used to demonstrate a relationship between an
influence factor X and the performance of the process-output Y. There are
various statistical tests. Which is the right one to use depends on the type of
data of X and Y.
Figure 7.0 contains the most commonly used combinations of X and Y, with
the associated tests. Next to above tests, we also deal with testing for
normality in Minitab Assistant under “Graphical Analysis” and Regression for
testing a continuous Y and X under “Regression”.
Figure 7.0
184
7.3.2 Normality test The normality test is used to see whether a data set is normally distributed.
This is important because it makes the analysis more powerful. The
normality test looks at the following items:
AB: the data is normally distributed
A�: the data is not-normally distributed
If P < 0.05, the data is not-normally distributed, with a 95% probability. For
example, a data set of the height of participants of a training course (figure
7.1). This yields the following result:
In Minitab: Stat -> Basic Statistics -> Normality test
Figure 7.1
185
The result is as follows:
P > 0.05, which means that the data is normally distributed.
The Y-axis of the graph shows the normal distribution as a percentage. 50%
is in the middle, and the extremes are furthest removed from that. Using
this scale, a straight line is created when the distribution is normal (this is
the so-called “fat pencil test”). In Minitab 17 and higher the same conclusion
is being drawn by using the Assistant (“normality test: pass”): Assistant ->
Graphical Analysis -> Graphical summary.
205200195190185180175170
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean 184,9
StDev 6,775
N 12
AD 0,175
P-Value 0,901
Height
Per
cen
t
Probability Plot of HeightNormal
Figure 7.2
186
7.3.3 1 Sample t-test
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 1 2 Mean against
specification
The one-sample t-test is used to test a mean against a specification. The test
can be carried out in a two-sided way (which is the default setting), with the
following hypotheses:
HB: µ = µB
HE: µF ≠ µB
Maximum 196
N 12Mean 184,92
StDev 6,7751Minimum 1725th percentile *
25th percentile 180Median 184
75th percentile 19095th percentile *
Descriptive Statistics
Mean (180,61; 189,22)Median (180,05; 190)
StDev (4,7994; 11,503)
95% Confidence Intervals
Decision PassP-value 0,901
Normality Test
200195190185180175170
190
180
170121086420
leng
te
Distribution of DataExamine the center, shape, and variability.
Data in Worksheet OrderInvestigate any outliers (marked in red).
Graphical Summary of lengteSummary Report
Table 7.0
Figure 7.3a
187
Or it can be carried out in a one-sided way:
HB: µ ≤ µB (or HB: µ ≥ µB)
HE: µ > µB (or HE: µ < µB)
In the example presented below, lamps are tested against the specification
of the supplier. The supplier indicates that they burn for 750 hours. Four
lamps are tested. The results are:
748.24 hours, 743.08 hours, 759.78 hours, 742.30 hours
Minitab: Assistant -> Hypothesis tests ->1 sample t-test
The result is:
In this case, we look at the Confidence Interval. We can say with 95%
certainty that the actual value of life expectancy of the lamps lies between
Sample size 4Mean 748,35
95% CI (735,52; 761,18)Standard deviation 8,0629Target 750
Statistics
0,05).The mean of hours is not significantly different from the target (p >
Yes No
0 0,05 0,1 > 0,5
P = 0,710
760750740
750
results.target. Look for unusual data before interpreting the test
• Distribution of Data: Compare the location of the data to thetrue mean is between 735,52 and 761,18.mean from sample data. You can be 95% confident that the• CI: Quantifies the uncertainty associated with estimating themean differs from 750 at the 0,05 level of significance.
• Test: There is not enough evidence to conclude that the
Does the mean differ from 750?
Distribution of DataWhere are the data relative to the target?
Comments
1-Sample t Test for the Mean of hoursSummary Report
Figure 7.3b
188
732.52 and 761.18 hours. 750 hours lies within the Confidence Interval,
which means that the lamps match the specification.
The follow-up question: when can we conclude that a batch of lamps -of
which we tested 4 samples, does not match the specs? This can be
calculated in the following way in Minitab and depends on the power of the
test (see also appendix 3). In the Diagnostic Report Minitab indicates what
differences give what significance level of the power (with 4 lamps).
If we also know the standard deviation of the life expectancy, we can also
make an estimate of the required sample size for a given difference. An
alternative route for this is via Stat -> Power and Sample size -> 1-sample t-
test
7.3.4 2 sample t-test
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 1 2 Mean of two
samples
Figure 7.3c
Table 7.2
189
The 2-sample t-test is used to compare the means of two samples. One
sample is compared to the other to determine whether or not they are
equal (two-sided) or whether one mean is higher than the other (one-sided).
HB: µF = µ�
HE: µF ≠ µ�
HB: µF ≤ µ� (or HB: µF ≥ µ�)
HE: µF > µ� (or HE: µF < µ�)
An example could be the life-time of two lamps of different brands, in which
case the hypothesis is:
HB: µF = µ�
HE: µF ≠ µ�
This is a two-sided test.
In the example presented below, we see whether there is a difference in the
lead time of filling a job vacancy during the “summer”, as compared to the
“rest of the year”. The test can be carried out via:
Minitab: Assistant -> Hypothesis test -> 2 sample t-test
190
The “Sample IDs”-field provides the column on the basis of which the 2
samples are separated. In this case, Summer is either “on” or “off”. We look
to see whether there is a difference between “on” (summer) and “off”
(normal). The results are shown in figure 7.5.
Individual Samples
Sample size 180 60
Mean 17,118 21,212 95% CI (16,33; 17,91) (19,717; 22,707)
Standard deviation 5,3803 5,7872
Statistics normal summer
Difference Between Samples
Difference -4,0933
95% CI (-5,7767; -2,4099)
Statistics *Difference
32282420161284
normal
summer
summer (p < 0,05).The mean of normal is significantly different from the mean of
Yes No
0 0,05 0,1 > 0,5
P < 0,001
0,0-1,5-3,0-4,5-6,0
Look for unusual data before interpreting the results of the test.
• Distribution of Data: Compare the location and means of samples.that the true difference is between -5,7767 and -2,4099.difference in means from sample data. You can be 95% confident
• CI: Quantifies the uncertainty associated with estimating the
significance.• Test: You can conclude that the means differ at the 0,05 level of
Distribution of DataCompare the data and means of the samples.
Do the means differ?
95% CI for the Difference
Is the entire interval above or below zero?*Difference = normal - summer
Comments
2-Sample t Test for cycle time by Season on/offSummary Report
Figure 7.4
Figure 7.5
191
P < 0.05, which means that hypothesis H0 is rejected, which can also be
concluded from the Confidence Interval for the difference, which indicates
that the difference between the two means lies between -5.777 and -2,410.
Both numbers are negative, so there is a difference (which is also the case
when both numbers are positive). If 0 falls within the Confidence Interval,
we cannot say with 95% certainty that there is a difference between the two
means. In this example the cycle time in summer is longer than in “normal”
season. Another important output-tab that is being generated is the Report
Card. In the tab is being checked if the sample size was sufficient and if the
sample is normally distributed, therefore: always check the report card!
7.3.5 2-sample Standard Deviation test
Y data type X data
type
Number
X’s
Number of
subgroups
Application
Continuous Discrete 1 2 Variance of 2
samples
The 2-sample standard deviation test is used to compare the standard
deviations of 2 samples. The one sample is compared to the other to assess
if they have equal spread (two-sided) or that the one spread is larger than
the other.
HB: σF = σ�
HE: σF ≠ σ�
HB: σF ≤ σ� (or HB: σF ≥ σ�)
HE: σF > σ� (or HE: σF < σ�)
For example: comparing the variation in the life-time of 2 different brands of
lamps. The hypothesis in this case is:
Table 7.3
192
HB: σF = σ�
HE: σF ≠ σ�
This is the 2-sided test.
In the previous example we compared the average lead-time to fulfill a
vacancy comparing summer to normal (in worksheet: Position fill cycle
time.mtw).
Now we can take the same dataset to compare the standard deviations. The
test can be found via:
Minitab: Assistant -> Hypothesis test -> 2 sample standard deviation
Figure 7.6
193
We assess if there is a difference in the spread of the lead-time between
summer and normal (so the other seasons). The results are shown in figure
7.7.
The P-value for the test is >0.05. So H0 is being accepted. The lead-time in
summer has not a significant different spread than the other seasons.
7.3.6 Paired t-test
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 1 2 Means of pairs
of two samples
The paired t-test is used when the objects that have to be measured already
exist in pairs. For example, to compare two measuring methods for the
Sample size 180 60
Mean 17,118 21,212Standard deviation 5,3803 5,7872 Individual 95% CI (4,891; 5,984) (5,031; 6,882)
Statistics normal summer
32282420161284
normal
summer
summer (p > 0,05).The standard deviation of normal is not significantly different from
Yes No
0 0,05 0,1 > 0,5
P = 0,436
summer
normal
6,56,05,55,0
for unusual data before interpreting the results of the test.
• Distribution of Data: Compare the spread of the samples. Lookdeviations do not differ significantly.• Comparison Chart: Blue intervals indicate that the standardstandard deviations differ at the 0,05 level of significance.
• Test: There is not enough evidence to conclude that the
Distribution of DataCompare the spread of the samples.
Do the standard deviations differ?
Standard Deviations Comparison ChartBlue indicates there is no significant difference.
Comments
2-Sample Standard Deviation Test for cycle time by Season on/offSummary Report
Table 7.4
Figure 7.7
194
same sample, for instance when online measurements are compared to lab
measurements for the same samples.
The example we present here involves a comparison of the ease of parking
of two cars. It is better to let the same person park both cars in the same
situation than to have different persons parking one of the cars. The time it
takes to park the cars is measured for both cars for each situation.
The hypotheses:
HB: µF = µ�
HE: µF ≠ µ�
Minitab: Assistant -> Hypothesis tests -> paired t test
Figure 7.8
195
The histogram shown above is based on the 20 values you get by looking at
the differences in parking time for the 2 cars in each situation. So, it displays
the differences Minitab calculated between car 1 and car 2. Based on the
sample, the confidence interval for the difference can be calculated for the
entire population (on which we can base the more general statement).
Because “0” is not part of the confidence interval for the differences (“0” is
just outside), we may say that with a more than 95% confidence the
difference in parking times is not equal to “0”. The same conclusion can be
drawn from the P-value of 0.034.
Paired Differences
Sample size 20Mean 1,9674 95% CI (0,17075; 3,7641)
Standard deviation 3,8389
Statistics Differences
*Paired
Individual Samples
Mean 34,868 32,900
Standard deviation 7,5907 7,2847
Statistics Car_A Car_B
(p < 0,05).
The mean of Car_A is significantly different from the mean of Car_B
Yes No
0 0,05 0,1 > 0,5
P = 0,034
10,07,55,02,50,0-2,5-5,0-7,5
0
interpreting the results of the test.differences to zero. Look for unusual differences before• Distribution of Differences: Compare the location of the
that the true mean difference is between 0,17075 and 3,7641.mean difference from sample data. You can be 95% confident• CI: Quantifies the uncertainty associated with estimating thethan zero.of significance. The mean of the paired differences is greater
• Test: You can conclude that the means differ at the 0,05 level
Do the means differ?
*Difference = Car_A - Car_B
Distribution of the DifferencesWhere are the differences relative to zero?
Comments
Paired t Test for the Mean of Car_A and Car_BSummary Report
Figure 7.9
196
7.3.7 1-sample % defective test (1-Proportion test)
Y data
type
X data
type
Number
of X’s
Number of
subgroups
Application
Discrete Discrete 1 1 Comparing a fraction
(proportion) with a
given boundary
Like the 1-sample t-test, the 1-sample % defective test compares a sample
and a given limit. In the case of the 1-sample t-test, we are dealing with
continuous data. In the case of the 1-sample % defective test, we are dealing
with discrete data in the form of proportions (% wrong). The proportion is
indicated with “p” (lower case p, in contrast to the upper-case P (for
Probability) that we will examine at the end of the test to accept or reject
the Null hypothesis). The 1-sample % defective test is used with hypotheses
about the fraction wrong. No data set is needed. Only the size of the sample
and the number of 'wrong' (is equal to the size of the sample minus the
number of 'right'). What is important when using a 1-sample % defective
test is the Confidence Interval, which in this case is based on the binominal
distribution. This Confidence Interval in turn indicates what we can say
about the fraction of the entire population based on the sample. The test
can be carried out one-sided or two-sided.
One-sided
HB: p ≤ pB (or HB: p ≥ pB)
HE: p > pB (or HE: p < pB)
Two-sided
HB: p = pB
HB: p ≠ pB
Table 7.5
197
In the example presented below, we discuss a one-sided test.
A clerk claims that fewer than 4% of his invoices are defect (i.e. contain a
mistake). We take a random sample of the invoices to determine what the
fraction of defective invoices is. The hypotheses are:
HB: p ≤ 4%
HE: p > 4%
400 invoices have been checked and 24 of them were wrong. Should the
clerk's claim be accepted or rejected? The fraction of the sample is 6%.
However, the Confidence Interval over the entire population is decisive
when it comes to accepting or rejecting the claim.
Minitab: Assistant -> Hypothesis Tests -> 1-Sample % Defective test
Figure 7.10
198
The result of the one-sided test:
This means that, after conducting a one-sided test, the Null hypothesis has
to be rejected, because there are significantly more than 4% errors. The
Confidence Interval for the number of errors has a lower limit of 4.17%,
which means that the claim that only 4% are wrong falls outside of the
Confidence Interval.
If we were to conduct a two-sided test, the result would be different(!)
Total number tested 400Number of defectives 24
% Defective 6,00 90% CI (4,17; 8,33)Target 4
Statistics
(p < 0,05).The % defective of Invoices is significantly greater than the target
Yes No
0 0,05 0,1 > 0,5
P = 0,034
87654
4
95% confident that it is greater than 4,17%.
that the true % defective is between 4,17% and 8,33%, andthe % defective from sample data. You can be 90% confident• CI: Quantifies the uncertainty associated with estimating
4% at the 0,05 level of significance.
• Test: You can conclude that the % defective is greater than
Is the % defective greater than 4%?
90% CI for % DefectiveIs the entire interval above the target?
Comments
1-Sample % Defective Test for InvoicesSummary ReportFigure 7.11
199
The Confidence Interval (CI) indicates that the fraction for the entire
population of invoices of this clerk lies between 3.888% and 8.796%, which
means that there is (just about ) insufficient reason to reject his claim. Based
on this sample, he is right. We see here that the 1-sided test in such a
questionable situation faster leads to a significant conclusion (reject H0)
than the 2-sided test. This rule counts for all tests with discrete X’s.
7.3.8 2-sample % defective test (2-proportions
test)
Y data
type
X data
type
Number of
X’s
Number of
subgroups
Application
Discrete Discrete 1 2 Comparing two
fractions
Total number tested 400Number of defectives 24
% Defective 6,00 95% CI (3,88; 8,80)Target 4
Statistics
target (p > 0,05).The % defective of Invoices is not significantly different from the
Yes No
0 0,05 0,1 > 0,5
P = 0,074
864
4 that the true % defective is between 3,88% and 8,80%.the % defective from sample data. You can be 95% confident• CI: Quantifies the uncertainty associated with estimatingdefective differs from 4% at the 0,05 level of significance.
• Test: There is not enough evidence to conclude that the %
Does the % defective differ from 4%?
95% CI for % DefectiveIs the entire interval above or below the target?
Comments
1-Sample % Defective Test for InvoicesSummary Report
Figure 7.12
Table 7.6
200
The 2-sample % defective test compares two fractions to determine
whether they are equal or different (i.e. a two-sided test) or whether the
one is smaller than the other (one-sided).
Hypotheses for the two-sided test:
HB: pF = p�
HE: pF ≠ p�
Hypotheses for the one-sided test:
HB: pF ≤ p� (or HB: pF ≥ p�)
HE: pF > p� (or HE: pF < p�)
Example
You want to know if some of the consumers sending back a questionnaire
can be influenced by sending them a small present along with the
questionnaire. The present is sent along with half of the questionnaires to
determine whether it works. 200 questionnaires are sent out, 100 with the
present, 100 without it. 78 of the people who were sent a present returned
the questionnaire, so 22 defects. Of the people without present only 54
were returned So 46 defects.
This is a two-sided test, so the option that the present may have an adverse
effect is left open:
HB: pF = p�
HE: pF ≠ p�
Minitab: Assistant -> Hypothesis Tests -> 2-sample %
201
The result:
The P-value (P < 0.001) is smaller than 0.05 and the Confidence Interval
indicates that there is a difference, because “0” does not fall within the
interval. This means that sending a present makes a difference.
Individual Samples
Total number tested 100 100
Number of defectives 22 46% Defective 22,00 46,00
95% CI (14,33; 31,39) (35,98; 56,26)
Statistics with sample without samp
Difference Between Samples
Difference -24,00
95% CI (-36,70; -11,30)
Statistics *Difference
the % defective of without samp (p < 0,05).The % defective of with sample is significantly different from
Yes No
0 0,05 > 0,5
P < 0,001
200-20
0
difference is between -36,70% and -11,30%.
difference from sample data. You can be 95% confident that the true• CI: Quantifies the uncertainty associated with estimating the
of significance.• Test: You can conclude that the % defective differs at the 0,05 level
Do the % defectives differ?
95% CI for the DifferenceIs the entire interval above or below zero?
*Difference = with sample - without samp
Comments
2-Sample % Defective Test for with sample vs without sampSummary Report
Figure 7.13
Figure 7.14
202
7.3.9 Analysis of Variance (ANOVA) One Way
Y data type X data
type
Number
or X’s
Number of
subgroups
Application
Continuous Discrete 1 2+ Testing whether there is
a significant influence of
stratification factors on Y
The one-way ANOVA is applied to determine whether discrete stratification
factors affect Y. Examples of factors are: seasons, departments, locations,
product types. With these factors we divide the data set into subgroups.
ANOVA is supported by graphical analyses in Minitab. ANOVA compares the
Y means of the different groups to each other.
The hypotheses are always 2-sided:
HB: µF = µ� = µ@ =… (there are no differences between the means of the
different groups)
HE: µF or µ� or µ@ …≠ µF or µ� or µ@ … (at least 1 mean is different from the
others)
When conducting a one-way ANOVA, stick to the following procedure:
1. Describe the problem you want to investigate
2. Determine the Null & Alternative hypothesis
3. Check:
- the independence (is it a random sample)
- check if there are deviating measurement results (“unusual data”)
- whether the sample is sufficiently large (guideline for number per
group is at 15, the assistant in Minitab gives a warning under 15
measurements per group)
- Check whether the distribution of the subgroups is normal
4. Generate ANOVA graphs and output
5. Draw conclusions
Table 7.7
203
Example
1. Problem description:
determine whether the season has a significant impact on the
number of days it takes to fill a job vacancy
2. The Hypotheses:
HB: there is no difference in the average number of days it takes to fill a job
vacancy per season
HE: there is a difference in the average number of days it takes to fill a job
vacancy per season
3. Checks
There is a random sample. We check the sample size and variation with
the ANOVA results. To check for a normal distribution of the subgroups,
we conduct a normality test via: Graph > Probability Plot > Multiple:
All 4 P-values are > 0.05: the data of the subgroups is distributed normally,
Generate ANOVA output
Minitab: Assistant -> Hypothesis Tests -> one-way ANOVA
403020100
99,9
99
95
90
80
7060504030
20
10
5
1
0,1
16,40 5,006 60 0,529 0,170
16,85 5,275 60 0,143 0,969
21,21 5,787 60 0,369 0,417
18 ,11 5,774 60 0,546 0,154
Mean StDev N AD P
cycle time
Perc
en
t
autumn
spring
summer
winter
Season1-4
Probability Plot of cycle timeNormal - 95% CI
Worksheet: POSITION FILL CYCLE TIME.MTW
Figure 7.15
204
Results:
Which means differ?
1 autumn 4
2 spring 43 winter 44 summer 1 2 3
# Sample Differs from
Differences among the means are significant (p < 0,05).
Yes No
0 0,05 0,1 > 0,5
P < 0,001
summer
winter
spring
autumn
22,520,017,515,0
practical implications.Consider the size of the differences to determine if they havenot overlap to identify means that differ from each other.• Comparison Chart: Look for red comparison intervals that do
means at the 0,05 level of significance.• Test: You can conclude that there are differences among the
Do the means differ?
Means Comparison ChartRed intervals that do not overlap differ. Comments
One-Way ANOVA for cycle time by Season1-4Summary Report
Figure 7.16
Figure 7.17
205
5. Draw conclusions
In both graphs, we see that the summer stands out. The question is whether
the summer is significantly different. The results show that P < 0.05: the H0
is rejected: there is at least one season where the mean lead time is
significantly different from the other seasons. The plot with the Confidence
Intervals, shows that the mean for summer is different from that for the
other seasons. When the CI of the individual factors (seasons) overlap, there
is no significant difference (as is the case with spring, autumn and winter).
When there is no overlap, there is a significant difference (like with
summer).
Minitab also provides a Report Card for checking the boundary conditions
for ANOVA:
- Unusual data: an outlier has been detected. Check if this is no
measurement error.
- Number of data points (N=60 for each subgroup) is sufficient.
- Equal variances: as of Minitab 17 an alternative method (Welch’s
method) is being used, allowing for unequal variances
These checks are performed automatically in figure 7.18:
The outlier that is mentioned under “Unusual Data” can be found in the data
of figure 7.19, which is also generated:
Figure 7.18
206
7.3.10 Standard Deviations Test Where one-way ANOVA compares the means of more than 2 subgroups, this
test does the same for the standard deviations of the subgroups. Especially
for Six Sigma projects, where we reduce the variation in a process, this can
be a useful test. Conducting the test is easiest using the Assistant.
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 1 2+ Testing whether
the variation in the
stratification
factors influence Y
30
15
0
30
15
0
30
15
0
30
15
0
autumn
spring
summer
winter
3224168
autumn
spring
summer
winter
Data in Worksheet OrderInvestigate any outliers (marked in red).
Distribution of Data
Compare the location and spread.
One-Way ANOVA for cycle time by Season1-4Diagnostic Report
Figure 7.19
Table 7.8
207
Doing the test is analogous to ANOVA. The main difference is the conclusion
of the test (by the P-value) that indicates whether the differences in the
variation of the subgroups are equal (null hypothesis) of different
(alternative hypothesis).
The conclusion is also displayed by the Assistant.
Figure 7.20
208
7.3.11 Analysis of Variance (ANOVA) Two Way
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 2 2+ Testing whether
stratification
factors influence Y
or each other
The two-way ANOVA (which until MINITAB 16 could be found as a separate
item in the menu structure) in principle, does the same thing as the one-way
ANOVA, but for two different X's at the same time. In the following example,
both the region and the type of packaging are examined as an X (factor) with
revenue as output (Y). The assistant in Minitab only provides the most
commonly used tests, which does not include the two-way ANOVA, for
which you must use the menu. In Minitab 17 this test can only be performed
using the General Linear Model in the ANOVA menu.
Which standard deviations differ?
1 autumn2 spring
3 summer None Identified4 winter
# Season1-4 Differs from
Differences among the standard deviations are not significant (p > 0,05).
Yes No
0 0,05 0,1 > 0,5
P = 0,692
winter
summer
spring
autumn
7654
significantly.
• Comparison Chart: Blue intervals indicate that the standard deviations do not differstandard deviations at the 0,05 level of significance.• Test: There is not enough evidence to conclude that there are differences among the
Do the standard deviations differ?
Standard Deviations Comparison ChartBlue indicates there are no significant differences. Comments
Standard Deviations Test for cycle time by Season1-4Summary Report
Table 7.7
Figure 7.21
209
Minitab 16: Stat -> ANOVA -> Two Way
Minitab 17 and later: Stat -> ANOVA -> General Linear Model -> Fit General
Linear Model, then, under “Model…” add the interaction term, by selecting
“Region” and “Packaging” in the “Terms” box and click: “Add”.
The two-way Boxplot can only be produced separately via: Graphs, Boxplot,
one Y with Groups. Under Data View one can add the “Mean Connect Line”
and one can indicate that “Region” is an attribute (i.e. discrete) variable.
region
packaging
321
point o
f sal
epla
in
colo
r
point o
f sa le
plain
colo
r
point o
f sal
epla
in
colo
r
1200
1000
800
600
400
200
sale
s
Boxplot of sales
Worksheet: 2way anova example.MTW
Figure 7.22a
210
The interpretation of the results is similar to the one-way ANOVA, but the
two-way ANOVA also provides a P-value for the interaction between the two
X's (region and packaging). The Null hypothesis here is: there is no influence,
so there is no interaction. Given that P = 0 for the interaction, there is
interaction between region and packaging. This means that certain types of
packaging perform better in certain regions than other types in those
regions, and that other regions prefer a different type of packaging.
7.3.12 Kruskal-Wallis test
Y data type X data
type
Number
of X’s
Number of
subgroups
Application
Continuous Discrete 1 2+ Comparing
medians
The Kruskal-Wallis test is applied to continuous data that is not normally
distributed . Instead of the means, the medians are compared to each other.
In addition, to the Kruskal-Wallis test, there are more tests for subgroups
with a non-normal distribution. Although we will not discuss them in this
book, we list them below:
Table 7.10
Figure 7.22b and 7.22c
211
• 1-Sample sign
• 1-Sample Wilcoxon
• Mann-Whitney
• Mood’s Median Test
• Friedman
As mentioned above, we limit ourselves to the Kruskal-Wallis test. The
hypothesis is formulated as follows:
HB: MF = M� = M@ =… (there are no differences between the medians of the
groups)
HE: MF or M� or M@ …≠ MF of M� of M@ … (the median of at least one group
is different from the others)
Example 1
Four sales departments use four different sales techniques. The question is
whether one of the techniques is more effective than the others. See also
Minitab Worksheet: Kruskal-Wallis-Example.mtw
Minitab: Stat -> Nonparametrics -> Kruskal-Wallis
Result:
Figure 7.23
212
Interpreting the results:
P > 0.05, which means that H0 has to be accepted. There is no significant
difference between the four methods. In the column with the Z-values you
can observe the degree to which the subgroups differ from each other. The
rule-of-thumb is that if the Z-value of 2 subgroups differs more than 3, these
subgroups differ significantly from each other. In the example, the highest Z-
value equals 1,11 and the lowest -1,19. So the difference is only 2,30. Hence
the test is not significant (P-value=0,565). In this case checking the P-value is
sufficient.
Example 2
Is there a difference in the growth of plants with different treatments? See
Minitab worksheet: Kruskal-Wallis exercise.mtw
Three types of treatment are compared. Because medians are being
compared, the boxplot helps provide insight into the differences.
Below the result:
213
In this example, H0 is rejected, because P < 0.05. So, there is a significant
difference between the various treatments.
Besides Kruskal-Wallis there are also other tests for non-normally
distributed data. These tests are called “Distribution free”. Below you can
find the overview of tests that can be applied as an alternative to the
normally distributed tests.
321
17
16
15
14
13
12
Treatment
Gro
wth
Boxplot of Growth
Worksheet: Kruskal Wallis Exercise.MTW
Figure 7.24
214
Distribution-free test Normally distributed test
1-sample Sign 1-sample t (asymmetric distribution)
1-sample Wilcoxon 1-sample t (symmetric distribution)
Mann-Whitney 2-sample t
Kruskal-Wallis 1- way ANOVA
Friedman 2-way ANOVA
7.3.13 Chi-square test
Y data
type
X data
type
Number
of X’s
Number of
subgroups
Application
Discrete Discrete 1 2+ Comparing
proportions
Whilst the ANOVA is for means, the Chi-square test is for % defectives.
When more than 2 subgroups need to be compared on % defective Chi-
square % defective is applied. The hypothesis:
HB: pF = p� = p@ =… (there are no differences between the proportions of
the subgroups)
HE: pF of p� of p@ …≠ pF of p� of p@ … (at least one proportion of a subgroup
is different from the others)
To carry out the test, there is the sample size and the number of defectives.
You need at least 5 defectives and 5 non-defectives to carry out the test.
Example
Five different clerks make invoices. Wherever people are working, they
make mistakes. In this case mistakes are made in the invoices. Every mistake
is a defect. Below, the summarized results for the 5 clerks:
Table 7.12
Table 7.11
215
Minitab: Assistant -> Hypothesis Tests -> Ch-Square % (use the columns
“Total” and “defects”). Use Minitab worksheet :ChiSquare_Example.mtw.
Figure 7.25
Figure 7.26
216
This provides the P-value of 0,285. So, P > 0.05, which means we have to
accept H0: There is no difference between the clerks with this number of
errors and invoices
Which % defectives differ?
1 Louise2 Joe
3 Donna None Identified
4 Mary5 Sid
# X Differs from
Differences among the % defectives are not significant (p > 0,05).
Yes No
0 0,05 0,1 > 0,5
P = 0,285
Sid
Mary
Donna
Joe
Louise
1612840
significantly.• Comparison Chart: Blue intervals indicate that the % defectives do not differdefectives at the 0,05 level of significance.• Test: There is not enough evidence to conclude that there are differences among the %
Do the % defectives differ?
% Defectives Comparison ChartBlue indicates there are no significant differences. Comments
Chi-Square % Defective Test for Test Items by XSummary Report
Figure 7.27
Figure 7.28
217
The Report Card of the Assistant states that the test is valid, by checking if
all requirements for the test are met. However, it mentions that adding
more data could lead to a different result where the different groups would
be significantly different. But with this (small) data set it is not significantly
different.
Comparing proportions with a nominal or ordinal response across different
groups
The Chi-square test can also be applied to a nominal or ordinal response
across different subgroups, which we explain on the basis of an example.
Three warehouse employees have taken a sample and determined how
many mistakes they have made (over comparable quantities of work!) of
different types. We want to test whether the mix of different types of errors
is different for each employee. X is the employee, Y is the type of error. Use
worksheet: Chi2 Exercise.mtw.
HB: there are no differences in the mixes in Y
HE: there are differences in the mixes in Y
Figure 7.29
218
Again, the assistant is the preferred way to perform this test:
“Assistant > Hypothesis Tests > Chi Square Test for Association”. One can
type in data or select “get from current worksheet”. Select with the
different drop down arrows the right columns, and if needed adapt the
number of rows or columns to the situation in the worksheet.
Figure 7.30
Figure 7.31
219
The results are as follows:
P = 0.048, which means it is just below 0.05, which means that H0 has to be
rejected. There is a difference in the mix of the errors. In the figure to the
right, you can see that operator A produces far fewer “wrong docs” and far
more “damaged”. The bottom right figure is actually a kind of Pareto chart,
but with positive and negative bars. The expectation (null hypothesis) is that
all persons do it the same, so have the same mix of errors. The bars to the
left indicate that a person has made fewer mistakes than expected (i.e. if
they all performed equally well or badly), and the bar to the right means
more errors have been made than expected. This leads to the improvement
option of putting operators A and B in the same room, so they can learn
from each other: A can teach B how to make documents, while B can teach
A how not to damage them (Damaged scores high with A and low with B).
In addition to the outcome presented in figure 7.32, Minitab also provides
the following results:
conclude there is an association between Outcomes and operator.
Differences among the outcome percentage profiles are significant (p < 0,05). You can
Yes No
0 0,05 0,1 > 0,5
P = 0,048
Operator C
Operator B
Operator A
Average
48%36%24%12%0%
Late
Wrong Quanti
Damaged
WrongDocs
difference between observed and expected counts.
• % Difference Chart: Look for long bars to identify outcomes with the greatest %
the average profile.• Percentage Profiles Chart: Use to compare the profile for each value of operator andprofiles at the 0,05 level of significance.
• Test: You can conclude that there are differences among the outcome percentage
Operator C
Operator B
Operator A
50%25%0%-25%-50%
Late
Wrong Quanti
Damaged
WrongDocs
24%
20%
31%
24%
24%
11%
45%
20%
9%
25%
37%
28%
19%
19%
38%
24%
Do the percentage profiles differ?
Percentage Profiles ChartCompare the profiles.
Comments
Expected Counts
% Difference between Observed and
Positive: Occur more frequently than expected Negative: Occur less frequently than expected
Chi-Square Test for Association: Outcomes by operatorSummary Report
Figure 7.32
220
In addition to what has been measured (“Observed”), the table also
indicates what was expected (“Expected”) , based on average % of mistakes
by type and number of defects found.
Note: Be aware that the data has to be about the same amount of work for
the different operators.
The Report card also checks the sample size and the “expected” value, to
see whether that is sufficient, it should be > 2.
7.3.14 Binary Fitted Line Plot
Y data
type
X data type Number
of X’s
Number of
subgroups
Application
Binary Continuous 1+ 2+ Influence of
continuous X’s on
the binary Y
Figure 7.33
Figure 7.34
Table 7.13
221
Binary Fitted Line Plot (BFLP) is used when the Y data can only have two
possible outcomes and the X is continuous. Examples of Y: right/wrong,
passed/failed, answered/not answered, works/is broken. The goal of this
test is to determine whether or not the continuous input (X) contributes
significantly and is able to predict a certain outcome of Y. The BFLP also
quantifies the impact of X as Yes or No for Y. The hypothesis:
HB: X has no influence on the outcome yes/no of Y
HE: X has an influence on the outcome yes/no of Y
The procedure that is followed with BFLP:
1. Organize your Y-data in a column with a binary outcome
(passed/failed, 0/1, go/no go)
2. Plot the data using Binary Fitted Line Plot (in Minitab)
3. Analyze the outcome
- is there an S (or Z) curve
- what is the equation to determine the outcome Y from X
- what is the P-value?
- calculate the probability of success
Example
We investigate the influence of the time spent on the intake of cases in a
call center. A case can either be filled in correctly or not. From several cases
the minutes spent have been recorded, as well as the result, being right or
wrong. The worksheet you need is: Binary Log Regression_EN.mtw
Plotting the data as well as finding the fit of the model and the analysis if
there is a significant impact of X on Y is done via:
Minitab: Stat -> Regression -> Binary Fitted Line Plot
222
6050403020
1,0
0,8
0,6
0,4
0,2
0,0
Minutes spent
Pro
bab
ilit
y o
f Ev
ent
Binary Fitted Line PlotP(Right) = exp(-7,77 + 0,316 Minutes spent)/(1 + exp(-7,77 + 0,316 Minutes spent))
Figure 7.35
Figure 7.36
223
We are looking for an S-shaped (or Z-shaped) curve to see whether there is a
shift from wrong to right at a certain number of minutes spent on the case.
In this case it is clearly visible.
It turns out there is a transition point from where spending enough minutes
on the case helps the registration to be correct. We will verify this using the
BFLP output from the Output Pane.
Binary Fitted Line: Right/Wrong versus Minutes spent
Method Link function Logit
Rows used 20
Response Information Variable Value Count
Right/Wrong Right 13 (Event)
Wrong 7
Total 20
Deviance Table Source DF Adj Dev Adj Mean Chi-Square P-Value
Regression 1 15,40 15,3984 15,40 0,000
Minutes spent 1 15,40 15,3984 15,40 0,000
Error 18 10,50 0,5833
Total 19 25,90
Model Summary
Deviance
R-Sq
Deviance
R-Sq(adj) AIC
59,46% 55,60%
14,50
Coefficients
Term Coef SE Coef VIF
Constant -7,77
3,61
Minutes spent 0,316
0,150 1,00
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI
Minutes spent 1,3712 (1,0227; 1,8385)
Regression Equation
P(Right) = exp(-7,77 + 0,316 Minutes spent)/(1 + exp(-7,77 + 0,316 Minutes spent))
224
This yields a host of outcomes. We will explain the most important ones. The P-value
that is provided for the number of minutes spent is 0.000, which means it is smaller
than 0.05. H0 is therefore rejected: the number of minutes spent on a case does have
an influence on the chance of it being correct.
The coefficients of the transfer function give the formula:
Log(chance of correct) = -7.77 + 0.316 * number of minutes(x). This can be used to
calculate what the chance of a correct file is with a certain number of minutes spent
on the case(x). To obtain the answer, this function has to be mathematically adjusted
due to the Log function it contains.
The Odds ratio of 1.37 indicates that you have a 37% greater chance of a correct file
for every minute you spend extra. With a 95% reliability, this ratio of 1.37 lies
between 1.02 and 1.84 (or a 2% and 84% greater chance of success per extra minute
spent studying). If 1.00 lies within the Confidence Interval, the X in question does not
necessarily influence Y (because if every increase in X can lead to a 0% increase in Y,
there is no increase). Using the formula for the odds of a correct case will
learn us that when we spend 20 minutes on the case we have a 18,8%
chance of success, with 25 minutes it is 53%, with 30 minutes 84,6% and
with 40 minutes 99%. To be 95% sure we need 34 minutes of work.
7.3.15 Correlation and regression
Y data type X data type Number
of X’s
Number of
subgroups
Application
Continuous Continuous 1(+) N.A. Influence of
continuous X’s
on the
continuous Y
A regression analysis between a continuous X and a continuous Y consists of
a correlation analysis and a regression. The hypotheses:
HB: X has no influence on the outcome of Y
HE: X has an influence on the outcome of Y
The hypothesis relates to the correlation between X and Y. Regression will
be discussed on the basis of an example.
Table 7.11
225
7.3.15.1 Simple Regression We would like to know if there exists and a correlation between the amount
(weight percent) of coating applied to a fibre and the rotational speed
(RPM) of the application roll (see figure 7.37)
To investigate the correlation, we use the Regression Analysis option in the
Assistant.
Apply a coating
Fiber roll
Figure 7.37
Figure 7.38
226
We also fill in the Y and the X and let Minitab determine the model:
The result speaks for itself:
(p < 0,05).The relationship between %Finish and RPM is statistically significant
Yes No
0 0,05 0,1 > 0,5
P < 0,001
regression model.97,01% of the variation in %Finish can be explained by the
Low High
0% 100%
R-sq = 97,01%
252015
7
6
5
4
RPM
%Fi
nis
h
causes Y.
A statistically significant relationship does not imply that X %Finish.that correspond to a desired value or range of values forpredict %Finish for a value of RPM, or find the settings for RPM
If the model fits the data well, this equation can be used to Y = - 4,162 + 0,8710 X - 0,01750 X^2relationship between Y and X is:The fitted equation for the quadratic model that describes the
Y: %Finish
X: RPM
Is there a relationship between Y and X?
Fitted Line Plot for Quadratic ModelY = - 4,162 + 0,8710 X - 0,01750 X^2
Comments
Regression for %Finish vs RPMSummary Report
% of variation explained by the model
Figure 7.39
Figure 7.40
227
There exists a significant correlation between X and Y (P<0,001), it is a
quadratic relationship and the function Y=f(X) is being displayed. The other
tabs provide additional checks. Always check the report card. In this case it
indicates that the sample size is not large enough to provide an accurate
estimate of the strength of the relationship (R2). Also, Minitab indicates that
line 16 needs to be verified if it contains a measurement error or otherwise.
7.3.15.2 Multiple Regression For a chemical process, we examine the influence of various X's like
throughput, temperature, velocity and delustrant on the viscosity of a
product. These X's can also influence each other. These X’s can influence
each other in their working. The Minitab worksheet is called: Viscosity.mtw.
We choose now in the Assistant under Regression for “Multiple Regression”
and fill out Y and the X’s to be modelled.
Figure 7.41
228
Minitab has sorted out which X’s do contribute significantly to Y and which
ones do not contribute, calculates the P-value, determines the R-square
value of 75% (indicating how well the model explains the variation in Y) and
checks if all is done correctly in the other Tabs.
INTERMEZZO 1: A relationship between two variables does not necessarily
indicate causality as is explained in the next figure.
statistically significant (p < 0,10).The relationship between Y and the X variables in the model is
Yes No
0 0,1 > 0,5
P < 0,001
model.
75,92% of the variation in Y can be explained by the regression
Low High
0% 100%
R-sq = 75,92%
for Viscosity.
the X variables that correspond to a desired value or range of valuesViscosity for specific values of the X variables, or find the settings for
If the model fits the data well, this equation can be used to predict
X4: Velocity
X1: Delustrantrelationship between Y and the X variables:
The following terms are in the fitted equation that models the
0,03
0,020,
01
680
660
640
2,14
2,12
2,10 250
245
240
6,00
5,75
5,50
Delustrant Throughput Quench Temp Velocity
Is there a relationship between Y and the X variables? Comments
Viscosity vs X Variables
A gray background represents an X variable not in the model.
Multiple Regression for ViscositySummary Report
% of variation explained by the model
7570656055
250
225
200
175
150
number of storks
Po
pu
lati
on
(th
ou
san
ds)
Fitted Line Plot of Population vs. number of storks
Figure 7.43
Figure 7.42
229
INTERMEZZO 2:
In Multiple Regression, Minitab searches for linear relationships between
the X’s and the Y. Also, it determines the best fitted-line (Y=aX+b, see also
figure 7.44) and finally determines is the correlation is significant. Caution:
in US and UK, so also in Minitab they use Y=a + bX. For the outcome it makes
no difference, except for the sequence.
Minitab also calculates the regression equation for more X’s.
Figure 7.44
Figure 7.45
230
The formula to calculate the viscosity Y as a function of the X’s stands in
figure 7.45.
Considering all aspects, the model displayed is the one that has the best fit.
This model is found by eliminating the not significant X’s from the model
and recalculate linear relationships with the significant X’s.
In the example, we chose the linear model. In some cases, the fitted line
plot may indicate to investigate alternative models.
7.4 The root causes In 7.3, we took a closer look at the procedure of testing hypotheses to
determine the vital X's and the root causes. The result of the procedure in
this chapter is a limited list with X's that we can focus on in the Improve
phase.
7.5 Exercises
Normal distribution
a. Is the data in graph below distributed normally?
231
b. Why is that important?
Standard deviation
In a data set that is normally distributed, the mean is 99 and the standard
deviation 3. Between which numbers is 68.26% of the data located?
Type of data for analysis
For the following analyses, indicate which data can be used:
Statistical test Y data type X data type
Binary fitted line plot
2 Sample t-test
Standard Deviations Test
Multiple Regression
ANOVA
%-defectives test and Chi2
1st Quartile 34,300
Median 43,610
3rd Quartile 53,900
Maximum 83,300
42,655 46,240
41,160 46,220
12,938 15,484
A-Squared 0,31
P-Value 0,547
Mean 44,447StDev 14,096
Variance 198,702
Skewness 0,192653
Kurtosis -0,184297
N 240
Minimum 9,310
Anderson-Darling Normality Test
95% Confidence Interval for Mean
95% Confidence Interval for Median
95% Confidence Interval for StDev
7560453015
Median
Mean
464544434241
95% Confidence Intervals
Summary Report for YFigure 7.46
232
233
PART 4: IMPROVE
In this fourth part, the IMPROVE phase of the DMAIC is discussed.
The goal of the Improve phase:
Identify improvement opportunities and demonstrate that the project
objectives will be realized with these improvements
The following two steps from the 12-step plan occupy a central position in
the Improve phase:
8. Determining the optimal solution
9. Testing the selected solution
After completing this part, you are able to:
• Apply the techniques to generate solutions
• Choose the best solution
• Test the solution to see if it leads to the objective
• Identify the risks involved in implementing the solution
• Carry out a pilot project of the proposed solution
After completing the Improve phase, the following items have been
delivered:
• A list with potential solutions
• The selected solutions
• Pilot and/or implementation plan
234
235
CHAPTER 8: DETERMINING THE OPTIMAL
SOLUTION
8.1 Introduction In the previous chapter, the potential causes of variation in Y have been
reduced to the root causes, which we will tackle in the Improve phase. In
this chapter, we look for the optimal solution to manage and limit the
influence of the root causes on Y, or to optimize them to ensure that the
output matches customer requirements more closely. This chapter focuses
on generating solutions and choosing the best solution.
The aim is to develop a fully functioning process improvement that has been
tested by the project team and that is ready to be used in a real business
setting. The optimal solution is selected on the basis of:
• Predicted process performance
• Costs
• Implementation requirements
• Risks
There are two basic strategies to arrive at a solution:
• Design of Experiments (optimizing from a model)
• Trial Experiments (choose the best solution from various
alternatives)
Design of Experiments is especially useful in industry. The Trial Experiments
method can be applied to any process.
236
8.2 Design of Experiments
8.2.1 Introduction DoE Design of Experiments (DoE) is used to build a model to predict the best
solution. The model provides a broad overview of all the possible settings of
X's to find the optimal setting for Y. An important precondition for the
application of DoE is that it has to be possible to adjust the X's
independently. The model takes interaction between the X's into account.
Within DoE, the term factors is often used, instead of X's.
DoE is especially useful when you have a project where several factors can
be adjusted independently, or several possible values. You could decide to
conduct all kinds of experiments at random, but DoE gives you the
opportunity to obtain as much information as possible with a limited
number of experiments, resulting in a good (mathematical) model of how
the various factors contribute to the output (which, in DoE, is called
“response”).
The higher the number of X's you can adjust, the more you will benefit from
DoE's systematic approach.
237
8.2.2 DoE terminology In this paragraph, the specific Design of Experiments terms are discussed in
greater detail.
(Experimental)
design:
The formal plan to conduct the experiment, which
contains the choices with regard to the outputs
(responses), the factors, the levels, the blocks and
the treatments. In addition, the plan contains tools
like blocking, randomizing and replication.
Factors: Controlled or uncontrolled variables (X's), the
influence of which on the response (Y) is being
studied in the experiment. Factors can be
quantitative (continuous) or qualitative (discrete).
Response: The entity to be measured that is used to quantify
the result of a combination of factors at given
levels. The response is always the Y or one of the
Y's.
Level: The values of the factor being studied in the
experiment. For the quantitative factors, every
chosen value becomes a level.
For example, when the experiment is conducted
with two different amounts of phone calls, this
factor (call rate) has two levels. For a qualitative
factor, this single factor (for example standard
procedure) has two levels (namely: standard
procedure and non-standard procedure).
238
8.2.3 The Design of Experiments approach In this paragraph, the procedure that is followed when conducting a
Designed Experiment is discussed.
1. Define the problem
2. Set the target
3. Select the output (response)
4. Select the input factor (X’s)
5. Select the factor levels
6. Select the experimental design
7. Collect the data
8. Analyze the data
9. Draw conclusions
1. Define the problem
Here, you can use the tools we discussed during the Define phase, to get
from a problem (cf. VOC) to a concrete description of what you want to
improve.
Which Y (response) do you want to know more about so you can influence
it. Generally speaking, this is your project Y or a secondary Y. Usually, this is
about Yield, Revenue, Size, Quality criteria, etc.
2. Set the target
DoE can have various targets. A number of reasons to carry out a DoE:
• Finding the relationship between the input factors (X's) and the output
factors (Y's)
• Separating the root causes from the less relevant causes
• Finding the interaction between input factors and their influence on Y
• Finding the optimal setting of the input factors (X's)
239
3. Select the output (response)
Generally speaking, the response of a DoE is the Y of your project, which has
been defined and operationalized in the Measure phase. In the case of a
DoE, the Y has to be a continuous property, or possibly a count.
4. Select the input factors (X’s)
The input factors for a DoE are the causes of the variation of Y (the X's),
which have been mapped in the Analyze phase and reduced to the root
causes. Factors (inputs) can either be continuous or discrete.
5. Select the factor levels
In the selection of the factor levels, a distinction is made between
continuous and discrete data.
Continuous data: when the experiment is carried out on two settings, the
factor has to have (at least) two levels, for instance two temperature
settings.
Discrete (attributive) data: when the experiment is carried out with two
levels, for instance cleaning or not cleaning, that factor has to have two
levels.
6. Select the experimental design
The experimental design depends on the number of experiments. Table 8.0
provides a guideline.
240
Number of
experiments
Type of design Explanation design
Many Full Factorial Studies All possible
experiments are
conducted, at 2 levels
per factor
Surface Methodology
(RSM)
Here, there are more
than 2 levels per factor,
and usually fewer
factors
Moderate Factorial studies When all experiments
have been conducted,
but not all the desired
factors or levels have
been included.
Few Fractionally factorial (5
to 20 factors), screening
studies
To determine which X’s,
are relevant and which
not.
Example of an experiment (steps 1 through 6)
The choice of a certain type of design is explained on the basis of an
example.
A golfer wants to improve his game. He plays with two types of clubs (Royal
and Custom), two types of golf balls (Nike and Dunlop) and on two types of
golf courses (a shielded course in the woods, with little wind, and a course
by the sea, with lots of wind). Below, we discuss the 6 steps to experimental
design:
• Define the problem: the number of strokes is too high. (VOC)
• Set the target: increase the distance from the tee. (CTQ)
• Select the output: the distance from the tee to where the ball lands (Y)
Table 8.0
241
• Select the input factors: clubs, balls, wind condition (the factors that
cannot be controlled need to be defined as well, like humidity, grass
length, fitness golfer, etc.)
• Select the factor levels
Factors Level 1 Level 2
Clubs Royal Custom
Balls Nike Dunlop
Wind condition A lot of wind No wind
• Select the experimental design
• A full factorial design means that all possible combinations are tested in
the experiment. In the example, the following 8 combinations are
possible.
Club Golf ball Wind condition
Royal Nike No wind
Custom Nike No wind
Royal Dunlop No wind
Custom Dunlop No wind
Royal Nike A lot of wind
Custom Nike A lot of wind
Royal Dunlop A lot of wind
Custom Dunlop A lot of wind
The number of experiments can be calculated via 2n, where n is the number
of factors and 2 the number of levels. Carrying out all the experiments is
often time-consuming and costly. If we assume that the higher order
interactions are small or negligible, fewer experiments will suffice. This is
called Fractional Factorial Design. This design is often applied at the start of
Table 8.1
Table 8.2
242
the project or analysis to screen the X's and quickly separate the root causes
from the less relevant causes.
Figure 8.0 shows the full experiment versus a fractional experiment:
Full Factorial Experiment Fractional Factorial Experiment
(Carry out all 8 experiments) (only do the “filled” experiments)
So, in a Fractional Factorial design not all experiments are being conducted.
What is interaction?
A common example where interaction plays a role is in the car. To set the
speed (Y) of the car (flat road, no wind) we apply 2 factors (X’s), namely
position of the shift level and position of the accelerator pedal. If the shift
lever is put in a higher position (e.g. 5th gear), then the effect of accelerator
pedal is larger than in 1st gear. So, Shift level and accelerator pedal are
interacted in their working toward speed (Y). In itself, they are independent.
Principle Sparsity of Effects
In addition to the influence of the main factors on the output, the factors
can also influence each other in their working. This is called interaction.
Generally speaking, it is assumed that the response of a main factor to Y
Figure 8.0
243
determines 90% of the result, and the interaction of two factors 10% of that
at the most. The interaction of 3 factors determines 10% of that effect, etc.
This principle is known as the Sparsity of Effects and is represented as
follows in table 8.3.
Interaction Contribution
Main effects of the factor A 90%
Two-way interaction of AxB 9%
Three-way interactions of AxBxC 0,9%
4-weg interaction of AxBxCxD 0,09%
We use this principle to enable us to reduce the number of experiments we
need; you could imagine that, for an experiment with 4 factors and 2 levels
per factor, we could conduct a total of 16 experiments (the full factorial
being 24 = 16). To save time and money, we want to conduct fewer
experiments, say half. The question is which experiments we can leave out
and which we need to leave in (think of the picture with the cube with 8 or 4
corners representing the experiments). To determine which experiments to
leave out, we first make a table with the first 8 of the 16 experiments. A -1
signifies the low level of the factor in question, while a +1 indicates the high
level of that factor.
Table 8.3
244
We set up the experiments in such a way that AxBxC=D always applies,
because that provides a beautifully distributed matrix (which is called
orthogonal).
EXP. A B C D
1 1 1 1 1
2 1 1 -1 -1
3 1 -1 1 -1
4 1 -1 -1 1
5 -1 1 1 -1
6 -1 1 -1 1
7 -1 -1 1 1
8 -1 -1 -1 -1
We might just as well have used the other half of the 16 experiments, in
which case the matrix would have looked as follows (now we have taken
AxBxC=-D):
9 1 1 1 -1
10 1 1 -1 1
11 1 -1 1 1
12 1 -1 -1 -1
13 -1 1 1 1
14 -1 1 -1 -1
15 -1 -1 1 -1
16 -1 -1 -1 1
Because we earlier discussed the principle of sparsity of effects, it does not
matter whether we would actually carry out the first or second 8
experiments. They both provide us with a well distributed (orthogonal)
matrix with 8 experiments where the effect (on Y) of the interaction of
AxBxC coincides with the (main) effect D (or -D) itself.
In both cases (1st 8 or 2nd 8 experiments), we can see the effects on Y of the
main effects and of the two-way interactions , but not of the three-way
interactions , because they coincide with the effect of D. We call that
245
“Aliased” (or “Confounded”), and we say: the three-way interaction AxBxC is
Aliased (or confounded) with D.
However, because we estimated that the effect of a three-way interaction is
a factor 100 smaller than the main effect, it is a calculated risk. The result is
that we need far fewer experiments than if we were to carry out all 16
experiments. If we were to carry them all out, that would allow us to
determine the effects of the three-way interactions independently of that of
factor D. Sometimes, “Aliasing” can cause problems, in which case you can
always decide to carry out all 16 experiments instead of only 8. We call that
folding the design. In this example, you develop from a so-called Half-
fraction Factorial Design to a Full Factorial Design.
In the following table, we also added the interaction terms of the X's, which
are AxB, AxC, AxD, BxC, BxD and CxD. We also added AxBxC (which we used
to select the D), and we added CxD. On closer inspection, this turns out to
be equal to AxB! Apparently, leaving out 8 of the 16 experiments not only
has the result that the effects of AxBxC are aliased with D, but the two-way
interaction effects of AxB are aliased with CxD!
EXP. A B C D AxB AxC BxC AxBxC CxD
1 1 1 1 1 1 1 1 1 1
2 1 1 -1 -1 1 -1 -1 -1 1
3 1 -1 1 -1 -1 1 -1 -1 -1
4 1 -1 -1 1 -1 -1 1 1 -1
5 -1 1 1 -1 -1 -1 1 -1 -1
6 -1 1 -1 1 -1 1 -1 1 -1
7 -1 -1 1 1 1 -1 -1 1 1
8 -1 -1 -1 -1 1 1 1 -1 1
This last item leads us to the term Resolution. Resolution is a measure of the
distinctive character of the design. When the three-way interactions are
aliased with main effects, and two-way interactions with other two-way
246
interactions, we call this a resolution IV design (as a memory aid: the IV can
be divided into 1 + 3 and 2 + 2).
There are also Designs with Resolution III, V, VI, etc.
The alias structure that applies is presented in table 8.4:
Resolution
III designs
Main effects (1st order effects) are aliased with two-way
interactions
Main effects are not aliased with main effects.
Resolution
IV designs
Main effects are aliased with three-way interactions.
There are no main effects aliased with other main effects
nor with two-way interactions.
2-way interactions are aliased with other 2-way interactions
Resolution
V designs
Main effects are aliased with four-way interactions, two-way
interactions are aliased with 3-way interactions.
The general notation to represent a fractional factorial design is 2�54
k is the number of factors to examine, 2k-p is the number of experiments, R is
the resolution, p represents the extent to which experiments are left out
compared to the Full Factorial. If p=1, we keep half of the experiments, if
p=2, a quarter, if p=3, one eighth, etc.
Minitab provides a guideline for the number of experiments, given the
number of factors:
Minitab: Stat -> DOE -> Factorial -> Create Factorial Design -> Display
Available Designs
Table 8.4
247
In figure 8.1, it can be deduced that the recommended design for an
experiment with 5 factors is “half-fractional”, because this yields resolution
V. In total, 16 experiments (instead of 32) have to be conducted. To design
this experiment in Minitab, go to:
Minitab: Stat -> DOE -> Factorial -> Create Factorial Design
Figure 8.1
248
Enter the number of factors and click on “Designs”
Figure 8.2
Figure 8.3
249
We do not need Center points and Blocks, so we keep them at their default
values. Later, we will use Center points to determine whether the effect of
an X is linear. We will use Blocks to make sure we spend less time on set-ups
between the experiments.
As indicated earlier, fractional factorial designs can be “folded”, to add
missing corner points to the design and, in doing so, turn a half-fraction
design into a full fractional design with two blocks. Folding can be
interpreted as adding missing corner points. All this teaches us that, when
the number of factors increases, you need fractional factorial designs to
limit the number of runs. A few basic rules for sample size:
• Preferably use 28 data points or more to optimize the design
• To estimate standard deviations, also use repetitions in the form of
replications (will be explained later)
• When P < 0.05, the effect you see is significant
• When P > 0.05 but < 0.10, the effect is less significant, but it may
still be sufficiently significant (and perhaps relevant to include).
Steps for a screening Design of Experiments
Generally speaking, the aim of screening DoE's is to select which X's are and
which X’s are not relevant. Especially in the case of systems or processes
that you do not know well, this is a very useful tool to quickly obtain
information about which X's you will need in your project.
In this course, we practice the Screening DoE as a Fractional Factorial Design
with 5 factors. If the number of factors is getting larger, you may have to
resort to Resolution III designs, which often means using Taguchi or Placket
Burman Designs. They work in a similar way but have been designed
specially to reduce the drawbacks of Resolution III designs.
250
Conclusion:
Design of experiments is a proactive tool. A well-designed experiment can
quickly provide insight into the process. The relationships and interactions
that you will find help you to make better decisions.
7. Collect the data
After making the design, it is time to conduct the experiments. The
measurement data for Y resulting from the experiment, is based on the
settings for the X's, provides the information to build a process model.
It is also theoretically possible to conduct a DoE based on historical data.
This requires measurements that can, as it were, serve as the corner points
of the DoE cube. It is to be expected that there will be more noise in
historical data compared to planned experiments. The pitfalls when
conducting a DoE based on historical date are:
• Causality: Is there really a causal relationship between Y and an X?
• Experimental possibilities: the data does not contain all the
experiments that you would have carried out in a planned
experiment.
To use historical data for building a model, you start with data analysis
(data-mining) to select the most suitable data. Use the data you would use
as if you were conducting a planned experiment (the extremes, see figure
8.4):
251
Line up the possible sources of variation and create the experimental design
with factors and levels. Organize your worksheet as though you would be
conducting a DoE and enter the historical data that match the settings of the
DoE. Also include all the replications at every factor level. Keep in mind that
historical data never contains exact replications. Replications are repeat
measurements over a long period, Repeats are repetitive measurements
that are carried out immediately one after another.
8. Analyze the data
In this step, the model is analyzed on the basis of the results of the
experiments.
The effect of a factor
The example presented below contains a 3 factor, 2 level experiment with
the results (Y).
Figure 8.4
252
Run A B C Y
1 -1 -1 -1 12,4
2 1 -1 -1 17,8
3 -1 1 -1 11,1
4 1 1 -1 12,2
5 -1 -1 1 13,2
6 1 -1 1 15,5
7 -1 1 1 14,1
8 1 1 1 12,2
avg+ 14,4
avg- 12,7
effect 1,7
The effect of factor A is determined as follows:
Avg+ = the average outcome of Y with all the high values of A, or:
M#N+ = 17,8 + 12,2 + 15,5 + 12,24 = 14,4
Avg- = the average outcome of Y with all the low values of A (in accordance
with the calculation presented above, the result in this example is 12,7).
The effect of A is the difference between avg+ and avg-, in this case: 1,7. So
the effect of “A” is the impact that ”A” has on the output when moving from
the low level to the high level of ”A”. A hypothesis can be used to see
whether this effect is relevant:
AB: UVW − UV4 = 0 and A�: UVW − UV4 ≠ 0
Table 8.5
253
The interaction effects can be calculated in a similar way. After the
interaction columns of the matrix have been generated, the same
calculations are carried out.
The “orthogonality” mentioned earlier (that means that the matrix is
mathematically speaking perfectly balanced) makes it possible to calculate
these effects in a simple manner. If the design were not orthogonal, the
calculations would be much more complex or even impossible.
Based on an example, we discuss the steps for analyzing experimental
designs. These steps are:
Step 1: looking at the outcomes practically
Step 2: looking at the outcomes graphically
Step 3: looking at the outcomes analytically
Example
In a production process for integrated circuits, the following DoE plan was
made and executed. The aim was to improve the yield of the production
process. In the DoE, the following 5 factors were examined:
A = aperture setting (small, large)
B = exposure time (20% below or above nominal
C = develop time (small, large)
D = mask dimension (small, large)
E = etch time (14.5 min, 15.5 min)
Making integrated circuits is a process that has a lot of similarities with
traditional (analogue) photography. A surface (matrix) is lit with a certain
amount of light (aperture setting determines the amount of light in
intensity, and exposure time is self-explanatory). Before lighting, the matrix
is exposed to etching fluid, which causes certain layers to dissolve (to be
etched away) after lighting. In this process, the development time (how long
is the material “fixed” to ensure it will not be removed) and Mask dimension
(how large are the areas that are exposed to the light) may also play an
important role.
254
Due to budget and time restraints, it was decided to use a 25-1 (screening)
design with 16 runs. See the worksheet below for the input. Check the
outcomes.
Step 1: looking at the outcomes practically
Go to:
Minitab: Stat -> Factorial -> Create Factorial Design
Choose 5 factors and select half factorial (25-1) and create the design.
The alias structure (which effects cannot be separated as the result of the
fact that it is not a full factorial design) is as follows:
Fractional Factorial Design
Design Summary
Figure 8.5
255
Factors: 5 Base Design: 5; 16 Resolution: V
Runs: 16 Replicates: 1 Fraction: 1/2
Blocks: 1 Center pts (total): 0
Design Generators: E = ABCD
Alias Structure I + ABCDE
A + BCDE
B + ACDE
C + ABDE
D + ABCE
E + ABCD
AB + CDE
AC + BDE
AD + BCE
AE + BCD
BC + ADE
BD + ACE
BE + ACD
CD + ABE
CE + ABD
DE + ABC
Step 2: looking at the outcomes graphically
We will analyze the results graphically in Minitab. The following graphical
analysis are generated (in this order):
- Pareto & Normal probability plot
- Main effects plots
- Interaction effects plots
- Cube plots
Pareto & Normal probability plot
Minitab: Stat -> DOE -> Factorial -> Analyze Factorial Design
Choose “Yield” as the response.
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Put under “Options” he confidence level on 90% (α=0.1) and Click: “Graphs”:
Check “Normal” and “Pareto”. Alpha (α) has already been set at 0.1 (which
means that we do not automatically assume that values between 0.05 and
0.10 are insignificant).
Figure 8.6
Figure 8.7
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Next, generate the graphs.
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Pareto Chart of the Effects(response is Yield; α = 0,1)
Lenth’s PSE = 0,9375
Figure 8.8
Figure 8.9
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In both graphs, we see which factors and interactions have the biggest
influence and, using the line in the Pareto, we can also see which ones are
significant at an α of 0.10. In the normal probability plot, these are
represented as red squares, which means that the contribution of these
factors and interaction is not considered accidental. This means they deviate
significantly from “coincidental” or Normality.
In addition to the graphs in figures 8.8 and 8.9, the following plots can be
generated:
Minitab: Stat -> DOE -> Factorial -> Factorial Plots
Select “Yield” as response.
Check under “Graphs” if the correct graphs are being made, with only the
Lower Left Matrix under “Interaction plot”
Figure 8.10
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Main effects plot setup and interaction plot setup:
Interaction plot setup in Minitab 16 is different:
Cube plot setup: select under Stat -> DoE -> Factorial -> Cube Plot and select:
Data Means
Figure 8.12
Figure 8.13
Figure 8.11
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Below, the results:
In the Main effects plot, we see the influence of the 5 factors on the Yield.
The inclination of the line says something about the extent to which the Y
Figure 8.15
Figure 8.16
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(yield) is influenced by this.
In the interaction plot, we see the possible interactions of different pairs of
factors. In every small graph, you can see what the Yield was, given the
settings of the two factors that the graph is about. When we see that, for
instance in the graph of Aperture against Exposure (left top graph), the lines
are NOT parallel, this means that a shift in a factor from low to high, has a
different effect depending on the setting of the other factor. This means
there is interaction. If the lines are parallel, there is no interaction.
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In the cube plot, we see which corner points of the cubes were included in
the experiments (and which were not) and what the measured value of
those corners was in the experiment.
Step 3: looking at the outcomes analytically
When generating the Normal Probability Plot and the Pareto chart, Minitab
presents the output in the Output Pane. After some searching, we
encounter the ANOVA table. See below:
Figure 8.17
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There are no P-values included (only asterisks), because with this design and
this resolution, there is a limited number of experiments and not enough
information to calculate everything. In the case of 16 measurements we can
only calculate 15 (n-1) independent data. As soon as we have reached that
number we do not have degrees of freedom (=information) left to calculate
the P-values and the residual error. This means that, in order to obtain P-
values, we need to stop calculating some less relevant outcomes.
In the model so far, all factors and 2-way interactions have been included.
However, we are interested in the root causes of variation. The question is
which factors and interactions are relevant. We can obtain P-values by
reducing the model, thus being able to calculate the P-values. This means
that we simplify the model by removing a number of less important terms
(factors/interactions). Of course, we start by eliminating the terms with the
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smallest effect. When we look at the Pareto chart, we see a transition
towards the AB interaction. The terms after that have a far smaller effect on
the response.
Reducing the model is done as follows:
Minitab: Stat -> DOE -> Factorial -> Analyze factorial design
Click on “terms” and select the most important terms to include in the
model.
This yields the following result (see Figure 8.19):
Figure 8.18
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The bold terms are significant. Despite the fact that factors D and E (mask
dimension and etch time) are not significant, they cannot be excluded from
the model, because their interaction (D x E) is significant. In light of the Alias
table we saw earlier, we can conclude with a relatively high degree of
certainty that it is not DE, but rather the interaction ABC that creates the
significant value here.
Figure 8.19
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Sometimes the term "Coded units" is used in outcomes. This means that the
levels -1 and 1 are taken into account for the factors. Sometimes the real
values of the levels are taken into account, and then Minitab calculates the
model in "Uncoded units". This is not always mentioned.
The principle to exclude terms with the least effect on Y can be a process of
trial and error. The P-value is the tool we use to decide whether or not
factors and interactions are significant. We "reduce" the table until there
are only significant terms and leave all main effects in the model.
Repeats and replicates
In the previous example, one data point was used per experiment. There
could have been repeats to obtain more data points. Although this would
not increase the number of degrees of freedom, it would increase the
sensitivity (less noise), because we would know what the standard deviation
and the noise of a data point. With one data point per experiment, no
statements can be made about that.
With real (short-term) repeats, the mean of the measurements can be used.
In addition, the standard deviation could have been used as an additional
response (as a 2nd column for Y), which would have provided insight into
which factors have the biggest influence on the variation of the response,
which basically makes this a sensitivity analysis.
If the repeats were actually (long-term) replicates (with other experiments
in between), the real error would be underestimated (as repeats only show
the short-term variation). More factors would be considered relevant that
are not actually relevant (type I error), because we think there is less noise
than there actually is.
The advantage of replicates is that the long-term variation is shown, and
they provide more information on which to base conclusions. Replicates can
be used by dividing the experiment into blocks, whereby all experiments are
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carried out once first, and then repeated a second time (the experiments
are divided into two blocks).
Diagnostic and residual graphs
Diagnostic graphs help to confirm whether the model is correct, and they
help to prevent unexpected disturbances from being unnoticed. The
diagnostic graphs detect problems like:
• Unknown special causes of variation that may have emerged during
the testing
• The presence of noise factors
• Variation that turns out not to be constant at different levels of
some factors (the assumption is that the variation is constant)
• Experiments that were carried out incorrectly or other errors
A Residual is defined as follows: Based on the data points, an optimal
(mathematical) model has been made that fits the data points optimally.
However, every data point has a certain deviation from this model. The
deviation between the measured value and the known value according to
the model is called the Residual. Analyzing the residuals is known as
“diagnostics”.
The diagnostic graphs that present these residuals can be generated in
Minitab as follows:
Minitab: Stat -> DOE -> Factorial -> Analyze Factorial Design
Click on “Graphs”
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Check the graphs under “Residual plots” each separately, or better choose
“Four in one”. This yields the following result (here we kept the separate
graphs for better readability):
Because the model is based on a best possible fit of the measured values,
we expect that, when we make a normal distribution graph of the residuals,
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Figure 8.20
Figure 8.21
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this will show that the residuals are distributed normally. This means that, in
a Normal distribution graph, the points are located on a straight line. In
practice, this means that most points are close to the model and that fewer
points are further away from the model. The points do indeed follow the
normal distribution.
When we create a histogram instead of a normal distribution graph, we
should also see the normal distribution. This is also the case here.
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Figure 8.22
Figure 8.23
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When we position the Residuals against the fitted values (the values of the
Yield that the model has calculated for the different data points), we expect
that the residuals will be distributed evenly across the entire range. We do
not want there to be a different deviation at the bottom of the range
compared to the top of the range, which would create a funnel-like shape
from left to right.
Finally, the residuals are positioned against the sequence of the
measurements. This graph must also not display a funnel-like shape, nor a
gradual increase or decrease, because that would mean that the deviation
grew or became less during the course of the experiment. This could be
related to an external factor that lost or gained influence during the
experiment, for instance wear or a decrease in the environmental
temperature.
The response optimizer
When the model has a good fit with the actual data, Minitab has a tool that
helps you find the best (desired) settings for a certain output of the process.
This tool is called the response optimizer.
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Figure 8.24
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Minitab: Stat -> DOE -> Factorial -> Response optimizer
Click "Setup". Choose "Maximize" for goal as we want to maximize the Yield.
0 is entered as the lower limit. The target is 100 in this case because the
yield percentage of a process can never exceed 100%.
Via the button “Options', the desired output values can be selected. Minitab
also needs an initial value to be able to start calculating (a solver is used).
This helps Minitab achieve the desired objective, through the trials with
settings based on the requested initial value.
Click “Setup”
Figure 8.25
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The settings depend on the goal you want to achieve. This can be a target-
based goal (for instance, reaching a certain distance with a Statapult) or a
goal that is as high or low as possible.
For each factor, the high and low settings are displayed in the first row. The
red numbers indicate the optimum setting. By double-clicking on them, they
can be changed. The red line in the graph also indicates the optimum setting
for the factor in question. In Minitab, the line of each factor can be moved,
to change the setting. The optimum output of Y is 62.5625. Changing the
optimum setting will reduce the Y.
Confirmation
This final step in the DoE analysis is one of the most critical steps.
Confirmation means that you accept the factors as calculated by the
Figure 8.26
Figure 8.27
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response optimizer and are going to measure the response to compare the
result with the calculated result. It is important to test various settings
across the board to determine whether or not the model applies to the
entire area. Enough data has to be collected to make a good assessment of
mean and standard deviation.
When testing of the model does not provide the desired results, the settings
need to be checked to see whether there is noise or special causes. If, after
checking and correcting, there are still deviations, there may be a problem
with the model:
• There may be an interaction that was not included in the model,
but that does have an influence
• There may have been a change in the process that you are not
aware of the assumption that Y has a linear to X is not correct. If we
had an experiment with 2 levels, only a straight line through the 2
observations can be drawn, and perhaps this should have been a
curve.
In that case, you may want to consider choosing a design with fewer (but
the main) factors, with more levels per X, to gain a better insight into the
course of the influence of those X's on Y.
The value of center points
A center point setting of a factor is the value between the two extremes
(Level low and Level high). In practice, the value this center point is 0 in the
case of a factorial model (because low was -1 and high was +1).
Based on the example discussed earlier involving Integrated Circuits, we
now discuss the value of the center points. The design in the example, we
include 3 center points to determine what the influence is of the center
point of the different factors.
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Adding Center points is only possible when you create a new DoE Design. If
you want to include center points, this has to be indicated as follows in
Minitab:
Stat > DoE > Factorial > Create Factorial Design, then select a design with
“Designs”.
In figure 8.28, there are 2 center points for each block. In case of a design
with only continuous X's, the result is 2 center points (actually, 2 replications
at the heart of the cube). This means that, instead of 16 experiments, there
are now 18. However, if you select 2 blocks, or if 1 of the factors is discrete
(and has no intermediate values for X), there are 4 center points (2 in every
side surface of the cube), which means there are 20 experiments in all.
If you select 3 blocks, or if 2 of the factors are discrete, there are 2
additional center points per block, so 6 in all, which are located halfway on
the axes of the cube, resulting in a total number of experiments of 16+6 =
22.
Figure 8.28
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Response surface design
In addition to the (much used) factorial designs discussed above, there are
many other experimental designs. If you have determined what the main
factors in your project are that contribute to your Y, and you want to
determine the optimum settings, a screening design is less suitable, and you
need an optimizing design. The Response Surface Modelling (RSM) design is
such an optimizing design, which allows you to carry out experiments on
several levels for a limited number of factors.
This means you do not just get the corner points of a cube, but also points
from a different geometric shape.
Suppose you have 2 important X's left for your project that you want to
optimize, then an RSM for 2 factors is an excellent choice.
Figure 8.29 contains an example of the experiments for such a design, with 2
X's. 3 or 5 levels per X and 13 experiments. These data points are also
distributed orthogonally.
To create this design in Minitab, select:
Stat > DoE > Response Surface > Create Response Surface design > Designs,
Figure 8.29 a and b
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You can see that 13 experiments are needed, a number of points (especially
the most important points in the middle) are carried out several times, the
center point as many as 5 times.
9. Draw conclusions
After carrying out the experiments, the analysis of this type of design is
carried out like you would for a factorial design. Again, a model is made,
graphs can be created and after determining the best model, you can use a
Response Optimizer to make predictions about what the Y will be, given
certain settings of the X's. Again, it is also possible to set a certain target for
Y, and Minitab will provide you with the corresponding settings of the X's.
Figure 8.30
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8.3 Trial Experiments If X's cannot be isolated or adjusted independently at specific values, you
need to conduct trial experiments.
You use trial experiments to test pre-selected solutions, without first making
a model indicating how X is related to Y.
To carry out trial experiments, use the following procedure:
1. Collect data
2. Develop alternative solutions
3. Screen the alternatives
4. Conduct a risk analysis
5. Select between the alternatives
In the following paragraphs, these steps are explained in greater detail and
worked out.
8.3.1 Data collection In the previous chapters, data was collected about the process output Y and
the factors influencing the process output, the X's. The data that is collected
for the trial experiments relates to possible solutions. Data collection is
focused on three domains.
The process history
• What was the performance in the past?
• Is the process stable over time?
• Has the problem been identified in previous Lean Six Sigma
projects?
• Have certain ideas or solutions been tried in the past?
• Are there best practices that can be applied to this problem?
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Limitations
• Are there certain preconditions that exclude certain solutions?
• What are the limitations that affect the solution?
• Are there limitations with regard to costs, sources or process
changes?
The operational environment
• What is the current performance and operational environment?
• If standardization is a problem, what variations does that cause in
the process?
• What is the current performance and operational environment of
others/the competition (benchmark)?
Collecting data with regard to these questions is a good preparation for
finding alternative solutions and prevents the generation of solutions that
have already been tried or are not possible.
8.3.2 Develop alternative solutions Developing alternative solutions is a creative process. In this step, as many
solutions as possible are considered with the Lean Six Sigma team. To make
sure it is a creative process, there have to be no restrictions on the
expression of ideas and creativity. “All ideas are good”, is the motto here.
Avoid obstacles for creative ideas, like:
• Staying “in the box”
• Not challenging existing assumptions or paradigms
• Fear of saying something wrong
• Looking for the “best” answer (in this phase, all answers are good)
• Focusing on logic
• Shooting down ideas before they are fully formed
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The synthesis consists of taking the best elements from all potential
solutions to generate better solutions. Focus on one cause (X) at a time.
Start with the most important root cause.
In the following sub-paragraphs, we discuss different tools that can be used
to generate ideas and solutions. The following creative tools are discussed:
• Brainstorming
• Interviews
• Thought inducing questions
• Mind mapping
• Six thinking hats
• Building on ideas
• Benchmarking
8.3.2.1 Brainstorming Brainstorming is a much-used technique. It encourages creativity and
broadens people's minds to allow them to identify all aspects of a problem
or solution. It gives a wide range of possibilities. By encouraging people to
mention any idea that comes up, it helps the group to develop many ideas
quickly. A good brainstorming session provides an environment where
people are not judged on their ideas but are encouraged to come up with
ideas. Because all the team members actively participate in the
brainstorming session, a level of ownership is created about the solutions
being discussed and activities following afterwards. When team members
can give a personal direction to a decision, it is more likely that they will
support the solutions. A brainstorming session can also be used as input for
other tools.
A brainstorming session contains the following steps:
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1. Clearly indicate the objective. Discuss and clarify the problem or wanted
solution.
2. Give everyone a few minutes of silence to think about the question and
write down their ideas individually
3. Collect the ideas and write them on a flip board
- do NOT discuss or criticize ideas
- build on the ideas of others
4. When the process slows down, break the session open by adding more
ideas
5. Finish the brainstorming session by evaluating the list with ideas
- make sure everyone understands every idea
- categorize similar ideas
- Clarify ideas and question, if necessary, more specific information
Finally, a number of do’s and don'ts for a brainstorming session:
Do
• Formulate ideas concisely
• Allow individuals to formulate their ideas
• Build on existing ideas
• Organize, categorize and evaluate only after the session
• Aim for quality
Don't
• Criticize ideas
• Passing judgment when ideas are suggested
• Paraphrase an idea from a team member when writing it down
• Dominate the session
There are a number of techniques to stimulate the generation of ideas:
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• Channelling: Actually, this is a reverse fish bone. Starting with the X you
have found to think about areas (6m's) that can lead to a solution
• Analogies: see where it works well and copy
• Anti-solution: think about what is needed to make it even worse. Turn
that around and you have improvements.
• Brain-writing: let people draw and write down what their solution is,
pass the sheets to the neighbour and let them build on that, until
everyone has provided their input to the idea.
• Force Field Analysis: the team brainstorms about forces which increase
the found X (arrows upwards) and after that about forces which
decrease that X. Then they try to balance these forces in the right
direction, order to achieve the needed increase or decrease.
8.3.2.2 Interviews
Interviewing the people involved in a process or service that is similar to the
one you want to develop, often results in new ideas. By interviewing people
on location, you get an idea for what works and what does not work. Collect
the ideas they have about improving the product, process or service. Include
in the interview what would give them greater pleasure and what bothers
them in their work. Often, looking at where you would like to be in the long
term, helps you to identify what is needed for the process. This is sometimes
called the “golden batch” or the “happy flow”.
8.3.2.3 Thought-inducing questions
Thought-inducing questions challenge conventional structures and methods.
To get an idea of how this technique works, some examples:
Figure 8.31
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• Who carries out the work? - Can someone else do it?
• Where is the work done? - Can it be done somewhere else?
• When is the work done? - Can the timing be changed?
• Which resources are required? - Where can other resources be found?
• Under what conditions is the work done? - Can it be changed?
• How is the work kept under control? - What is the value-added part?
• What does the customer really need? - How does the customer use the
product/service?
8.3.2.4 Mind Mapping
The graphic technique Mind Mapping organizes the thought process in a
quick and clear way. A Mind Map fits the way your brain works, which is not
only linear, but also by associating. This allows the Mind Map to reveal
hidden information.
Procedure for Mind Mapping:
1. Write or draw the subject in the center of the page
2. Write down the associations (using different colours) in keywords
3. Use these keywords for the next round of associations
4. Give the Mind Map a tree-like structure by using thick and thin
branches
5. Replace as many words as possible by drawings
6. Improve the Mind Map by adding structure. If possible, establish
connections
7. Use the 6 questions: When? What? How? Why? Where? Who?
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8.3.2.5 Six Thinking Hats technique The six thinking hats technique (by de Bono) encourages people to look at
solutions from different perspectives. Every thinking hat represents a
different perspective. It forces people to move beyond their normal way of
thinking and provides a more complete picture of the situation. A second
advantage is that people can focus on one perspective at a time, which can
prevent confrontations.
For example: many people think from a rational, positive perspective, which
means they fail to look at a problem from an emotional, intuitive, creative or
negative perspective. This may mean that they underestimate resistance to
plans, fail to make creative leaps and do not make essential contingency
plans.
The perspectives have been translated into hats with a certain colour.
Figure 8.32
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White hat: thinking in the form of facts, figures and information. With the
white cap, the aim is to achieve maximum objectivity. Look for holes in the
information and try to take them into account or fill them in.
Red hat: look at problems from emotions, gut feel and intuition. Try to keep
in mind how other people react emotionally. Try to understand people's
reactions when they do not know the exact reason behind an idea.
Black hat: (the negative person), focus on everything that can go wrong, is
incorrect or is risky. This is important, because it means focusing on the
weak points of a plan. It allows you to eliminate them or think of an
alternative.
Yellow hat: think positively and constructively. Look for opportunities. The
yellow hat helps you to go on in times of adversity.
Green hat: be creative and generate new ideas.
Blue hat: structure the process, define the problems and organize the
translation into various tasks. Is carried by the person chairing the meeting.
How to use the six hats
The six hats can be used in different ways during a meeting or session:
• A participant puts one of the hats on or takes it off
• A facilitator asks a participant to put one of the hats on or take it
off
• All participants temporarily wear a hat
Figure 8.33
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• A participant is designated to wear a certain hat for a certain
amount of time
• All participants wear a hat they do not normally wear
Example case
The directors of a real estate company are considering whether or not to
build a new office. The economy is doing well, and vacant office space is
limited. As part of their decision-making process, they decide to use the Six
Thinking Hats.
White hat: Analyses the available data. Researches the trend in empty office
space, which shows a sharp decline. They assume that, by the time the
office will be ready, there will be a shortage of office space. Current
government predictions show a steady economic growth for at least the
building period.
Red hat: The suggested building looks ugly. Even though it may be cost-
efficient, maybe nobody will want to work there.
Black hat: Government predictions may be wrong. The economy can be at a
cyclical turning point, in which case the office will be empty for a long time.
If the building is not attractive, organizations may decide to locate in a
different, better looking office with the same rent.
Yellow hat: If the economy keeps growing, the company can make a huge
profit. If things go well, the office could be sold before the next economic
downturn, or it could be leased on the basis of long-term contracts that will
survive any recession.
Green hat: Consider altering the design to make the building more pleasant
to work in. Perhaps it can be turned into prestigious office that people will
want to rent regardless of the economic climate. As a short-term
alternative, money can be invested to buy real estate at a low price when a
recession hits.
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Blue hat: Used by the chairman of the meeting to move among
perspectives. He or she can change the hat of participants if necessary.
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8.3.2.6 Building on ideas The technique “building on ideas” is used to build on ideas that may at first
seem unusable or absurd. The team changes the idea in such a way that it
becomes better and more usable. One idea leads to another ….
8.3.2.7 Benchmarking Benchmarking is a tool that companies use to compare their performance or
process to that of the “best in the class”. By examining how these “best in
the class” realized their current status and using this information for their
own processes, ideas for improvement can be generated. It prevents people
from having to reinvent the wheel and leads to speedy results.
Figure 8.34
Figure 8.35
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The knowledge can be obtained externally from competition or other
sectors, or possibly internally from other Business Units of departments.
Sources of information:
• Benchmarking companies (who maintain databases)
• Suppliers
• Customers
• Company visits
• Databases
• Telephone research
• Personal interviews
• Publications
• Trade magazines
• Trade meetings
8.3.3 Assess the alternative solutions Using the techniques discussed in the previous paragraph, we generated as
many potential solutions as possible. In the initial screening, the number of
potential solutions is reduced by testing them against the minimal
requirements for the solution based on the customer CTQ's and Business
CTQ's. We think for instance about legislation, company policy, customer or
business demands or budget restrictions.
Based on the initial screening, a number of solutions will be dropped. A risk
assessment is carried out on the remaining solutions using an FMEA.
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8.3.4 Risk assessment, FMEA Before experimenting with a possible solution, the potential risks are
evaluated with regard to the following categories:
Safety: are there any safety risks (environment, external security) connected
to this experiment of to the change in the process or procedures?
Customers: are there potential adverse effects from customers as a result of
new and untested process changes or of potential defects?
Employees: can there be resistance with regard to people's cooperation in
the experiment?
Business: does testing a new process have a negative effect on other
business objectives?
A risk assessment relates to two aspects:
• Technical quality
• Acceptance by the parties involved
The two cannot be separated. Implementing the best solution (in terms of
quality) that is not accepted by the organization will not be successful. A
good solution (though maybe not the best) that is accepted will be more
successful. Assess both aspects:
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Technical quality Acceptance
Customers Do we risk customers being
confronted with defects?
Will the customers accept
the change?
Employees Does the new process affect
the safety of the employees?
Will the employees accept
the change?
Stakeholders Does the new process have a
negative impact on business
objectives like costs or on
the environment?
Did the main stakeholders
accept the change?
Collaboration Are there problems around
working together?
Will people accept and
follow the new procedures?
For each solution, consider the way the implementation can influence:
customers, costs, safety, IT, environment and other possible areas.
Risks can also come from external sources, like suppliers, technological
changes, economic circumstances, policy requirements, competition.
A Cause and Effect diagram (Ishikawa, fish bone) or a Cause and effect
Matrix can be used to map the risks.
An FMEA is a perfect tool to carry out a risk assessment. The FMEA was
discussed in paragraph 6.2.4. Risks are quantified with the FMEA and, where
possible, countermeasures are defined that limit or eliminate the risks.
8.3.5 Select the best of the alternative solutions A part of the potential solutions has been eliminated due to “must be”
requirements, and another part will be too risky for the implementation or
experiment. The number of potential solutions has been reduced. In this
final step of Trial Experiments, the best fitting alternative needs to be
identified. Three tools that can help reach a decision are discussed below.
They are similar to the Cause & Effect matrix discussed earlier.
Table 8.6
291
8.3.5.1 Decision matrix A decision matrix is used to weigh the different alternatives based on the
desired criteria. The criteria are assigned greater weight if they are
considered more important than others. The alternatives are scored
(between 1-10) with regard to the extent to which they meet a particular
criterion. This score is multiplied by the weight factor, and all the weighed
scores are then added together, which produces a ranking of the
alternatives that is used as input for the ultimate decision.
Example – selecting a house
8.3.5.2 Pugh Matrix The Pugh matrix has been developed by the Scottish scientist Dr. Stuart
Pugh. He developed this method to select concept solutions. The method
formalizes the decision-making process to select the solution. Alternative
solutions are compared against each other on the basis of the project CTQ's
and their weighed evaluation criteria. What makes this tool powerful is that
even stronger alternatives are created from weaker alternatives or a hybrid
version of the best solutions. A second distinction of “Pugh” versus the
earlier mentioned decision matrix is that alternative one-on-one are being
compared against a baseline (datum) solution.
Figure 8.36
292
Approach
Constructing a Pugh matrix involves the following steps:
1. Define evaluation criteria
2. Weigh the evaluation criteria
3. Select one of the alternative solutions as a baseline for the alternatives
4. Rate all the solutions against the baseline for each criterion
5. Select the best solution
1. Define evaluation criteria
Evaluation criteria are based on the CTQ's of the project and what the
business considers important. Examples of criteria against which alternative
solutions can be assessed:
• In line with strategy
• Impact on costs/revenues
• Time required for implementation
• Capital investment
• Operational costs
• Implementation risks
• In line with government requirements
• Environment/security
• Political restrictions
Make a selection of the criteria that are the most relevant to the project in
question. Do not use too many criteria, 5 to 8 is a good number.
293
2. Weigh the evaluation criteria
3. Weigh the criteria based on their level of importance. Use a numerical
scale (often from 1-5), rank the criteria in order of relative importance.
Try to realize a certain amount of spread (not all 4's and 5').Select a
baseline (datum)
Select one of the alternatives as the baseline. Choose an alternative which is
well known to all stakeholders, such that it can serve as the basis for
comparison with the other alternatives.
4. Rate all the solutions against the baseline for each criterion
First run
Compare all the alternatives against the baseline for each criterion, using:
• Significantly better than the baseline alternative (+2 in the matrix)
• Clearly better than the baseline alternative (+1 in the matrix)
• Equally good as the baseline alternative (0 in the matrix)
• Clearly worse than the baseline alternative (-1 in the matrix)
• Significantly worse than the baseline alternative (-2 in the matrix)
For each alternative, add the positive and negative scores separately and
put them at the bottom of the matrix. Do this again, but now first multiply
the scores by the weight factor of the criterion. Put these scores below the
matrix and calculate the Total and Weighted scores (sum + and – scores).
294
Analyze the first run
Analyze the outcome of the first run and summarize the alternative
solutions to select and improve the strong solutions. Start by focusing on the
alternative with the highest number of pluses and the smallest number of
minuses. Analyze the weak scores on criteria. Can these weak scores be
improved by changing something in the alternative without affecting the
positive scores on other criteria? Can the strengths of other alternatives be
used to reduce the weaknesses? If that results in a modified solution, add
that solution to the matrix.
5. Select the best solution
Remove solutions that are clearly weak from the matrix and score the
alternatives again in a second run. Use the strongest solution as baseline
alternative. If this confirms the strength of the baseline alternative, then
select this alternative, if not, continue analyzing and scoring until you have a
clear winner.
Figure 8.37
295
8.3.5.3 AHP Matrix The Analytic Hierarchy Process (AHP) was developed by the mathematician
Thomas Saaty. Its power lies in its ability to provide an objective weighing of
the criteria that are used to make a selection. AHP provides an excellent tool
for making complex decisions. AHP provides a simple yet powerful way to
identify, weigh and analyze selection criteria. This reduces the discussion
and speeds up the decision-making process. AHP is especially useful in
complex decisions, because the entire decision-making process is split into
smaller sub-decisions that are less complex, while together they constitute
the entire complex decision. In combination with the Pugh matrix, the AHP
is a powerful tool for selecting the best solution.
Approach
The AHP contains the following steps (example, see figure 8.38):
1. Fill in the evaluation criteria
2. Indicate the hierarchy with a score (for instance, costs are more
important than speed: 5/1)
3. Compare every criterion with the others in that way
4. Calculate the relative weight (add the scores for each column, put the
sum of all the relative scores per criterion in the calculation column,
whereby the relative scores are divided by the sum in each column). See
example.
5. Use the weight factors (rating scores) you have identified in the Pugh
matrix.
Speed of
implemen-
tation
impact on
the
Environment
impact on
CTQ
Acceptance
by society
Cost to
implement
calculation
column
Rating
score
Speed of implemen-
tation 1 1/3 1/5 1/3 1/5 0,25 5
impact on the
Environment3
1 1/3 1 1/3 0,61 12
impact on CTQ 5 3 1 5 1 1,85 37
Acceptance by
society3 1 1/5
1 3 1,04 21
Cost to implement 5 3 1 1/31 1,24 25
17 8 1/3 2 3/4 7 2/3 5 1/2 5 100
Figure 8.38
296
To clarify step 4, take a closer look at speed. The score of 0.25 in the
calculation column was calculated as follows:
FF\ +
F @]^F @] +
F _]�@ `] +
F @]\� @] +
F _]_F �] = 0,25
The final rating score (weight for this criterion) is calculated from the total in
the calculation column (in this case 5, the bottom value) transferred to 100%
(multiply by a factor of 20). Thus, the rating score for each criterion is
calculated by multiplying the number in the calculation column by 20, which
in the case of “speed” means 20 * 0.25 = 5.
To determine the hierarchy between the criteria, a scale of 1-9 measures
with the following definitions, works best (according to Saaty):
1 Equally important
3 A little more important
5 Much more important
7 Very much more important
9 Overwhelmingly more important
In the matrix, the reverse of these definitions translates to 1, 1/3, 1/5, 1/7
and 1/9 for the equal (1) to less important valuations.
8.3.6 Conducting the trial experiment In the previous steps, the techniques for developing and selecting the
solution to the problem were discussed. Now that the solution has been
selected, a trial experiment will have to show whether the solution has the
desired effect. This trial experiment is conducted as a limited pilot under
business circumstances. The pilot is discussed in chapter 9. If it turns out
that the solution does not have the desired effect, an alternative solution
can be tested.
297
8.4 Exercises
Six Thinking hats technique
The six thinking hats technique is used as a brainstorming tool.
Indicate which perspectives the hats displayed above represent.
298
299
CHAPTER 9: TESTING THE SOLUTION
9.1 Introduction In the previous chapter, we determined what the optimum solution will be
to the problem. This solution should lead to an improvement in the
performance of Y. The choice is backed up by data and knowledge from the
organization. However, every solution has to prove itself in practice. A broad
implementation of a solution can be a major change and have consequences
for the organization, which is why it is recommended to test the solution on
a small scale, which will provide insight into its effect and shows us how to
roll it out effectively on a larger scale. This small-scale roll-out is called a
pilot. In this chapter, we discuss the execution of a pilot to test a solution
without proceeding to a full-scale implementation.
9.2 Executing a pilot
A pilot is executed to test a proposed solution in practice. A pilot should
provide us with answers to the following questions:
• Will we realize our objective with this solution?
• Do the effects match our expectations?
• Did we miss anything?
• How does the organization respond to the solution?
• What is the best way to handle a full-scale roll-out of the solution?
By executing a pilot, you limit the risk of failure and get a more accurate
prediction of the (cost) savings as a result of the project. This can be used to
fine-tune the Business Case further as a foundation for a full-scale
implementation.
When updating or rolling out new software, there is almost always a pilot.
Large companies, like multinational companies, always use pilots whenever
300
a process needs to be modified. In production environments – for instance
where machines or equipment is made – pilots are standard practice, and
they are often referred to as a prototype.
9.3 Managing the pilot Executing a pilot is a project in itself and it is often best to adopt a project-
oriented approach. Because small-scale changes will be made within a
process that in most cases affect the organization, it is important to make
sure that (top) management is on board. Make sure the following elements
are in place:
• Gather a steering group (including the client and the main
stakeholders)
• Appoint a project leader or take on that role yourself
• Make a plan (including planning, responsibilities, investments)
• Train the people involved in the process with regard to the changes
to the process resulting from the selected solution
• Make a data collection plan and collect data during the pilot to
enable a thorough evaluation after the pilot. Make sure that the
necessary inputs and process conditions are tested in the pilot.
As part of the data collection, include possible external factors and
possibly additional X's that can be of influence. Continue the pilot
long enough to obtain reliable baseline data.
• Organize briefings with the departments involved and
communicate your plan
• Monitor the pilot implementation and report to the steering group
on the planning and execution
The improvement team is closely involved in the execution and monitoring
of the pilot. The learning experience is important for the preparation of the
complete roll-out of the solution.
301
9.4 Analyzing the pilot results The pilot has two learning objectives:
1. Is the proposed solution really the solution to our problem?
2. How should we handle the full-scale implementation?
The collected data should answer the first question. A possible evaluation
method is to determine the new Process Capability against the desired
performance. You can also compare it to the old Process Capability, to
quantify the improvement. Determine whether or not the new Process
Capability meets the desired process CTQ sufficiently.
If the objective is to cause a shift in the mean, in the percentage of defects
or a reduction in variability, carry out a hypothesis test using the following
hypotheses:
HB: the proposed solution has not caused a significant improvement in the
process
HE: the proposed solution has caused a significant improvement in the
process
Wherever possible, also evaluate the results or behaviour of the other X's
mentioned earlier when you analyze the cause-effect results in the Analyze
phase. This is done in the same way: collect data during the Pilot with regard
to the X's in question and of the Y and determine whether the X (still, or
more or less) has an effect on Y.
The second part of the evaluation has to do with the execution of the pilot
itself. Evaluate the pilot based on questions like:
• Were the instructions clear?
• Were the instructions carried out?
• What bottlenecks did emerge?
302
• Was the plan executed as planned?
• Which tools or forms would have helped?
• Have new problems with regard to the process come to light?
All the answers are input for the implementation plan for the full-scale roll-
out of the solution. Write an evaluation report to inform the steering group
and the customer about the results and lessons learned. Based on the
report, the client, possibly together with management, can make a decision
about the implementation of the solution.
9.5 Practice tips for a successful pilot Finally, a few tips from practice: a number of points of attention that are
sometimes overlooked but help to make the pilot successful.
• The improvement team must be present during the pilot process; the
investment in time is worth it
• Run the pilot long enough to get reliable baseline data
• Make a thorough registration of all activities during the pilot
• Actively update your implementation plan
• Collect data from process factors and external factors that may affect
the outcome
• If possible, ensure that all inputs and process conditions are tested in
the pilot
• Expect "upscaling" difficulties even after a successful pilot
• Identify differences between the pilot environment and the
implementation environment; eliminate potential problems before the
rollout takes place.
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304
305
PART 5: CONTROL
In this last part, we discuss the fifth step of the DMAIC approach. The goal of
the Control phase:
Implement the selected solution and make sure that it is embedded in the
process and in the organization. Share the solutions with other stakeholders
who (may) have a similar process problem.
The following three steps from the 12-step plan play a central role in this
phase:
10. Securing and analysis of the measuring system,
11. Implementation and demonstration of the improvement,
12. Project documentation and hand-over.
After this part, you will be able to:
• Secure the solution so improvements will have a lasting effect,
• Roll out the solution in the organization,
• Demonstrate the improvement,
• Document the project information,
• Identify possibilities to apply the learnings to other projects.
After completing the Control phase, the following elements have been
delivered:
• An implementation plan
• A demonstrated improvement
• A control plan
• Project documentation
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307
CHAPTER 10: SECURING AND
MEASUREMENT SYSTEM ANALYSIS
10.1 Introduction In the implementation of the solution to the process problem, specific
attention is required for making sure that the change that is implemented is
a lasting one. Securing the solution is the focus of this chapter. Below, we
will discuss the tools that can be used to do so.
Again, one of the elements is measuring and monitoring the performance
and the main factors that affect that performance, in other words, the vital
X's and the Y. To make sure that this measurement is reliable, we once more
carry out a Measuring System Analysis, or we check to see whether the
earlier analysis is still valid with the new values of X and Y. This analysis is
also discussed in this chapter.
Figure 10.0
308
10.2 Control plan The process changes are secured in the control plan. For each root cause, it
is indicated how it will be managed operationally. In addition, it is indicated
in the control plan how the project Y will be monitored and controlled.
Furthermore, it is indicated in the control plan who is responsible for
correcting any problems with the regard to X or Y when they emerge, and
what action or procedure they will use. In a number of industries, the
control plan is referred to as the OCAP (Out of Control Action Plan).
Finally, the control plan records when checks or audits are carried out with
regard to the process and process changes, to make sure that the changes
are lasting.
Figure 10.1 provides a template for a control plan.
Each row corresponds with one element that needs to be managed (X or Y).
Control plan
Project: Core Team: Date (Orig):
Key Contact: Date (Rev):
Phone: Authorized By: Date:
Sponsor: Signature:
Mea surement
Technique
Sa mple
Size
Fre-
quency
Who
Mea sures?Action Timing Owner
Response PlanDepa rtment/
Individua l
Wha t must be
controlled?
Project
Y,X,or
other?
Requirements
(specs)
Ongoing C ontrol
Mecha nisms
Mea surement Pla n
Figure 10.1
309
Table 10.0 contains a description of the headers of the columns:
Department,
individual
Person or group responsible for the maintenance
and execution of the plan
What must be
controlled?
Brief description of the process element that
needs to be controlled
Project Y, X or
other?
Indicate whether this element is a project Y, a X or
something else
Requirements
(specs)
Target and specifications of this element to meet
the CTQ
Ongoing control
mechanism
Description of the procedures, instruments that
make sure that this element is controlled within
the required specifications (like mistake proofing,
Robust Process Design, Control charts; see next
paragraphs)
Measuring plan Specifies how/whether measurements are
collected of this process element. Usually, this
data is represented in a control chart
Response plan Describes which corrective actions the person
responsible will execute in case of deviations.
Type of action, timing and owner are recorded. Is
usually indicated in a control chart
The control plan is handed to the sponsor of the project. The sponsor is the
person authorizing the project and also the person with a long-term interest
in making sure that the control plan secures the improved performance.
10.3 Control Mechanisms In this paragraph, we discuss the mechanisms that can be used to make sure
that the improvement is permanent or that action is taking quickly in case of
deviations. We discuss Mistake proofing, Robust Process Design, Visual
Management, Procedures (or work instructions) and Control Charts.
Table 10.0
310
10.3.1 Mistake Proofing Mistake proofing is a technique to eliminate defects by:
• Predicting when a defect can occur and taking action to prevent it
from occurring
• Quickly detecting when a mistake has occurred and taking the
appropriate action before it leads to a defect or making sure that
the defect does not proceed to the next step.
The basic idea is to build in a mechanism that makes it hard or impossible
for something to go wrong or for people to make a mistake. Mistake
proofing is especially useful in the case of process steps that are repetitive
and that require human action that may involve predictable mistakes.
Figure 10.2
311
Some examples:
Detecting
mistakes
Making tasks easier
• Spelling checker in Word,
• Auto correction in Word,
• Bar code scanning
• Colour coding wires and
plugs that belong
together
Preventing
mistakes
Automating
necessary decisions
• Programming cash
registers to calculate
change,
• Programming telephone
numbers.
Eliminating
potential mistakes
• Interlocks when
photocopiers are opened
(stops automatically),
• Child-proof locks on car
doors.
312
Figure 10.3 shows how costs can increase when defects remain in the
process up to the customer.
The ultimate goal is to make sure that nothing can go wrong (Poka Yoke).
The focus has to shift from looking for defects and making sure they do not
reach the customer, to looking for the mistake leading to the defect and
making sure it cannot happen again.
Some Poka Yoke examples from daily life
Figure 10.3
Figure 10.4
313
The following approach is used to create a Poka Yoke:
1. Identify and describe the defect
2. Determine where it occurs and where it is discovered
3. Analyze the process where the defect or mistake occurs
4. Determine the root cause of the defect
5. Implement and test the Poka Yoke.
The requirements for a Poka Yoke are, that it ensures the solution to the
defect, has to cost less than £500, and is easy to implement and maintain.
Figure 10.5
314
10.3.2 Robust Process Design A robust process design makes sure that a process is designed in such a way
that it meets the requirements, even under less than ideal circumstances.
This means that it is less susceptible to:
• Variations in the skill levels of the operators
• Variations in operational conditions, raw material, etc.
A robust process design is part of the solution and is considered in the
Improve phase. In the case of Design projects (which deliver new products
or processes), this is done early on in the design phase. Ultimately, it
simplifies the control plan, because something that is less susceptible to
variation will lead to fewer defects and needs fewer corrections. A robust
process also ensures that the long-term variation will be of a similar
magnitude as the short-term variation.
For example, if we applied a regression analysis in the Analyze phase and for
example found a 3rd order (or ‘cubic’,y=f(x3)) relationship between an X and
the Y, as in figure 10.6, then it makes sense to choose the boundaries of the
X's working area in such a way that the variation in X leads to minimal
variation in Y. X may for example be the temperature of an oven and Y the
strength of the product made.
Figure 10.6
315
10.3.3 Visual Management A simple and logical way to ensure that the Y in our process produces less
variation or errors, is by using Visual Management. Put simply, this means
that we must make visible what must be done, and the explanation of the
possible consequences of errors, by means of pictures, photographs or real
(damage to) parts. Think for example of an Ikea manual: there is no text in it,
and yet it is clear, even for people who cannot read, how the cupboard
should be put together. It is also independent on the language, and people
are warned with exclamation marks or pictures when you have to pay extra
attention or what could go wrong. In the Lean training a separate chapter is
devoted to the subject Visual Management.
10.3.4 Procedures Procedures (or work instructions) provide a documented order of steps and
other instructions that are needed to carry out an activity correctly. The
technology and method are documented in writing to make it easier for
everyone to carry out the work in the right way. Writing a consistent
Figure 10.7 Oil level of a gearbox with red and green indication.
316
procedure that is not open to wide interpretation is a sometimes-
underestimated effort.
Many organizations have a quality system in which the standard for writing
procedures is laid down in a quality handbook, procedures and instructions.
Many of these systems are ISO certified. Procedures and instructions will be
set up in accordance with the existing formats. The effectiveness of the
procedures/instructions depends on the way they match everyday practice
and the extent to which they are applied by the employees.
Some guidelines for effective procedures:
• Be complete: provide enough information so that new staff can use
them to carry out the work.
• Be specific: write down exactly which actions should be executed
and where and when they should be executed. Clarify tasks and
responsibilities.
• Keep the procedure simple.
• Use the 80/20 rule: do not include every problem and every
exception in the procedure. Focus on the most important inputs
that influence the outputs.
• Follow standards: conform to the existing quality system.
• Involve the users in writing and designing the
procedure/instruction.
• Train all users in the procedures and document the training for
future users. Make sure that everyone is informed and trained
(checklist)
• Carry out audits to ensure that people adhere to the procedures.
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10.3.5 Control Charts Control Charts, also known as Statistical Process Control (SPC) or process
performance graphs, are tools that are used to determine whether a
production or business process is statistically under control. Control Charts
are:
• A tool based on statistics to monitor a process real-time
• A graphical representation that shows the process performance
over time
• A set of rules to determine when a process is under control
statistically speaking, and when corrective actions are needed
• A trigger to initiate the response plan (as part of the control plan)
A control chart can be made for every X or Y that you want to control. The
mean (represented by the center line) is based on at least 25 points
collected over a period that is long enough to see all process variation.
Figure 10.8
318
The (upper and lower) control limits are determined statistically based on
the sample size and the expected range of the values, in many control charts
the UCL and LCL are calculated on the mean plus 3*sigma and mean minus
3*sigma levels, so they are independent of the specifications. Each data
point can be an individual measurement, or it can be based on several
measurements within a group. A process is considered to be statistically
under control when all data points vary randomly around the center line and
fall within the control limits.
Corrective action is needed when:
• Isolated points are outside the control limits
• Long-term trends go up or down
• The mean shifts away from the target
There is a set of rules, that signal above mentioned trends and deviations.
These are called the “Western Electric” rules. These rules are broadly
applied and are based on the zone division in figure 10.10:
Figure 10.9
319
Corrective actions are needed if:
• One point falls outside zone A
• Two of the three consecutive points fall in or outside zone A
• Four of the five consecutive points fall in or outside zone B
• Nine consecutive points are on the same side of the center line
You could call all these situations special, in the sense that you will not often
find these in a random sample from a normally distributed dataset.
Therefore, violation of these "rules" is also called "Special Cause Variation",
while if the process does not violate any rules, we call this "Common Cause
Variation". See also $ A1.5.2.
In Minitab you can adjust these rules and also other rules yourself and
switch them on or off.
There are many types of control charts, each with its own set of rules,
similar to the rules mentioned above. As indicated, the control chart, as well
as the Upper Control Limit (UCL) and Lower Control Limit (LCL) are
independent of the customer specifications (USL and LSL) that are used for
the Process Capability. The customer specifications are derived from the
Voice of the Customer, while the control limits in the control charts
represent the Voice of the Process (VOP) and are derived from the process.
Figure 10.10
320
To clarify, a list of the differences:
Customer specification limits
(VOC)
Control limits (VOP)
Based on customer wishes and
requirements
Based on sample plan and the
demonstrated performance
Helps determining whether the
process produces defects
Helps determining whether the
process is statistically under control
Plotted on histograms Plotted on control charts
Changes when customer wishes,
and requirements change
Changes when there is a significant
change in the process
Represents Voice of the
Customer as LSL and USL
Represents Voice of the Process as
LCL and UCL
The type of Control Chart depends on the type of data: continuous or
discrete (“attribute”). Figure 10.10 indicates which chart to use in which
situation:
Table 10.1
Figure 10.11
321
Minitab helps you (through the Assistant) to choose the right control chart
for a given situation. Counts are considered to be Discrete. By "subgroups"
we mean that the data belong together as a set of numbers that belong to
about 1 batch or 1 sample. Another example of a subgroup is when 5 items
are sampled from a production line every hour.
With defects per unit is meant that not only the number of errors is
measured but that the group in which those errors has not always the same
size. We practice with an example:
Example 1:
A Lean Six Sigma team in the corporate IT department is working on
improving the service to customers who call the help desk. After the pilot of
the proposed improvements during the Improve phase, the team wants to
set up a control chart to measure the number of times a customer is put on
hold by the employee to ask the manager for help in answering the
customer's question. Every day, the number of callers was logged, as well as
Figure 10.12
322
the number of times someone was put on hold. The Minitab Worksheet can
be found as: “Helpline Calls.mtw”.
We are dealing with data whereby the occurrence of defects varies in every
subgroup (the number of calls is different each day), which brings us to the
U-chart.
Minitab: Stat -> Control Charts _> Attribute Charts -> U-chart
Result: We see in the results in figure 10.14 below. It appears that the
process is stable and does not require any adjustment. Probably because it
is already an improved process. In this phase of this project, the control plan
indicates what exactly to do if the data in the control chart does indicate
that adjustments must be made.
Figure 10.13
323
Example 2
Orders are received by the order department. The data is the time
customers have to wait before they are attended to. The delays are a
problem, because customers can hang up, which means the order is lost. An
improvement has been implemented (distinguished in the data by the “old”
situation and the “new” situation). The data can be seen in the column with
situation "old" and "new". The worksheet is called: "Order taking with
improvement.MTW”
Figure 10.14
Figure 10.15
324
We are dealing with continuous data and individual data points (so no
subgroups), which is why we choose an Individuals Range Chart I-MR.
According to the scheme in Minitab Assistant, this results in an "Individuals -
Moving Range Chart". Moreover, there is a "Before" and an "After" situation
here. Minitab: Assistant -> Before/After Control Charts -> Before/After I-MR
Chart.
We fill in everything according to Figure 10.17.
Figure 10.16
325
We then get the result in figure 10.18:
old 23 11,174 2,4581 3,7978
new 10 6 1,3790 1,2472
Stage N Mean StDev(Within) StDev(Overall)
Yes No
0 0,05 0,1 > 0,5
P = 0,014
Yes No
0 0,05 0,1 > 0,5
P < 0,001
Consider whether these changes have practical implications.improvement.
• The mean is significantly lower (p < 0,05). Make sure the direction of the shift is an
• The standard deviation was reduced by 43,9% (p < 0,05).After a process change, you may want to test whether the standard deviation or mean changed:
20
10
0
Ind
ivid
ua
l V
alu
e
_X=6
UCL=10,14
LCL=1,86
old new
3128252219161310741
10
5
0
Mo
vin
g R
an
ge
__MR=1,56
UCL=5,08
LCL=0
Was the process standard deviation reduced?
Did the process mean change?
Comments
StDev(Within)Control limits use
Before/After I-MR Chart of Ave. Hold Time by situationSummary Report
Figure 10.17
Figure 10.18
326
The 2 P-values indicate whether the spread has decreased significantly and
whether the mean is significantly different. Both appears to be the case. So,
it is statistically demonstrated that the improvement project is successful.
The upper control chart (Individual Value) shows the individual measured
values themselves, and the bottom (Moving Range) always shows the
(absolute) difference between 2 consecutive measured values. The latter
says something about the spread or variation in the short term. The red
points are the points where corrective action must be taken.
Apply control charts to every element in your control plan where Statistical
Process Control is needed. Follow the following procedure:
1. Determine which measurement to plot
2. Collect initial data and choose and make the control chart
3. After 25 measurements, record the control limits and the mean and fix
these numbers
4. Continue to collect data and plot on a continuous basis
5. Use Control Chart decision rules to recognize when corrective action is
necessary
6. Initiate the response plan from the control plan when corrective action
is required
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10.4 Measurement System Analysis
Because we want to stay in the improved situation, and because some vital
X’s perhaps more accurately than before have to remain under control, it is
useful in this phase to look back at the Measurement System analysis. We
want to ensure that the set values of the vital X's are accurate enough and
precise. That is why we check for both the Y and the vital X’s whether the
measurements meet the requirements. We use the same tools as in the
Measure phase: we check for Resolution, Accuracy, Linearity, Stability,
Repeatability and Reproducibility, insofar as these terms apply to our X and
Y. The guidelines remain the same: no more than 10% noise, and not too
much operator influence (reproducibility) or influence of the measuring
device itself (repeatability).
If work instructions or procedures have been adjusted, check here whether
the employees can always carry out the new working method in the same,
newly defined manner, and whether the registration is done correctly.
10.5 Exercises
Mistake proofing
What is the Japanese term for mistake proof?
And what does it mean?
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CHAPTER 11: IMPLEMENTATION AND
CONFIRMATION OF THE IMPROVEMENT
11.1 Introduction In this phase of the project, the solution has already been selected and
possibly already tested on a small scale. In this chapter, we discuss the full-
scale implementation of the solution. The discipline of “project
management” plays a role here in this step of the 12-step plan. There is a
defined solution that needs to be implemented in the organisation in a
controlled way.
After the full-scale implementation of the solution, we want to show that
the solution has improved the process performance that was defined as the
objective.
11.2 Implementation As indicated, the goal of this phase is to implement the solution in the
process and the organization in a controlled way. Carefully planning the
implementation is a mandatory pre-condition. Many organizations have
embraced their own project management method, for instance Prince 2. It is
recommended to join the existing project management method under the
condition that a plan of action or implementation is drawn up that contains
at least the following elements:
• Project definition
• Project organization
• Project planning
• Necessary resources and budget
• Risk management plan
• Communication plan
• Training requirements
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Here, the “project” - for instance in terms of Prince2 – is the implementation
plan of the LSS trajectory. The project definition contains both the control
plan and the control mechanisms.
11.3 Confirming the improvement After implementing the solution, it needs to be verified whether the Lean Six
Sigma project has realized the intended improvement. In chapter 5, we
formulated an objective on the basis of the baseline performance. You now
need to again calculate the Process Capability to determine the new process
performance. Based on the hypotheses tests (see chapter 7), it can be
determined whether or not this improvement is significant and whether it
meets the objective. Look for any additional steps to realize the intended
improvement if the solution has not yet (completely) succeeded.
You can apply the following steps for this:
1. Go through all the steps of your DMAIC process to see if you have not
missed something along the way
2. Check your measurement accuracy and your measurement system
analysis
3. Go back to the brainstorming at the beginning of the Analyze phase; are
there possible X’s missed (too much asking for common things), or are
there X’s put aside, which in retrospect perhaps turn out to be
important? Then organize a new brainstorming with possibly other
experts, who can tell you more about the process and make a new
selection of vital X’s that can still be tested
4. Run through your list your list of vital X's that you had already filtered
out earlier. How much variation, or shift in the mean can you explain by
comparison with your improvement goal, as set at the end of the
Measurement phase? You can do this by checking your hypothesis test
again and making a summation of the effects that your vital X’s have on
the performance of your Y. If you do not have enough, you have missed
a vital X.
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5. Collect new data about these X or X’s, together with the performance of
your Y (maintain “flat file” format) and investigate if you now can
explain all variation in Y.
6. If you already can explain enough variation of Y with your original vital
X’s, then go back to the execution of your pilot and the implementation
of your improvements. Check in your logbook of the pilot to see to what
extent the optimal settings and the working methods you have worked
out for the optimal settings have actually been followed. If necessary,
carry out the pilot again and measure your Process Capability once
more.
Eventually propose additional projects if it turns out there is further room
for improvement. Include them in the “lessons learned” and in the project
documentation.
In some cases, it takes a long time before the entire implementation is
completed or until enough new process data has been collected. For
instance, in the case of an international implementation of a process that
was piloted in a local market. In that case, the implementation must be
handed over to the project organization, and the Lean Six Sigma Leader
closes the project, on the basis of the significant improvements that have
been accomplished in the Pilot. If, for whatever reason, the roll-out of a part
of the solution is delayed (for instance due to adjustments in collective work
agreements or pending approval from members/unions, the phasing out of
contracts, etc.), an implementation plan is made only for the
implementation of those parts of the solution, and the project is handed
over to the sponsor, in accordance with chapter 12.
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CHAPTER 12: PROJECT CLOSURE AND
HAND-OVER
12.1 Introduction In this final chapter, we discuss the project closure, the hand-over to the
sponsor and the project documentation.
12.2 Hand-over to the sponsor After the implementation, the project can be handed over to the line
organization. The first contact for this hand-over by the Black Belt or Green
Belt is the sponsor, who is the owner of the problem and ultimately the
owner of the solution. In the concluding toll-gate review, the following
subjects are discussed:
• Securing the solution
• The expected business case and the actual business case (if the new
Process Capability has already been determined)
• Lessons learned, what have we learned and what next time we
would do the same or different
• Possibilities for Replication (in other words, where else can it be
applied)
The sponsor is the person who declares the project closed.
12.3 Project documentation
A good project documentation provides a reference for the current process
owner and for future process owners. That is why it is important to
document the reasons for the changes in the process and the implemented
solutions, with the associated benefits. It prevents people from reinventing
the wheel in the future. In addition, it is important to document the lessons
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learned for future projects to ensure that the organizational skill of carrying
out projects also improves over time. The format and structure of the
documentation is defined by the company. In organizations that work with
Lean Six Sigma a lot, a Lean Six Sigma tracking system may have been
implemented that needs to be updated.
NB: project documentation is not an inexhaustible source of all records, data
and communication, but a carefully organized file of the main aspects of the
project.
The following subjects are recurring elements in project documentation:
• Summary of the project
• The problem definition
• Baseline data of the original process performance
• A list of main causes (vital X's)
• The selected solutions for those X's
• The control mechanisms
• Performance metrics (DPMO, process capabilities)
• Lessons learned/best practices
• Financial results
• Translation of the improvement to other areas
Many organizations have a staff department archiving the projects.
12.4 Lessons learned, suggestions for follow-up
projects, striving for perfection Because Lean Six Sigma belongs to the Operational Excellence “School”, not
only processes should be improved, but also the process of improving
processes, which is why the “lessons learned” are a crucial element in any
Lean Six Sigma project. What did we learn from this project that we might
do differently next time to be even more successful? Often, best practices
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can also be distilled from the project, which can be shared with other
project leaders or the organization. Furthermore, many Six Sigma projects
provide valuable insight into the organization and its processes, along with
ideas for possible improvement, which can lead to new improvement
projects. The aim of excellent organizations is to become better all the time.
The aim is not to reach perfection in one step, but to gradually work
towards that, by becoming a little better each time again.
12.5 Project audit Some organizations audit the improvement projects for their execution and
results. This is not a goal in itself, but a way to get better at doing projects.
They want to learn from the execution of the projects and from the
assessment of their feasibility prior to their execution. This in turn helps gain
approval for new projects and for training new belts. In addition, the
Champion, who initiates these audits, will be able to use the results to
generate more commitment from the MT or from the board.
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APPENDIX 1: BASIC STATISTICS
A1.1 Introduction Statistics play an important role within Lean Six Sigma. In this appendix, we
will discuss the basic statistics required in the Measure phase to analyze the
current process we will later on use the statistics in the Analyze phase, to
make sure the Lean Six Sigma project is executed correctly, and you
understand the data.
An important element in statistics is how the central tendency and variation
are both important in describing a process, by summarizing the process
using a few core numbers.
Central
tendency:
The “center” of the process. This is where we expect
most data points to be located
Variation: Tells us how much “spread” there is in the data. The
smaller the spread, the more
consistent/reliable/predictable the process is.
The determination of both the central tendency and the variation is
important in describing a data set. Often, people refer to the central
tendency, but they forget to talk about and quantify the variation.
A1.2 Statistics Within Lean Six Sigma, statistics are used to make data driven decisions that
can be proven and communicated effectively.
But what are statistics actually? Below, some definitions:
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1. The quantitative method for collecting, classifying, presenting and
analyzing numerical data and drawing conclusions based on these data.
2. A part of applied statistics, which relates to the collection and
interpretation of quantitative data and the use of definitions to estimate the
population parameters (usually around a central tendency and variation).
3. The mathematical procedure to describe chances and probability
distributions based on observations.
4. A number of mathematical theories that help analyze data by adding
significance to the results.
The topics covered will play a role in the statistics we apply within Lean Six
Sigma.
A1.3 Statistical values In the introduction, it is stated that, during the analysis of data and the
improvement of processes, Lean Six Sigma uses the values as central
tendency and variation of the process data. These two core values can be
expressed in different measures:
Central tendency:
• Mean (or Average)
• Median
• Mode
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Variation (or spread):
• Range
• Inter Quartile Range
• Mean deviation
• Variance
• Standard deviation
Why so much focus on measures relating to variation?
Uncontrolled variation in processes and products results in defects, it leads
to rework and rejects and an increase in costs and delays. Ultimately it
results in a lack of possibilities to meet the customer's expectations. It leads
to processes which are unreliable and unpredictable. That is why many Lean
Six Sigma processes are aimed at ensuring variation is manageable and then
reducing variation itself.
In the following paragraphs, the measures will be explained in greater detail.
A1.3.1 The Mean (or Average) The mean is the sum of all values divided by the number of values (the
number of observations). As a formula:
ab = ∑ d
?
ab (“X Bar”) is the sign for the mean of a sample, while μ (“mu”) represents
the mean of the entire population. The calculation of both is the same, only
the name and symbol are different.
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The mean is sensitive to outliers.
A1.3.2 The Median
The median is the middle value of a series of data ordered by size. Whit an
even number of observations (when there is not one single central value)
the median is the average of the two middle values.
For instance, in the series displayed below
X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11
The value of X6 is the median, while in the following series
X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12
The value of the median is (X6+X7)/2
The median is less sensitive to outliers than the mean.
Figure A1.0
341
A1.3.3 The Mode The mode is mostly used with discrete data like counts and with continuous
data. The mode is the value that occurs most frequently. If there are two
groups or values that occur most frequently, this is called “bimodal”.
A1.3.4 Range When talking about terms in relation to variation, range is the simplest
term. The range is the highest value minus the lowest value of a data set.
That makes it easy to determine, but it is very sensitive to outliers.
Example. In the data set presented below for the number of phone calls per
day to a help desk, the range (72-15) = 57 calls.
40, 54, 72, 48, 35, 56, 50, 24, 40, 30, 15, 40, 15, 40
A1.3.5 Quartiles
Quartiles are related to the median. Quartiles are the (3) values that divide
an ordered series of outcomes into four equal parts. Each quartile contains
25% of the outcomes. See the example below.
Figure A1.1
342
15, 15, 24, 30, 35, 40, 40, 40, 40, 48, 50, 54, 56, 72
1st quartile 2nd quartile 3rd quartile
The 2nd quartile is identical to the median, the 1st and 3rd quartiles can be
determined after determining the median and then taking the median of the
lower half (Q1) and of the upper half (Q3). You also need these quartiles to
determine the following entity:
A1.3.6 Inter Quartile Range (IQR) The Inter Quartile Range is another measure for variation, this time by
subtracting the 3rd quartile from the 1st quartile. If we use the example from
the previous paragraph, this means:
IQR = (Q3-Q1) = (50 – 30) = 20
The IQR is considerably less sensitive to outliers than the Range. By
definition, 50% of the measured values are within the IQR.
A1.3.7 Mean Deviation The mean deviation is a term that is not used very often, but that is easy to
understand. To calculate the mean deviation of a data set, you start by
determining the mean. Next, you calculate the absolute value per
observation of the difference with the mean. By calculating the mean of
these means, it is possible to determine the mean deviation.
A1.3.8 Variance The variance is our next measure of variation. It is calculated in a way similar
to the Mean Deviation, but now we first take the square of the deviation,
before calculating the mean.
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The symbol for variance is σ2. The following formula can be used:
�� = ∑ edf4 µghifjk
?
See the example below.
A1.3.9 Standard deviation The standard deviation is the measure for variation that is the most
commonly used. The symbol for the standard deviation is σ. It is the square
root of the variance and is calculated as follows:
σ = l∑ edf4 µghifjk?
Both the standard deviation and the mean are needed to describe a normal
distribution.
Figure A1.2
344
A1.4 Sample in relation to population In the previous paragraph, we defined some important statistical measures.
Mean and standard deviation can relate to the entire population (for
instance, “all Dutch people”) or to the data that was used for a sample (for
instance, 1000 people who filled in a questionnaire). The symbols and
formulas that are used for the entire population and for a sample are
different:
Population
Sample
Mean µ
ab em − �!�g
Variance �� = ∑ edf4µghifjk
?
"� = ∑ edf4 dbghifjk
?4F
Standard deviation σ = l∑ edf4µghifjk
?
s = l∑ edf4 dbghifjk?4F
The difference for calculating Variance and Standard Deviation is the
subtraction of 1 from the sample size. This provides a better estimate of the
variation projected onto the entire population. In practice, you will rarely
have to calculate the variance or standard deviation manually, but it is
important to understand the concept and to be able to distinguish between
the outcomes of a sample and the entire population. Later, we will learn
how to translate the results on the (parameters of) a sample onto the entire
population.
An additional variable to express the relative variation is the Variation
Coefficient, or the “relative standard deviation”. This is the standard
deviation divided by the mean. Since it has no unit of measure, it is a relative
measure, and can be used to compare different processes. As a formula:
Variation Coefficient = /n x 100%
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A1.5 The distribution of data
A1.5.1 Distributions In the previous paragraphs, we used the mean and standard deviation to
summarize data that were generated by a process. Another way to
summarize data is to show the distribution as a graph. The distribution
shows the number of times (the frequency) that certain data occurs in the
data set. The “peak” of the distribution shows the central tendency. The
spread of the distribution tells us something about the variation that is
present in the data.
A number of examples of distributions:
By analyzing the distribution, we can see patterns that are hard to discover
in a simple table or in numbers. Different processes and expressions will
show different patterns. Both natural variation and variation with a special
cause will show in the distribution.
In an ideal symmetrical distribution of data, a normal distribution, the mean,
median and mode will all have the same value. If they are separated, this
Figure A1.3
346
means that the distribution is skewed. If higher values are overrepresented
versus the mode, it is positively skewed. If the lower values are
overrepresented versus the mode, it is negatively skewed.
The term kurtosis is a measure for the 'peaked shape' of the distribution. A
high kurtosis indicates a distribution, or data, with a high peak. This means
that extreme values, high or low, are rare. A low kurtosis indicates a flat
distribution of data. In that case, the variation is primarily caused by a
relatively large number of less extreme values.
A1.5.2 Histogram A much-used graphical tool to represent distributions is the histogram,
which is created by taking the difference between the highest and lowest
outcomes and distributing the outcomes among a number of intervals with
equal width, called classes. The number of observations in each class is
counted and the number (frequency) is represented as a bar per interval.
Figure A1.4
347
The characteristics of a histogram:
• Most widely recognized and used quality tool
• Provides a quick overview of how a process behaves
• Allows you to visualize the shape of the distribution
• Provides insight into the distribution of the data
• Is very visual, easy to understand and to interpret
A histogram is usually divided into 5-12 classes. A rule of thumb is to take
the square root of the total number of observations to determine the
number of classes (for instance, 100 observations means 10 classes).
Interpretation of histogram data
When the variation is natural, in other words, without a special or
identifiable cause, the histogram will look like the one presented in figure
A1.6, with high frequencies around the central tendency, decreasing
towards the extremes. The underlying process that generates the data is
stable and the value of each data point is random and fits within the
distribution.
Figure A1.5
348
When the variation does have a special cause, this observation does not fit
within the rest of the distribution. The figure below contains two examples.
The first histogram contains an outlier, while the second histogram contains
a bimodal pattern. Within Lean Six Sigma projects, we look for the
underlying causes (the X's), which means that we do NOT just throw these
outliers or patterns away.
Common Cause Variation and Special Cause Variation:
Figure A1.6
Figure A1.7
349
A1.5.3 Normal distribution The normal distribution or Gauss distribution (named after the German
mathematician Carl Friedrich Gauss) is continuous distribution with two
parameters, the expectation value or mean value μ and the standard
deviation σ. Due to its shape, it is also referred to as the bell curve or the
Gauss curve.
The X-axis contains all the possible values that the observations may show.
The Y-axis contains the likelihood that a certain value will occur. The line
never touches the X-axis. The likelihood of a certain value occurring
becomes ever smaller, the farther you move away from the mean. The
surface below the graph always is equal to 1 (or 100%).
Many phenomena can be described using the normal distribution. They are
phenomena where the distribution is concentrated symmetrically around a
central value, while deviations from this central value become less likely if
50,0
2,0
4,0
6,0
8,0
0,1
5- 4- 3- 2- 1- 0 1 2 3 4
m
elbairaV
1:vedts 0 :naem
4,0:vedts 0 :naem
2:vedts 0 :naem
7,0:vedts 2-:nae
Figure A1.8
350
the deviation gets larger. This type of distributions occurs when, whenever
there are special circumstances have an equal chance that they will lead to a
reduction or to an increase in the observed values. In the case of lead times,
where special circumstances are more likely to lead to an increase of the
lead time than to a reduction, the distribution will not be symmetrical, but
skewed to the right.
The central limit theorem states that, when you take several samples from a
population, and place the mean of each sample in a distribution graph (like a
histogram), you will always end up with a normal distribution, regardless of
what the distribution of the population originally was. This can sometimes
be useful to obtain normal data.
The normal distribution is not always a good approximation. In the case of
exponential growth, or in the case of skewed distributions like income,
prices and lead times, which are skewed to the right, other distributions
provide a better match. Because the statistics of normal distributions are
simpler and more powerful, we will in many cases try to get as far as we can
with (an approximation of) the normal distribution, or we can use a section
of the statistics that was designed especially for non-normal data.
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Normal distributions can vary with regard to two parameters:
1. Differences in mean eµg.
2,82,72,62,52,42,32,2
60
50
40
30
20
10
0
Mean 2,497
StDev 0,1043
N 500
dimension
Freq
uen
cyHistogram of dimension
Normal
Figure A1.9
Figure A1.10
352
2. Differences in the standard deviation σ
As indicated, the sum of the surface below the curve is 1 (or 100%). In the
case of a normal distribution, the following also applies:
• 68% of the values lies between -1 standard deviation and +1
standard deviation
• 95% of the values lies between -2 standard deviations and +2
standard deviations
• 99.7% of the values lies between -3 standard deviations and +3
standard deviations
Figure A1.11
Figure A1.12
353
A1.6 Exercises
Statistical measures Month Check-Out
speed
Customer-
friendliness
Overall satisfaction
Jan 8,75 7,91 7,52
Feb 8,59 7,74 7,33
Mar 8,6 7,81 7,7
Apr 8,45 7,98 7,64
May 8,6 8,01 7,81
Jun 8,39 7,79 7,54
Jul 8,58 7,87 7,83
Aug 8,27 7,46 7,28
Sep 8,22 7,45 7,3
Oct 8,41 7,7 7,22
Nov 8,15 7,24 6,89
Dec 8,16 6,77 6,54
Jan 8,41 7,38 7,31
Feb 8,58 7,67 7,32
Mar 8,33 7,15 7,2
Apr 8,32 6,7 6,65
May 8,54 7,34 7,36
Jun 8,29 7,03 6,92
For the table presented above, calculate the mean, the median and the
mode of the total satisfaction
Histogram
Take values from the total satisfaction column from the previous exercise
and draw a histogram for these values (use Minitab or Excel if you like).
Next, calculate the standard deviation
Is this data normally distributed?
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APPENDIX 2: INTRODUCTION MINITAB
A2.1 Introduction Minitab is statistical software that is often applied in Lean Six Sigma
projects. Within the Lean Six Sigma training courses of The Lean Six Sigma
Company, this tool is used as a basis. Minitab supports the statistical
analyses and, when used correctly, increases the quality of the project. In
this appendix, we introduce Minitab. More information about Minitab and
licenses can be found on www.minitab.com.
A2.2 Building and lay-out Minitab consists of worksheets with data, graphs, numerical outputs and
more. We come back to this in the following paragraphs. In a Lean Six Sigma
project, you want to keep all the analyses together under one project. The
collection of analyses and data sheets can be stored under a project with a
specific project name (an .mpx file).
The basis for the data analysis is the worksheet, which looks like a
spreadsheet. The data needs to be stored in columns as a flat file with
column heads. Every column is a variable. No formulas are used in the
worksheet, which only contains data. Worksheets can be stored separately
Figure A2.0
356
as .mtw. In addition, Minitab uses an “Output Pane”, where the result of the
calculations is represented as text. It is also the log for the actions that have
been carried out. Advanced users can use this interface to enter commands
via the command prompt and to use macros.
There are various ways to enter data:
• Typing them in the worksheet
• Copying and pasting from excel (most common)
• Copying and pasting from a different application, like Access
• Use an ODBC to Query a real-time database
Figure A2.1
357
A2.3 Minitab menus Below, we briefly discuss the different menus of Minitab.
The File menu
The items that are used the most are new (project or worksheet), open
worksheet, open project and save project.
The Edit menu
The term that is used the most here is “Edit Last Dialog” to go on with the
last window that was used (this is possible via Ctrl+E).
Figure A2.2
358
The
The Data menu
The item that is used the most in the DATA menu is “Stack Columns” and
“Unstack Columns”. This allows you to combine different columns in one
Figure A2.3
Figure A2.4
359
column, or to divide one column into different columns.
The Calc menu
The Calc menu contains many things, including the following items:
• Calculator: allows you to carry out mathematical and statistical
calculations
• Column statistics (which calculates the statistical entities like Mu and
Sigma).
• Make patterned data
• Random data
Figure A2.5
360
The Stat menu
The stat menu is the menu that is the menu that is used the most. It
contains most of the statistical functions and analyses:
• Basic statistics
• Regression
• ANOVA
• DoE
• Sample Size determination, etc.
These functions are discussed further down this chapter.
Figure A2.6
361
Figure A2.7
Figure A2.8
362
The Graph menu
The graph menu contains many ways to create graphs from the data:
• Time series plots
• Boxplots and Dotplots
• Histograms
• Bar and Pie charts
• Contour plots
The Graph menu is gradually being replaced by ’Graphical Analyses’ via the
Assistant (see further)
The View menu
Via the View menu, you can navigate to what you need to see and what you
need, choosing from the different views available.
Figure A2.10
363
The help menu
The help menu provides support in the use of Minitab and can help you to
select the right tool at the right moment. Help will take you to the Online
Minitab Help which will answer all you Minitab questions, like choosing the
right tool at the right moment.
The Assistant
The assistant of Minitab contains several wizards which help you do the
more difficult tasks in the right way. Often it uses a decision-making tree to
select the right tool within in Minitab.
Figure A2.11
364
A2.4 Working with Minitab We explain how Minitab works on the basis of a case. The basis of this case
is a data file of a bank that processes loan applications. The data file
contains one month of the work carried out by four employees. Every line is
one day's work of one employee. There are different ways to make
mistakes, which are represented in columns C5-C8 (see the worksheet
below).
Figure A2.12
365
The use of the calculator
The calculator can be used in this case by adding up the mistakes for each
employee in a new column. The sum of the mistakes is placed in column C9,
as follows:
• Give the new column, C9, a name, in this case “Total Mistakes”
• Go to the Calc menu and select Calculator
• Indicate that the results of the calculation need to be placed in the
column “Total Mistakes” (select C9 Total Mistakes and click on select)
• Show the expression in “Expression” by selecting the columns in
question and using the calculator. It is not necessary to use = in the
expression. Click on “OK” and Minitab calculates all rows at once.
Figure A2.13
366
The result is shown in column C9 (see the worksheet below).
Figure A2.14
Figure A2.15
367
Graphical summary and histogram
To get a quick overview of the data, the Graphical Summary is used via the
assistant: Assistant -> Graphical Analysis -> Graphical Summary. In our case,
we do this for ‘Total Requests’, the total number of applications per day for
each employee.
The result is as follows (see figure A2.17):
Figure A2.16
Figure A2.17
368
We can do the same for the number of mistakes (use CTRL-E)
When interpreting histograms, pay close attention to the number of data
points that is used for the histogram. To be reliable, there should be at least
30, but the more, the better.
Graphical summary by variable
In the graphical summary, we have just summarized all data. In many cases
you want to analyze the data per variable (or you want to split Y into X). In
case of the case you would like to know how the data is distributed per
employee. This can be done in the following way:
Assistant -> Graphical Analysis -> Graphical Summary.. It is the same
command so you can use Control-E. Then enter the ‘Categorical X for
Grouping’ field with the column you want to use as a stratification factor. In
Figure A2.18
Figure A2.19
369
this case, “Person”. Notice that you cannot select text columns when filling
in Y (for example number of errors or number of forms). However, you can
use discrete data (such as text) for the X’s, because then a subdivision is
made to a limited number of groups.
This gives the result as below in figure A2.21
Figure A2.20
370
Descriptive statistics
Using the (nowadays less used) function ‘Descriptive Statistics’, it is possible
to obtain some non-graphical statistical parameters from a data set, via:
Stat → Basic staJsJcs → Display Descriptive Statistics. Select the column
Total Mistakes and click on “Statistics”. You can choose which entities you
want to display.
371
The result is shown in the Output Pane:
Also, here we can calculate the descriptive statistics by variable. If we put
“person” in the field “by variable”, we obtain the Descriptive Statistics by
“person”, which provides the following result:
Figure A2.23
372
Capability analysis
An important step in the Lean Six Sigma project is determining the
performance of the process or of the project Y. The Capability Analysis is a
useful tool in this regard. The Lower Spec Limit (LSL) and the Upper Spec
Limit (USL) can be entered in the analysis. Minitab approaches the process
like a normal distribution and indicates in how many cases (in parts per
million) the process performs outside of the specifications.
To make a good capability analysis we first have to make a column with the
percentage of errors ("percent mistakes" in column C10), for this we need
the calculator again.
Now we can perform the Capability Analysis of the process by subgroup
“person”
Go to Stat → Quality Tools → Capability Analysis → Normal
In “single column”, select the Y and indicate for the subgroup “person” (If
there are no subgroups (blocks of related measurements), fill in “1”). Fill in
the LSL and the USL (in our case, 0, a boundary because one can not get
below, and 8, respectively). Under Options it is best to select Benchmark Z’s,
in order to get Z-values (sigma levels) instead of only Cp(k)’s.
Figure A2.24
373
This provides the following result:
9,07,56,04,53,01,50,0
LB 0Target *USL 8Sample Mean 4,55809Sample N 124StDev(Overall) 1,72955StDev(Within) 1,0168
Process Data
Z.Bench 1,99Z.LB *Z.USL 1,99Ppk 0,66Cpm *
Z.Bench 3,39Z.LB *Z.USL 3,39Cpk 1,13
Potential (Within) Capability
Overall Capability
PPM < LB 0,00 * *PPM > USL 16129,03 23292,34 355,83PPM Total 16129,03 23292,34 355,83
Observed Expected Overall Expected WithinPerformance
LB USL
OverallWithin
Process Capability Report for Percent Mistakes
Figure A2.25
Figure A2.26
374
The overall performance indicates how well the process performs in relation
to the specifications. In this case, the ‘Within performance’ is the short-term
or ‘within subroup’ performance, in this case within the subgroup ‘person’.
The expectation (Performance: "Expected Overall") is that in 2,3% of the
cases the process overall (i.e., in the long term) is out of specification,
because the PPM Expected Overall is 23292. The Cpk (Potential, short-term,
or within) value of 1.13 indicates that the process can perform at an
acceptable Z-level of 3.39 in the short term. The Overall capability of Z =
1.99 is not good enough (with a benchmark of Z = 3 or Cp = 1).
Boxplots
Boxplots are based on the median and the quartiles. A boxplot quickly
provides insight when the performance of groups or stratification factors is
compared. In the loan application case, we compare the performance of the
four employees.
Go to Assistant -> Graphical Analysis -> Boxplot
375
Then choose "Total Mistakes" as Y and choose "Person" as the only (1)
“Categorical X for grouping”.
Figure A2.27
Figure A2.28
376
The result is as follows:
The tails (“whiskers”) of the boxplots run from the minimum to the first
quartile (Q1) and from the 3rd quartile (Q3) to the maximum. The box itself
(the square) is the Inter Quartile Range (IQR) area between the first and the
third quartiles (Q1 and Q3). Outliers above the maximum or below the
minimum are indicated as a separate asterisk. Outliers are defined (by
Minitab) as points that are more than 1.5 times the Inter Quartile Distance
below Q1 or above Q3.
Time series plot
The time series plot is used to analyze trends over time.
NOTE: In order to do this correctly, first sort all columns according to the
column "Date" so that the oldest data is at the top. (with: Data> Sort)
Figure A2.29
Minimum
Q2 Q3
IQR =Median
Q1
Maximum
377
Then go to Assistant -> Graphical Analysis -> Time series plot
Figure A2.32
Figure A2.31
378
You get this graph by choosing Total Requests for the Y (output) axis. On the
X-axis, the graph then shows the row number of the data. In this case, the
date of the measurement would be more interesting. To show the date do
the following:
Double-click on the graph, then double click on the X-axis, and then choose
the second tab, “Time”. Select ‘Stamp’ and choose the Date column.
Figure A2.33
Figure A2.35
379
The date is now shown on the X-axis:
Pareto and stacking
The Pareto chart is often used to gain a quick insight into which causes (X's)
contribute the most to the variation of Y. To be able to do this, all the
defects have to be in 1 column. (in Excel you could use a pivot table for this.)
In our case, every type of mistake is shown in a different column. To create a
Pareto, all the columns need to be stacked, which is done as follows:
Go to: Data → Stack → Columns
Choose a new worksheet and give it a name (in this case “stacked defects
for Pareto”)
Indicate (with a check mark) that the column headings (“variable names”)
have to be used in the column that will be used for the Pareto.
Figure A2.36
380
This gives the following result with two stacked columns, which you still
have to give a logical name: (for example "Defects" and "Count")
To create the Pareto, go to: Assistant -> Graphical Analysis -> Pareto and fill
in as follows:
Figure A2.37
Figure A2.38
381
Do not forget to put a checkmark at ‘show cumulative line’ as this is a vital
part of a useful Pareto-graph.
Figure A2.39
Figure A2.40
382
Sending to the wrong address is the first X to focus on in our attempts to
improve the process.
A2.5 Saving the project
Finally, we want to save the analyses. Save them as a project (NOT as a
worksheet) via
File → Save Project As (give it an appropriate name).
383
384
385
APPENDIX 3: HYPOTHESIS TESTING
A3.1 Introduction In this appendix, we discuss the statistical testing and the Confidence
Intervals that are determined to be able to state something about a
population based on a sample. In the statistics we will discuss here, the
reasoning however works the other way around. First, a hypothesis is made,
and then it is tested against data from a sample, to see whether the
hypothesis is rejected or accepted. The central question in this regard is how
sure we can be that a hypothesis is either accepted or rejected. This has to
do with the reliability of the test. In the following paragraphs, we discuss the
creation and testing of hypotheses and the reliability of these tests.
A3.2 Confidence intervals In the earlier appendix “Basic Statistics”, we discussed the mean and
standard deviation, which are calculated on the basis of a sample. However,
based on the sample, we can also state something (with a certain degree of
certainty) about the population. In Appendix 2 (Minitab), we looked at the
graphical summary on the basis of a case involving a number of loan
applications, which yielded the graph in figure A3.0.
386
We assume that the loan application case involves a sample. In the bottom-
right box, a 95% confidence interval is mentioned for the mean, median and
standard deviation. The confidence interval indicates the level of certainty
with which you can make a statement about the actual and expected value
of the Mean, Median and Standard Deviation of the population, based on
the given sample. In this case, it is possible to say with 95% certainty that
the actual value of the mean of the population for the total number of
applications per day lies between 321.17 and 343.19.
The 95% reliability also means:
If we draw 100 samples, each with several data points, and we state
something about the mean of the population, the confidence interval will
contain the actual mean of the total population in 95 cases, and in 5 cases,
the actual value of the mean of the population will be outside of the
confidence interval we calculated.
1st Quartile 290,00
Median 330,00
3rd Quartile 370,00
Maximum 480,00
321,17 343,19
320,00 343,69
55,07 70,78
A-Squared 0,41P-Value 0,335
Mean 332,18
StDev 61,94
Variance 3836,68
Skewness 0,222922
Kurtosis -0,366636
N 124
Minimum 200,00
Anderson-Darling Normality Test
95% Confidence Interval for Mean
95% Confidence Interval for Median
95% Confidence Interval for StDev
480420360300240
Median
Mean
345340335330325320
95% Confidence Intervals
Summary Report for total requests
Worksheet: BANKING PRIVATE LOAN FORM.MTW
Figure A3.0
387
We therefore have a 95% chance that the statement we make corresponds
to reality, and 5% that it is not. This 5% is also referred to as the Alpha or α-
risk.
How certain do you want to be of your statement depends on the
consequences of the statement. Some examples:
• In the automotive industry, 95% confidence intervals are used for the
data
• In the medical industry, 99.9% confidence intervals are used
• In an administrative environment with data being collected by human
beings and possible a lot of noise, you sometimes settle for 90%
reliability and 90% confidence intervals.
Generally speaking, 95% confidence intervals are used, in other words, a 5%
chance of getting it wrong.
Summary:
Confidence intervals are used to calculate means and standard deviations
from samples and to translate them to a range within which the mean and
the standard deviation are expected to be with a certain degree of certainty.
Calculating the confidence interval
When discussing the normal distribution, we found that 95% of the data
points (rounded) lies between -2 times the standard deviation and +2 times
the standard deviation from the mean. (The not rounded value for +2 and -2
standard deviation is 95.45%).
The confidence interval of a quantity (for example the mean or standard
deviation) can be generally speaking calculated as follows:
Confidence interval = value of the quantity in the sample +/- constant *
standard error
388
What we mean by quantity here is: mean/variance/median, etc.
The constant is based on a statistical distribution that depends on the entity
for which the confidence interval is determined:
• For the translation of sample to population mean, it is the t-distribution
• For the translation of the standard deviation of the sample to that of
the population, it is a Chi-square distribution
The t-distribution and the Chi-square distribution are related to the number
of data points that is used for a sample, i.e. the sample size and the Alpha
(α) risk (the 5% chance that we accept we can be wrong with a 95%
reliability).
The standard error for determining the mean is defined as: :
√?, so it is first
calculated by determining the standard deviation (of the sample) and divide
it by the square root of the number of observations (of the sample).
In the formula shown below, the limits of this confidence interval are further
worked out, in this case for the confidence interval of the mean:
m̅ - �q �,?4F]:
√? ≤ µ ≤ m̅ + �q �,?4F]:
√?
s = standard deviation of the sample
n = sample size
n-1 = number of degrees of freedom (by definition)
m̅ = sample mean
t = value from the t-table (appendix 6)
α = Alpha risk (chance of drawing an incorrect conclusion, usually 5%)
389
:√? = standard error (by definition)
The t-value comes from the t-distribution, which is a bell-shaped
distribution, very much like the normal distribution, but more flattened,
depending on the sample size. The smaller the sample, the flatter and
broader the distribution will be. When the sample size is very large, the t-
distribution approaches the normal distribution. The values are shown in
appendix 6. Figure A3.1 gives an example:
Sample size. The size of the confidence interval for a given confidence (for
instance 95%, α = 0.05) depends on the distribution that is used for the
constant (like the t-distribution) and the standard error. The standard error
is inversely proportional to the square root of the number of data points.
This means that, the higher the number of data points, the smaller the
standard error will be, and so will the confidence interval. If the confidence
interval is small, you are more certain about the actual mean (or the
standard deviation) of the population.
Figure A3.1
390
The standard deviation "s" stands opposite of the number of data points.
This means that the confidence interval is broader when there is more
variation in the sample. So, the variables that determine the confidence
interval are s, n and α. The standard deviation is calculated from the sample.
When we want to narrow the confidence interval, we need to collect more
data points OR accept a lower level of reliability (for instance, α = 0.10,
which means we accept a 10% chance of drawing the wrong conclusion).
A3.3 Hypothesis Testing
Hypothesis testing is an important part of statistical inference. In Lean Six
Sigma improvement projects, hypothesis testing plays an important role. In
the quest for X's that may be the cause of variation, we want to be able to
draw statistically significant conclusions about the effect and influence on Y
of one value of X versus another value of X. When we select an X to work on
in order to find a solution to Y, this X has to demonstrable contribute, and
after implementing the improvement, it has to produce a significant
improvement of Y. Some examples:
Figure A3.2
391
A Black Belt has just conducted a pilot for a new process involving loan
applications, and he wants to know if there is a statistically shorter lead time
compared to the old process.
The manager of an order-processing department wants to compare two
order entry procedures to determine if one of them is quicker than the other.
A hospital has two locations that both use scans for diagnostic purposes. The
hospital wants to know if there are differences with regard to the quality of
this services between the two locations, especially with regard to the number
of scans that are lost, which need to be redone, and with regard to the
average waiting time.
In all three cases, hypothesis testing can provide an answer.
Hypothesis testing starts with the null hypothesis. The null hypothesis is an
assumption that is tested to determine whether or not the assumption is
true. We always assume that the null hypothesis is true, until proven
otherwise. The null hypothesis is always based on a status quo (so the
normal situation): we assume the X makes no difference, so has no effect on
Y. The notation that is used for the null hypothesis is HB. Examples of null
hypotheses (HB: µF = µ�)
H0: the new process for loan applications shows the same result as the old
process
H0: both order entry procedures show the same result
H0: the quality of the two locations with regard to MRI scans is the same
The alternative hypothesis assumes that there are differences. The
alternative hypothesis is true when there is enough evidence to reject the
null hypothesis. The notation that is used for the alternative hypothesis is
Ha.
HE: µF ≠ µ�
392
Figure A3.3 The image below shows what hypothesis tests might involve:
changes in mean and spread.
Figure A3.3
393
Plan of approach for hypothesis testing
We will discuss the testing of hypotheses based on a step-wise plan:
1. Determine what it is you want to investigate (for instance your Y)
2. Determine the null and alternative hypotheses
3. Determine the acceptance level of the α and β risks
4. Collect the data and conduct the test
5. Compare the test result (P) with the critical value of α
6. Reject or accept the null hypothesis
7. Determine the sample size (in Minitab)
8. Take appropriate action
Step 1 Determine what it is you want to investigate
In the first step, you determine what you want to investigate. Use the
operational definitions of the parameters you want to examine (Y or X) and
indicate whether it is the mean or the variation.
Step 2 Determine the null hypothesis and the alternative hypothesis
The null hypothesis will always be: “there is no effect of X on Y” or “there is
no difference”:
HB: µF = µ� or HB: σF = σ�
The alternative hypothesis will always claim: “there is an effect of X on Y” or
“there is a difference”:
HE: µF ≠ µ� or HE: σF ≠ σ�
Step 3 Determine the acceptable levels of the α and β risks
The α and β risks are the risks of making a wrong decision with regard to the
null hypothesis and the alternative hypothesis and have to do with the
conclusion that will be drawn from the sample with regard to the truth
394
(which we do not know, but about which we want to say something based
on the sample). Figure A3.4 shows the options we have with regard to
making a decision based on the sample and the truth:
There are two types of errors you can make:
Type-I: Rejecting H0 and concluding that there is a difference when in
fact there is no difference. The probability for this situation we
call α.
Type-II: Accepting H0 and concluding that there is no difference when
in fact there is a difference. The probability for this situation
we call β
The usual value for α = 0.05 (5%) and for β = 0.10 to 0.20 (10% - 20%). The α
Figure A3.4
395
risk is called a Type-I error, and the β-risk a Type-II error. The Type-I error is
also known as the manufacturer's risk. Action is taken when nothing is
wrong (for instance in the case of a proactive product recall). A Type-II error
is also called the consumer's risk. No action is taken while action was
needed.
The likelihood of a test demonstrating a difference when there actually is
one is called the Power of the test. The null hypothesis is rejected correctly.
The power of a test is related to the β risk and can be calculated as follows:
Power = 1 – β.
In figure A3.5, the acceptance or rejection of the null hypothesis is shown in
a normal distribution.
Step 4 collect the data and conduct the test
The various types of tests are discussed in chapter 7 of this book, data
collection is discussed in chapter 3.
Figure A3.5
396
Step 5 Compare the test result (P) to the critical value of α
With regard to the normal distribution outlined earlier, when there is no
effect of X, the value is expected to be within the 95% confidence interval.
This is almost equal to the 2 sigma boundaries, though not exactly (2 sigma
boundaries are at 95.45%). To get 95% boundaries, we have slightly less
than 2 sigma (1.96 sigma, to be precise). We can say that the 95%
confidence interval is defined by the 1.96 sigma boundaries, which are the
boundaries within which the null hypothesis is accepted. Beyond lies 5%
(our α). The statistical test we conduct (whether or not in Minitab) will
always have an outcome that we need to compare to that critical boundary
of 5% (or α).
The outcome of the statistical test is called the P-value, which we will
compare to α (0.05). If our P-value is located in the extremes (P < α), that is
unexpected, and we conclude that something is special (or extraordinary, or
not normal) which means we reject the null hypothesis. If the outcome of
the test is a P-value that is not within the critical area, that means P > α and
we accept the null hypothesis.
As such, the P-value can be seen as the probability of the null hypothesis. If
the probability is less than 0.05, the null hypothesis needs to be rejected in
favour of the alternative hypothesis.
Please note: if α is set at 0.10 (which means we accept a higher likelihood
that we get it wrong), that value of 0.10 is used as boundary for rejecting or
accepting the null hypothesis. In that case we will reject the null hypothesis
for a P value lower than 0.10.
In every hypothesis test in Minitab, the P-value is the most important
outcome. The smaller the P-value, the more clearly the null hypothesis has
to be rejected. In most cases, the critical value is 0.05. If P < 0.05, the null
hypothesis is rejected, and the alternative hypothesis is considered valid.
The rule of thumb is:
397
If P is low, H0 must go!
In other words, if the P value is smaller than the α level we accept, we will
reject the null hypothesis
With regard to the critical values, there are two possible situations:
1. Two-sided tests
2. One-sided tests
We discuss both, to clarify the difference:
1. Two-sided tests
In a two-sided test, the hypothesis applies to two populations that are
considered equal in the null hypothesis. For example:
H0: Belgians (1) are just as tall as Dutchmen (2), or:
Ha: Belgians (1) and Dutchmen (2) are not as tall, or:
H0 is rejected when Belgians are either significantly taller or significantly
shorter than Dutchmen.
In the case of two-sided tests with a confidence interval of 95%, 5% (0.05)
lies outside the critical value. 2.5% of this lies at the lower side (left) and
2.5% at the upper side (right, so 0.025 on either side.
Figure A3.6
398
2. One-sided tests
In a one-sided test, the hypothesis applies to statements like: A is taller than
B. For example:
HB: Belgians (1) are not taller than Dutchmen (2), or HB: µF ≤ µ�
HE: Belgians (1) are taller than Dutchmen (2), or HE: µF > µ�
H0 is true when Dutchmen are taller than Belgians, or when they are equally
tall. If we want to make a claim with a 95% confidence interval, that means
that the critical value is located on one side of the curve. See figure A3.8.
In both tests, we check whether the P-value that is the result of the test lies
below the critical value of 0.05, but with the one-sided test, the entire
critical area (where the null hypothesis is rejected) lies on one side of the
curve (so 5% of the surface of the curve on one side) and in the case of the
two-sided test, there is 2.5% on both sides of the curve. This means that in
the case of a two-sided test a value has to be more extreme (deviate from
the center) to fall within the critical area compared to a one-sided test. It
also means that a one-sided test yields a significant result more quickly.
Conversely, if a two-sided test yields a significant result (P < 0.05), it will also
yield a significant result in a one-sided test. As a result, if a two-sided test
yields a significant result, a one-sided test has not to be conducted.
Figure A3.7
399
Step 6 Accept or reject the null hypothesis
As discussed in the previous step, the P-value of the sample is evaluated
against the critical value. If the P-value lies below the critical value, the null
hypothesis is rejected, if P lies above the critical value, the null hypothesis is
accepted.
Step 3 Check your power and sample size
Often, we are looking for a significant relationship between X and Y. The
power of a test increases when there is a stronger relationship between X
and Y, and when more data is collected. A common requirement is that the
power should be 0.80 of more (so β < 0.20).
To determine the sample size, you need the following parameters:
• The α-level (usually 0.05)
• The power (1-β = 0.8; β = 0.2)
• The difference you want to detect (for instance a 20% reduction in
lead time after implementing a new procedure, which means that a
smaller reduction will not be detected as a difference)
• An estimate of the standard deviation, for instance based on earlier
measurements
Minitab checks via the assistant, after doing the statistical test, whether
your power was acceptably high. Especially if you fill in the optional value
for the difference you want to detect. If NOT, Minitab will sometimes give
you the advice to collect more data. Furthermore, you can calculate the
sample size BEFORE doing the test via Minitab → Stat → Power and Sample
size. It depends on what test you are going to be conducting, and you have
to have an estimation of your standard deviation. This is discussed in
chapter 7.
400
Below, the relationships between the different parameters:
Step 8 Take appropriate action
The actions depend on the goal of the test. If an improvement in a pilot has
made a significant difference, and this has been demonstrated with a
hypothesis test, a full-scale roll-out of the improvement will be the follow-
up action. If a certain X has a significant negative influence on the variation
of Y, the follow-up action will be to find a solution to reduce the influence of
X on the variation.
Figure A3.8
n
401
APPENDIX 4: ANSWERS TO EXERCISES EXERCISES CHAPTER 0.12
Rolled Throughput Yield: Answer: 10% fall-out per step (90% * 90% * 90% * 90% * 90%) = 59% correct
Defects:
Answer: 0.33 or 33% (1 defect divided by 3 opportunities)
DMAIC
Answer:
Define, Measure, Analyze, Improve, Control (DMAIC)
Quality:
Answer: a: Effectiveness and Efficiency
b: Effectiveness is about doing the right things (do our activities match the customer's needs?).
Efficiency is about doing things right (do we carry out our activities with a minimum of
resources?)
Six Sigma Origin
a. Sigma is the standard deviation from the process and indicates the amount of variation in
the process. The number of Sigma’s says something about the level of predictability of the
process, and a higher number of Sigma’s within the predefined limits is an indication that
the process is going well.
b. The concept of Six Sigma originated at Motorola, which used Six Sigma as the standard for
every process. It means having a distance of 6 times a st. dev. away from your average.
Six Sigma Roles: Answer:
a. Champion and or deployment leader, Sponsor/Process owner, Master Black Belt, Black
Belt, Green Belt, Yellow Belt
b. 1 Champion per management area, 1 Sponsor per process, 1 Master Black Belt per 50
Black Belts
1 Determine project and scope; 2 Definition of the defect; 3 Determining project output (Y) and
analyze the measurement system; 4 Determine baseline performance;5 Set the improvement
objective based on the baseline performance;6 Identifying potential causes of variation;7
Determine root causes; 8 Determine optimum solution; 9 Test the solution; 10 Secure and
measure improvements; 11 Implement and demonstrate improvement; 12 Set up project
documentation and organize hand-over.
402
Exercises chapter 1.4
Project selection: Answer:
1. Identify the elements in the organization that determine value
2. Identify chances and opportunities
3. Examine the list of options
4. Scope and define projects
5. Prioritize the list with projects
Voice of the …. Answer:
a. Voice of the:
Customer
Process
Business
Management
Employee
b. The Voice of the Customer. If the customer does not think the product or service is good
enough, it will not be bought, and it will no longer be viable.
VOC: Answer:
1. Price: the right price
2. Quality: the right quality
3. Time: at the right moment (usually as quickly as possible)
Kano Model: Answer:
Enthusiastic: b, h, j Desirable: a, g,
Indifferent: d, e, f Must: c, i,
Exercises Chapter 2.6:
Project Benefits Answer:
Net revenues £ 1.000.000
Total project expenses (400K) £ 400.000 -
Profit tax (20% of extra profit 600.000) £ 120.000 -
EVA £ 480.000
403
Cost reduction project: Answer:
a. Savings (£ 450.000 * 60% * 50%) £ 135.000 per month
b. Revenues (£135K*12months) £ 1.620.000
LESS: expenses unknown
LESS: taxes (1.620K*25%) £ 405.000
NOPAT £ 1.215.000
LESS: WACC unknown
EVA £ 1.215.000 per year Increased revenue project: Answer:
Net revenues (£10K*5*18%*12) £ 108.000
LESS: Taxes (£108K*25%) £ 27.000
NOPAT / EVA (no investment) £ 81.000
Decrease of working capital project:
Answer:
a. £540K*80%*50%) £ 216.000
b. WACC 10% £ 21.600
EVA £ 21.600
Avoided capital investment project: Answer:
Avoided investment value £ 500.000
Yearly net revenues (500k * 10% WACC) £ 50.000
EVA £ 50.000
SIPOC
Answer:
Supplier Input Process Output Customer
employee
original
copier
paper
Put original
on glass
Set machine
to copying
Press start
Remove copy
and original
copy employee
404
Exercises chapter 3.5
Sample Size
What do you want to know about the population? Minimum recommended
sample size
Mean value of a population 5
Standard deviation of a population 25
Defective proportion (P) in a population 30
Frequencies of values in different categories (from
histogram to Pareto chart)
50
Relationship between variables (like in scatter diagram
or correlation)
25
Stability over time 25
Pareto
Operational Definition: Possible answer:
Standard: no form of rust is tolerated on products that are ready
Procedure: visual inspection at the end of the production line. Inspection is carried out under
bright light (minimum number of lumen) by an appraiser with good eyesight (20/20)
Decision: the product is approved when, on inspection, no rust is found
occurences 57 31 24 12 8 4 4
Percent 40,7 22,1 17,1 8,6 5,7 2,9 2,9
Cum % 40,7 62,9 80,0 88,6 94,3 97,1 100,0
No a
ssist
ant a
vaila
ble
Fire
alar
m
Not e
noug
h be
ds
X-ra
y occ
upied
No
doctor a
vaila
ble
patie
nt n
ot re ad
y
no sur
gery
room
avail.
140
120
100
80
60
40
20
0
100
80
60
40
20
0
occ
ure
nce
s
Per
cen
t
Pareto Chart of cause for cancellation of surgery
405
Data Types
Binary Continuous
A, B, I D, H, K
Ordinal Nominal/category
E, G, L C, F, J
Data collection plan for Post Office case
See answer in the lesson / slide pack
Repeatability, reproducibility, accuracy Upper right: Reproducibility better, Repeatability worse, Accuracy better (!)
Lower left Reproducibility worse, Repeatability better, Accuracy can be either good or bad
Lower Right: Reproducibility better, Repeatability better, Accuracy worse
Exercises chapter 4.4
Specification Answer:
Lower Spec Limit (LSL) and Upper Spec Limit (USL)
Process Capability Answers:
In the case of continuous data, the normal distribution can be used. In the case of discrete data,
we look at the number of defects, translated into DPMO. Based on the DPMO, the sigma level
can be determined.
By translating the performance of the process into Cp, Cpk or Z-score, processes can be
compared to each other. The results say something about the level of effectiveness of the
process.
Exercises chapter 5.4
Improvement goal: Usually one of the following:
Champion
Master Black Belt
CFO/Controller
Process Owner/Sponsor
406
Exercises chapter 6.4
Graphs
# Name Purpose
A Boxplot Provides a picture of the rough patterns in the distribution of data
B Multi-Vari Shows influence of several X’s on one Y and each other
C I-MR Shows variation in output (Y) over time
D Pareto Shows the most common defects (80/20 rule)
E Histogram Provides a graphical display of the variation in output (Y)
Exercises Chapter 7.5
Normal Distribution
a. Yes (P>0,05)
b. With a data set with a normal distribution, statements can be made about the
likelihood of the expected output occurring.
Standard deviation Between 96 and 102 (plus or minus 1 standard deviation)
Types of data for Analysis Answer:
Statistical test Y data type X data type
Binary Logistic Regression binary continuous
2 Sample t-test continuous discrete
Standard Deviations Test continuous discrete
Multiple regression continuous continuous
2 Way ANOVA continuous discrete
% defectives-test and Chi2 discrete discrete
Exercises Chapter 8.4
Six Thinking Hats
407
Exercises Chapter 10.5
Mistake Proofing
Poka Yoke is about preventing mistakes. The process is organized in such a way as to make it
(virtually) impossible to make mistakes. So, no instructions or control are needed with the Poka
Yoke actions.
Exercises appendix 1.6
Statistical measures Answer:
Mean 7,3 (7,297777778)
Median 7,3 (7,315)
Mode there is no mode with 2 decimals.
(with 1 decimal, the mode is 7,3 (5 observations)
Histogram
Answer:
Standard deviation 0,36
Normal distribution 0,282 (data is distributed normally)
408
409
Appendix 5: Project charter 1. PROJECT AUTHORIZATION
410
2. PROJECT DEFINITION
411
3. PROCESS DESCRIPTION
412
4. RESOURCES
5. STAKEHOLDERS
413
6. PROJECT PLANNING
7. FINANCIAL STATEMENT
414
Appendix 6: T-Table
α/2
(n-1) 0.4 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
1 0.325 3.078 6.314 12.706 31.821 63.657 127.321 318.309 636.619
2 0.289 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.599
3 0.277 1.638 2.353 3.182 4.541 5.841 7.453 10.215 12.924
4 0.271 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610
5 0.267 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869
6 0.265 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.959
7 0.263 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408
8 0.262 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.041
9 0.261 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.781
10 0.260 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587
11 0.260 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437
12 0.259 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4.318
13 0.259 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.221
14 0.258 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.140
15 0.258 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073
16 0.258 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015
17 0.257 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.965
18 0.257 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.922
19 0.257 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883
20 0.257 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.850
21 0.257 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819
22 0.256 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792
23 0.256 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.768
24 0.256 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745
25 0.256 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.725
26 0.256 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707
27 0.256 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690
28 0.256 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674
29 0.256 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659
30 0.256 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646
40 0.255 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551
60 0.254 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460
120 0.254 1.289 1.658 1.980 2.358 2.617 2.860 3.160 3.373
1000 0.253 1.282 1.646 1.962 2.330 2.581 2.813 3.098 3.300
415
Appendix 7: Normal distribution
Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
1 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
2 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
3 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007
3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
3.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4.1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4.2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
416
Appendix 8: standard Z Table
Z surface Z surface Z surface Z surface
-4.0 0.000032 -2.0 0.022750 0.0 0.500000 2.0 0.977250
-3.9 0.000048 -1.9 0.028717 0.1 0.539828 2.1 0.982136
-3.8 0.000072 -1.8 0.035930 0.2 0.579260 2.2 0.986097
-3.7 0.000108 -1.7 0.044565 0.3 0.617911 2.3 0.989276
-3.6 0.000159 -1.6 0.054799 0.4 0.655422 2.4 0.991802
-3.5 0.000233 -1.5 0.066807 0.5 0.691462 2.5 0.993790
-3.4 0.000337 -1.4 0.080757 0.6 0.725747 2.6 0.995339
-3.3 0.000483 -1.3 0.096800 0.7 0.758036 2.7 0.996533
-3.2 0.000687 -1.2 0.115070 0.8 0.788145 2.8 0.997445
-3.1 0.000968 -1.1 0.135666 0.9 0.815940 2.9 0.998134
-3.0 0.001350 -1.0 0.1586553 1.0 0.841345 3.0 0.998650
-2.9 0.001866 -0.9 0.184060 1.1 0.864334 3.1 0.999032
-2.8 0.002555 -0.8 0.211855 1.2 0.884930 3.2 0.999313
-2.7 0.003467 -0.7 0.241964 1.3 0.903200 3.3 0.999517
-2.6 0.004661 -0.6 0.274253 1.4 0.919243 3.4 0.999663
-2.5 0.006210 -0.5 0.308538 1.5 0.933193 3.5 0.999767
-2.4 0.008198 -0.4 0.344578 1.6 0.945201 3.6 0.999841
-2.3 0.010724 -0.3 0.382089 1.7 0.955435 3.7 0.999892
-2.2 0.013903 -0.2 0.420740 1.8 0.964070 3.8 0.999928
-2.1 0.017864 -0.1 0.460172 1.9 0.971283 3.9 0.999952
-2.0 0.022750 0.0 0.500000 2.0 0.977250 4.0 0.999968
417
Appendix 9: Z to DPMO with shift
Z DPMO Z DPMO
0 933,193 3 66,807
0.1 919,243 3.1 54,799
0.2 903,200 3.2 44,565
0.3 884,930 3.3 35,930
0.4 864,334 3.4 28,717
0.5 841,345 3.5 22,750
0.6 815,940 3.6 17,864
0.7 788,145 3.7 13,903
0.8 758,036 3.8 10,724
0.9 725,747 3.9 8,198
1 691,462 4 6,210
1.1 655,422 4.1 4,661
1.2 617,911 4.2 3,467
1.3 579,260 4.3 2,555
1.4 539,828 4.4 1,866
1.5 500,000 4.5 1,350
1.6 460,172 4.6 968
1.7 420,740 4.7 687
1.8 382,089 4.8 483
1.9 344,578 4.9 337
2 308,538 5 233
2.1 274,253 5.1 159
2.2 241,964 5.2 108
2.3 211,855 5.3 72
2.4 184,060 5.4 48
2.5 158,655 5.5 32
2.6 135,666 5.6 21
2.7 115,070 5.7 13
2.8 96,800 5.8 8.5
2.9 80,757 5.9 5.4
3 66,807 6 3.4
418
Appendix 10: �� to P-value
n-1 P P P
0.1 0.05 0.025
1 2.71 3.84 5.02
2 4.61 5.99 7.38
3 6.25 7.81 9.35
4 7.78 9.49 11.14
5 9.24 11.07 12.83
6 10.64 12.59 14.45
7 12.02 14.07 16.01
8 13.36 15.51 17.53
9 14.68 16.92 19.02
10 15.99 18.31 20.48
11 17.28 19.68 21.92
12 18.55 21.03 23.34
13 19.81 22.36 24.74
14 21.06 23.68 26.12
15 22.31 25.00 27.49
16 23.54 26.30 28.85
17 24.77 27.59 30.19
18 25.99 28.87 31.53
19 27.20 30.14 32.85
20 28.41 31.41 34.17
21 29.62 32.67 35.48
22 30.81 33.92 36.78
23 32.01 35.17 38.08
24 33.20 36.42 39.36
25 34.38 37.65 40.65
26 35.56 38.89 41.92
27 36.74 40.11 43.19
28 37.92 41.34 44.46
29 39.09 42.56 45.72
30 40.26 43.77 46.98
419
Appendix 11: abbreviations GB Green Belt Y Output variable
BB Black Belt X Input variable
MBB Master Black Belt KPI Key Performance
Indicator
B&C Benefits & Concerns EVA Economic Value
Added
SS Six Sigma C&E Cause & Effect
DMAIC Define, Measure, Analyze,
Improve, Control
FMEA Failure Mode &
Effects Analysis
DPMO Defects Per Million
Opportunities
RPN Risk Priority Number
DPO Defects Per Opportunity Cp, Cpk Process Capability
Index
PPM Parts Per Million CI Confidence Interval
σ Sigma = standard
deviation
AB Null Hypothesis
CTQ Critical to Quality A� Alternative
Hypothesis
WIP Work in Progress MTBF Mean Time Between
Failure
VOC Voice of the Customer MTTF Mean Time to Failure
VOB Voice of the Business LSL Lower Spec Limit
VOP Voice of the Process USL Upper Spec Limit
VOE Voice of the Employee DOE Design of Experiments
SPC Statistical Process Control MSA Measure System
Analysis
RTY Rolled Throughput Yield
SIPOC Supplier, Input, Process,
Output, Customer
420
INDEX Topic Page
1 Sample T-test 186
1-sample % defective test 196
2 sample T-test 188
2-sample % defective test 199
Accuracy 111
Affinity diagram 57
Aliasing 245
Alpha risk 388
Analysis of Variance (ANOVA) 202
Analytic Hierarchy Process (AHP) 295
Attribute 103
Baseline performance 147
Basic needs 58
Basic statistics 337
Benchmarking 287
Benefit & Effort matrix 51
Binary Logistic Regression 220
Black Belt 29
Boxplot 173
Brainstorming 279
Building on ideas 287
Business Case 74
C_p 146
C_pk 146
Calibrating 114
Cause & Effect diagram 159
Cause & Effect matrix 163
Central tendency 337
Champion 27
Chi-square test 214
Confidence intervals 385
Continuous 103
Contribution 121
Control Charts 317
Control Mechanisms 309
421
Control phase 305
Control plan 308
Correlation 224
Costs of poor quality (COPQ) 25
Critical to Quality (CTQ) 56
Customer requirements 63
Data collection plan 97
Decision matrix 291
Defect 63
Deployment Leader 27
Design of Experiments 236
Detection 169
Discrete 103
Distributions 345
D-M-A-I-C 30
DoE 236
DPMO 22
DPO 22
DPU 22
EBITDA 76
Economic Value Added 75
Excitement needs 58
Experimental design 239
Failure Modes & Effect Analysis 165
Financial benefits 74
FMEA 166
Fractional Factorial 242
Full Factorial 242
Gauge R&R 116
Green Belt 29
Hidden factory 23
Histogram 172, 346
Hypothesis Testing 183
Iceberg theory 26
Improve 233
I-MR 324
Instrument 104
Inter Quartile Range (IQR) 342
422
Interviews 281
Ishikawa 159
Kano Analysis 58
Kappa 132
Kendall's Coefficient 132
Kruskal-Wallis test 210
Lessons learned 334
Level 237
Linearity 113
Living document 66
Master Black Belt 28
Mean 339
Measure phase 87
Measurement System Analysis 109
Median 340
Mind Mapping 282
Minitab 355
Mistake Proofing 310
Mode 167, 341
Multi vari chart 175
NEBIT 76
NOPAT 76
Normality test 184
Occurrence 168
One-sided tests 398
Operational definition 100
Opportunities 22
Out of Control Action Plan 308
Paired T-test 193
Pareto analysis 92
Pareto chart 176
Performance needs 58
Pilot 299
Population 104
PPM 22
Precision 114
Problem definition 67
Procedures 315
423
Process Capability 139
Process history 69
Project charter 65
Project definition 67
Project documentation 333
Project Limits 68
Project restrictions 68
Project Selection 43
Project sponsor 28
Project team 69
Project time line 72
Project Y 95
Pugh Matrix 291
QFD 94
Quality Function Deployment 65, 93
Quartiles 341
RACI matrix 70
Random sampling 107
Range 341
Reactive data 56
Regression 224
Repeatable 114
Reproducible 114
Resolution 104, 111, 245
Response surface design 275
Risk Priority Number 169
Robust Process Design 314
RPN 170
RTY 24
Sample 104
Sample frequency 106
Sample size 106
Scope 53, 95
Selecting a project 43
Severity 167
Sigma level 20, 143
SIPOC 79
Six Thinking Hats 283
424
Sixpack 52
Special Cause Variation 348
Stability 112
Stakeholder assessment 72
Stakeholders 71
Standard deviation 343
Standard error 389
Statistical Process Control (SPC) 317
Stratification 101
Stratified random 108
Suitable project 36
Systematic random 108
Team members 29
The Voice of the Customer 46
Tolerance 121
Toll-gate Review 73
Tree-diagram 64, 90
Trial experiments 277
Twelve steps 32
Two-sided tests 397
Types of data 103
Value Creation 77
Value Stream Mapping 82
Variable data 103
Variance 342
Visual Management 315
Voice of Business 46
Voice of the Customer 50
Weighted Average Cost of Capital 76
Yellow Belt 29
Z-score 143
The Lean Six Sigma Company provides training, coaching and implementation support in the field of Lean and Six Sigma. We assist and coach organizations as well as individuals to achieve their ambition to improve processes utilizing Lean Six Sigma methodologies. Training courses are organized on an “in-company” basis as well as “open enrollment”.
The courses are directed at the practical application of Lean Six Sigma. The content of courses meets internationally recognized standards as set by the ASQ, the IASSC and ISO (ISO13053).
Every year the Lean Six Sigma Company trains hundreds of Lean Six Sigma professionals, also providing them with active coaching in project execution.
In addition The Lean Six Sigma Company supports many organizations with the implementation of Lean Six Sigma thus enabling these organizations to realize their ambitions aimed at improving process capability.
Visiting address The Lean Six Sigma Company Van Nelleweg 1, 3044 BC ROTTERDAMThe Netherlands
T: +31 (0)10 22 22 860W: www.theleansixsigmacompany.comE: [email protected]
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