Introduction to Engineering Statistics and Lean Six Sigma Theodore T

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Introduction to Engineering Statistics and Lean Six Sigma Theodore T. Allen Introduction to Engineering Statistics and Lean Six Sigma

Statistical Quality Control and Design of Experiments and Systems

Third Edition Theodore T. Allen Industrial and Systems Engineering The Ohio State University Columbus, OH, USA

ISBN 978-1-4471-7419-6 ISBN 978-1-4471-7420-2 (eBook) https://doi.org/10.1007/978-1-4471-7420-2

Library of Congress Control Number: 2018957066

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Dedicated to my wife and to my parents Preface

Tere are four main reasons why I wrote this book. First, six sigma consultants have taught us that people do not need to be statistical experts to gain bene- fts from applying methods under such headings as “statistical quality control” (SQC) and “design of experiments” (DOE). Some college-level books inter- twine the methods and the theory, potentially giving the mistaken impression that all the theory has to be understood to use the methods. As far as possible, I have attempted to separate the information necessary for competent application from the theory needed to understand and evaluate the methods.

Second, many books teach methods without sufciently clarifying the context in which the method could help to solve a real-world problem. Six sigma, statistics and operations-research experts have little trouble making the connections with practice. However, many other people do have this difculty. Terefore, I wanted to clarify better the roles of the methods in solving problems. To this end, I have re-organized the presentation of the techniques and included several complete case studies conducted by myself and former students.

Tird, I feel that much of the “theory” in standard textbooks is rarely pre- sented in a manner to answer directly the most pertinent questions, such as:

Should I use this specifc method or an alternative method? How do I use the results when making a decision? How much can I trust the results?

Admittedly, standard theory (e.g., analysis of variance decomposition, con- fdence intervals, and defning relations) does have a bearing on these questions. Yet the widely accepted view that the choice to apply a method is equivalent to purchasing a risky stock investment has not been sufciently clarifed. Te theory in this book is mainly used to evaluate in advance the risks associated with specifc methods and to address these three questions.

Fourth, there is an increasing emphasis on service sector and bioengineer- ing applications of quality technology, which is not fully refected in some of the alternative books. Terefore, this book constitutes an attempt to include more examples pertinent to service-sector jobs in accounting, education, call centers, health care, and sofware companies.

In this third edition, a new perspective emerges: Lean six sigma can be viewed as human-in-the-loop data-driven decision processes. To a real extent, lean six sigma training is solid preparation for machine learning and artifcial intelligence work and research. Both disciplines relate to formalized decision processes and statistical concepts. Also, lean six sigma relates to more VII Preface than half of procedures sofware in Minitab and JMP. Much of the remaining sofware methods in Minitab and JMP relate to human-not-in-the-loop decision-making or machine learning.

In addition, this book can be viewed as attempt to build on and refocus material in other books and research articles, including: Harry and Schroeder (1999) and Pande et al. (2000) which comprehensively cover six sigma; Montgomery (2001) and Besterfeld (2001), which focus on statistical quality control; Box and Draper (1987), Dean and Voss (1999), Fedorov and Hackl (1997), Montgomery (2000), Myers and Montgomery (2001), Taguchi (1993), and Wu and Hamada (2000), which focus on design of experiments.

At least 50 books per year are written related to the “six sigma movement” which (among other things) encourage people to use SQC and DOE techniques. Most of these books are intended for a general business audience; few provide advanced readers the tools to understand modern statistical method development. Equally rare are precise descriptions of the many methods related to six sigma as well as detailed examples of applications that yielded large-scale returns to the businesses that employed them.

Unlike many popular books on “six sigma methods,” this material is aimed at the college- or graduate-level student rather than at the casual reader, and includes more derivations and analysis of the related methods. As such, an important motivation of this text is to fll a need for an integrated, principled, technical description of six sigma techniques and concepts that can provide a practical guide both in making choices among available methods and applying them to real-world problems. Professionals who have earned “black belt” and “master black belt” titles may fnd material more complete and intensive here than in other sources.

Rather than teaching methods as “correct” and fxed, later chapters build the optimization and simulation skills needed for the advanced reader to develop new methods with sophistication, drawing on modern computing power. Design of experiments (DOE) methods provide a particularly useful area for the development of new methods. DOE is sometimes called the most pow- erful six sigma tool. However, the relationship between the mathematical properties of the associated matrices and bottom-line profts has been only partially explored. As a result, users of these methods too ofen must base their decisions and associated investments on faith. An intended unique con- tribution of this book is to teach DOE in a new way, as a set of fallible methods with understandable properties that can be improved, while providing new information to support decisions about using these methods.

Two recent trends assist in the development of statistical methods. First, dra- matic improvements have occurred in the ability to solve hard simulation and optimization problems, largely because of advances in computing speeds. It is VIII Preface now far easier to “simulate” the application of a chosen method to test likely outcomes of its application to a particular problem. Second, an increased interest in six sigma methods and other formal approaches to making businesses more competitive has increased the time and resources invested in developing and applying new statistical methods.

Tis latter development can be credited to consultants such as Harry and Schroeder (1999), Pande et al. (2000), and Taguchi (1993), visionary business leaders such as General Electric’s Jack Welch, as well as to statistical sofware that permits non-experts to make use of the related technologies. In addition, there is a push towards closer integration of optimization, marketing, and statistical methods into “improvement systems” that structure product-design projects from beginning to end.

Statistical methods are relevant to virtually everyone. Calculus and linear algebra are helpful, but not necessary, for their use. Te approach taken here is to minimize explanations requiring knowledge of these subjects, as far as possible. Tis book is organized into three parts. For a single introductory course, the frst few chapters in Parts One and Two could be used. More advanced courses could be built upon the remaining chapters. At Te Ohio State Uni- versity, I use each part for a diferent 11 week course.

Te second edition featured expanded treatment of lean manufacturing and design for six sigma (DFSS). Specifcally, many lean methods are added to Chaps. 5 and 21 is entirely new. Also, there was additional design of experiments (DOE) related introductory material in Chap. 10. Te new material includes coverage of full factorials, paired t-testing, and additional coverage of analysis of variance (ANOVA). Finally, several corrections have been made particularly relating to design of experiments theory and advanced methods.

Te third edition expands substantially on four major topics of increasing relevance to organizations interested in lean six sigma. First, the material is tied more directly to the Certifed Quality Engineer (CQE) exam from ASQ. Second, motivation and change management are critical subjects for achieving valuable results. Tey are also covered on the CQE exam. Tird, reliability, maintenance, and product safety are covered in order to span the CQE body of knowledge more completely. Fourth, new material provides additional to sofware including Minitab.

In addition, the third edition provides more introductory material on analysis of variance and multiple comparisons. Feedback from instructors sug- gested that more material be provided on these standard topics. Te author IX Preface would like to thank the National Science Foundation for Support under grant #1409214. Tis support helped to create awareness of the results of lean six sigma to cybersecurity.

Theodore T. Allen Columbus, USA

References

Besterfeld D (2001) Quality control. Prentice Hall, Columbus Box GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New York Breyfogle FW (2003) Implementing six sigma: smarter solutions using statistical methods, 2nd edn. Wiley, New York Dean A, Voss DT (1999) Design and analysis of experiments. Springer, Berlin Fedorov V, Hackl P (1997) Model-oriented design of experiments. Springer, Berlin Harry MJ, Schroeder R (1999) Six Sigma, the breakthrough management strategy revolu- tionizing the world’s top corporations. Bantam Doubleday Dell, New York Montgomery DC (2000) Design and analysis of experiments, 5th edn. Wiley, Hoboken Montgomery DC (2001) Statistical quality control, 4th edn. Wiley, Hoboken Myers RH, Montgomery DA (2001) Response surface methodology, 5th edn. Wiley, Hoboken Pande PS, Neuman RP, Cavanagh R (2000) The six sigma way: how GE, motorola, and other top companies are honing their performance. McGraw-Hill, New York Taguchi G (1993) Taguchi methods: research and development. In: Konishi S (ed) Quality engineering series, vol 1. The American Supplier Institute, Livonia Wu CFJ, Hamada M (2000) Experiments: planning, analysis, and parameter design optimization. Wiley, New York Acknowledgements

I thank my wife, Emily, for being wonderful. I thank my sons, Andrew and Henry, for putting good eforts into their schooling. I also thank my parents, George and Jodie, for being exceptionally good parents. Both Emily and Jodie provided important editing and conceptual help. In addition, Austin Mount-Campbell helped greatly in generating much of the new content for the second edition. Also, Sonya Humes and editors at Springer Verlag including Kate Brown and Anthony Doyle provided valuable editing and comments. Discussions with Jack Feng were helpful in planning the third edition. In particular, his knowledge and experiences relating to leadership and the ASQ Certifed Quality Engineering exam were inspirational.

Gary Herrin, my advisor, provided valuable perspective and encouragement. Also, my former Ph.D. students deserve high praise for helping to develop the conceptual framework and components for this book. In particular, I thank Liyang Yu for proving by direct test that modern computers are able to opti- mize experiments evaluated using simulation, which is relevant to the last four chapters of this book, and for much hard work and clear thinking. Also, I thank Mikhail Bernshteyn for his many contributions, including deeply involving my research group in simulation optimization, sharing in some potentially important innovations in multiple areas, and bringing technology in Part II of this book to the marketplace through Sagata Ltd., in which we are partners. I thank Charlie Ribardo for teaching me many things about engineering and helping to develop many of the welding-related case studies in this book. Waraphorn Ittiwattana helped to develop approaches for optimization and robust engineering in Chap. 14. Navara Chantarat played an important role in the design of experiments discoveries in Chap. 18. I thank Deng Huang for playing the leading role in our exploration of variable fdel- ity approaches to experimentation and optimization. I am grateful to James Brady for developing many of the real case studies and for playing the leading role in our related writing and concept development associated with six sigma, relevant throughout this book.

Also, I would like to thank my former M.S. students, including Chaitanya Joshi, for helping me to research the topic of six sigma. Chetan Chivate also assisted in the development of text on advanced modeling techniques (Chap. 16). Also, Gavin Richards and many other students at Te Ohio State University played key roles in providing feedback, editing, refning, and developing the examples and problems. In particular, Mike Fujka and Ryan McDorman provided the student project examples.

In addition, I would like to thank all of the individuals who have supported this research over the last several years. Tese have included frst and foremost XI Acknowledgements

Allen Miller, who has been a good boss and mentor, and also Richard Rich- ardson and David Farson who have made the welding world accessible; it has been a pleasure to collaborate with them. Jose Castro, John Lippold, William Marras, Gary Maul, Clark Mount-Campbell, Philip Smith, David Woods, and many others contributed by believing that experimental planning is important and that I would some day manage to contribute to its study.

Also, I would like to thank Dennis Harwig, David Yapp, and Larry Brown both for contributing fnancially and for sharing their visions for related research. Multiple people from Visteon assisted, including John Barkley, Frank Fusco, Peter Gilliam, and David Reese. Jane Fraser, Robert Gustafson, and the Industrial and Systems Engineering students at Te Ohio State Uni- versity helped me to improve the book. Bruce Ankenman, Angela Dean, Wil- liam Notz, Jason Hsu, and Tom Santner all contributed through discussions.

Also, editors and reviewers played an important role in the development of this book and publication of related research. First and foremost of these is Adrian Bowman of the Journal of the Royal Statistical Society Series C: Applied Statistics, who quickly recognized the value of the EIMSE optimal designs (see Chap. 13). Douglas Montgomery of Quality and Reliability Engi- neering International and an expert on engineering statistics provided key encouragement in multiple instances. In addition, the anonymous reviewers of this book provided much direct and constructive assistance including forc- ing the improvement of the examples and mitigation of the predominantly myopic, US-centered focus.

Finally, I would like to thank seven people who inspired me, perhaps unin- tentionally: Richard DeVeaux and Jef Wu, both of whom taught me design of experiments according to their vision, Max Morris, who forced me to become smarter, George Hazelrigg, who wants the big picture to make sense, George Box, for his many contributions, and Khalil Kabiri-Bamoradian, who taught me many things. Scott Sink brings passion, ideas, and experience that are much valued by me and other members of our department. His comments have helped with developing this book. XIII

Contents

1 Introduction...... 1 1.1 Purpose of This Book...... 2 1.2 Systems and Key Input Variables...... 2 1.3 Problem-Solving Methods ...... 7 1.3.1 What Is “Six Sigma”?...... 8 1.3.2 What Is “Lean Manufacturing”?...... 10 1.3.3 What Is the “Theory of Constraints (ToC)”?...... 11 1.3.4 What Is “Theory of Constraints Lean Six Sigma (TLS)”? ...... 11 1.4 History of “Quality” and Six Sigma...... 11 1.4.1 History of Management and Quality...... 12 1.4.2 History of Documentation and Quality...... 16 1.4.3 History of Statistics and Quality ...... 16 1.4.4 The Six Sigma Movement...... 19 1.5 The Culture of Discipline...... 20 1.6 Real Success Stories...... 22 1.7 Statistics...... 23 1.7.1 Inference and Probability...... 23 1.7.2 Inferential Statistics...... 24 1.7.3 Probability Theory...... 26 1.7.4 Events and Independence ...... 29 1.8 Overview of This Book ...... 30 1.9 Problems...... 31 References...... 35

Part I Statistical Quality Control

2 Quality Control and Six Sigma ...... 39 2.1 Introduction...... 40 2.2 Method Names as Buzzwords...... 40 2.3 Where Methods Fit into Projects...... 42 2.4 Organizational Roles and Methods...... 43 2.5 Specifcations: Nonconforming Versus Defective...... 44 2.6 Standard Operating Procedures (SOPs)...... 47 2.6.1 Proposed SOP Process...... 48 2.6.2 Measurement SOPs...... 50 2.7 Problems...... 51 References...... 54 XIV Contents

3 Defne Phase and Strategy ...... 55 3.1 Introduction...... 56 3.2 Systems and Subsystems...... 56 3.3 Project Charters ...... 58 3.3.1 Predicting Expected Profts ...... 60 3.4 Strategies for Project Defnition...... 61 3.4.1 Bottleneck Subsystems...... 62 3.4.2 Go-No-Go Decisions...... 62 3.5 Methods for Defne Phases...... 63 3.5.1 Pareto Charting ...... 63 3.5.2 Benchmarking...... 65 3.6 Formal Meetings...... 70 3.7 Signifcant Figures...... 71 3.8 Chapter Summary ...... 75 3.9 Problems...... 76 References...... 83

4 Measure Phase and Statistical Charting...... 85 4.1 Introduction...... 86 4.2 Evaluating Measurement Systems...... 87 4.2.1 Types of Gauge R&R Methods...... 87 4.2.2 Gauge R&R: Comparison with Standards...... 88 4.2.3 Gauge R&R (Crossed) with Xbar & R Analysis ...... 92 4.3 Measuring Quality Using SPC Charting...... 96 4.3.1 Concepts: Common Causes and Assignable Causes...... 96 4.4 Commonality: Rational Subgroups, Control Limits, and Startup. . . . . 98 4.5 Attribute Data: P-Charting...... 100 4.6 Attribute Data: Demerit Charting and u-Charting...... 105 4.7 Continuous Data: Xbar & R Charting...... 108 4.7.1 Alternative Continuous Data Charting Methods...... 115 4.8 Chapter Summary and Conclusions ...... 116 4.9 Problems...... 118 References...... 127

5 Analyze Phase...... 129 5.1 Introduction...... 130 5.2 Lean Production...... 130 5.2.1 Process Mapping and Value Stream Mapping...... 130 5.2.2 5S...... 132 5.2.3 Kanban...... 134 5.2.4 Poka-Yoke ...... 134 5.3 The Toyota Production System...... 135 5.4 Process Flow and Spaghetti Diagrams...... 136 5.5 Cause and Efect Matrices...... 139 5.6 Design of Experiments and Regression (Preview)...... 141 XV Contents

5.7 Failure Mode and Efects Analysis...... 143 5.8 Chapter Summary ...... 147 5.9 Problems...... 149 References...... 159

6 Improve or Design Phase...... 161 6.1 Introduction...... 162 6.2 Informal Optimization...... 162 6.3 Quality Function Deployment (QFD)...... 165 6.4 Formal Optimization...... 170 6.5 Chapter Summary ...... 173 6.6 Problems...... 174 References...... 177

7 Control or Verify Phase...... 179 7.1 Introduction...... 180 7.2 Control Planning...... 181 7.3 Acceptance Sampling...... 184 7.3.1 Single Sampling...... 184 7.3.2 Double Sampling...... 186 7.4 Documenting Results...... 188 7.5 Chapter Summary ...... 189 7.6 Problems...... 190 Reference...... 193

8 Advanced SQC Methods...... 195 8.1 Introduction...... 196 8.2 EWMA Charting for Continuous Data...... 196 8.3 Multivariate Charting Concepts...... 200 8.4 Multivariate Charting (Hotelling’s T2 Charts)...... 204 8.5 Summary...... 208 8.6 Problems...... 208 References...... 209

9 SQC Case Studies...... 211 9.1 Introduction...... 212 9.2 Case Study: Printed Circuit Boards...... 212 9.2.1 Experience of the First Team...... 213 9.2.2 Second Team Actions and Results...... 216 9.3 Printed Circuitboard: Analyze, Improve, and Control Phases ...... 218 9.4 Wire Harness Voids Study...... 221 9.4.1 Defne Phase...... 222 9.4.2 Measure Phase...... 222 9.4.3 Analyze Phase...... 224 9.4.4 Improve Phase...... 225 XVI Contents

9.4.5 Control Phase...... 225 9.5 Case Study Exercise...... 226 9.5.1 Project to Improve a Paper Air Wings System...... 227 9.6 Chapter Summary ...... 230 9.7 Problems...... 231 References...... 233

10 SQC Theory ...... 235 10.1 Introduction...... 236 10.2 More on Probability Theory ...... 236 10.3 Continuous Random Variables...... 239 10.3.1 The Normal Probability Density Function...... 243 10.3.2 Defects Per Million Opportunities...... 249 10.3.3 Independent, Identically Distributed and Charting...... 250 10.3.4 The Central Limit Theorem...... 253

10.3.5 Advanced Topic: Deriving d2 and c4...... 256 10.4 Discrete Random Variables...... 257 10.4.1 The Geometric and Hypergeometric Distributions...... 260 10.5 Xbar Charts and Average Run Length...... 263 10.5.1 The Chance of a Signal...... 263 10.5.2 Average Run Length...... 265 10.6 OC Curves and Average Sample Number...... 266 10.6.1 Single Sampling OC Curves...... 267 10.6.2 Double Sampling...... 269 10.6.3 Double Sampling Average Sample Number...... 271 10.7 Chapter Summary...... 271 10.8 Problems ...... 272 References...... 274

Part II Design of Experiments (DOE) and Regression

11 DOE: The Jewel of Quality Engineering...... 277 11.1 Introduction...... 278 11.2 Design of Experiments Methods Overview...... 278 11.3 The Two-Sample T-Test Methodology and the Word “Proven”...... 280 11.4 T-Test Examples...... 283 11.5 Randomization Testing and Paired T-Testing...... 286 11.6 ANOVA for Two Sample T-Tests...... 291 11.7 Full Factorials...... 294 11.8 Randomization and Evidence ...... 295 11.9 Errors from DOE Procedures...... 297 11.10 Chapter Summary ...... 298 11.11 Problems...... 300 References...... 305 XVII Contents

12 DOE: Screening Using Fractional Factorials...... 307 12.1 Introduction...... 308 12.2 Standard Screening Using Fractional Factorials...... 308 12.3 Screening Examples ...... 317 12.4 Method Origins and Alternatives...... 322 12.4.1 Origins of the Arrays...... 322 12.4.2 Alternatives to the Methods in This Chapter...... 324 12.5 Standard Versus One-Factor-at-a-Time Experimentation...... 326 12.6 Chapter Summary ...... 328 12.7 Problems...... 328 References...... 333

13 DOE: Response Surface Methods...... 335 13.1 Introduction...... 336 13.2 Design Matrices for Fitting RSM Models...... 336 13.3 One-Shot Response Surface Methods ...... 339 13.4 One-Shot RSM Examples...... 343 13.5 Creating 3D Surface Plots in Excel...... 352 13.6 Sequential Response Surface Methods...... 352 13.7 Origin of RSM Designs and Decision-Making...... 359 13.7.1 Origins of the RSM Experimental Arrays...... 359 13.7.2 Decision Support Information (Optional)...... 362 13.8 Appendix: Additional Response Surface Designs ...... 365 13.9 Chapter Summary ...... 365 13.10 Problems...... 371 References...... 374

14 DOE: Robust Design...... 375 14.1 Introduction...... 376 14.2 Expected Profts and Control-by-Noise Interactions...... 377 14.3 Robust Design Based on Proft Maximization...... 380 14.4 Extended Taguchi Methods ...... 387 14.5 Literature Review and Methods Comparison...... 391 14.6 Chapter Summary ...... 393 14.7 Problems...... 394 References...... 395

15 Regression...... 397 15.1 Introduction...... 398 15.2 Single Variable Example...... 398 15.2.1 Demand Trend Analysis...... 399 15.2.2 The Least Squares Formula...... 400 15.3 Preparing “Flat Files” and Missing Data...... 401 15.4 Evaluating Models and DOE Theory ...... 402 15.4.1 Variance Infation Factors and Correlation Matrices...... 403 XVIII Contents

15.4.2 Normal Probability Plots and Other “Residual Plots”...... 406 15.4.3 Summary Statistics...... 411 15.4.4 Calculating R2 Prediction...... 412 15.5 Analysis of Variance Followed by Multiple T-Tests...... 414 15.6 Regression Modeling Flowchart...... 417 15.7 Categorical and Mixture Factors (Optional)...... 422 15.7.1 Regression with Categorical Factors...... 422 15.7.2 DOE with Categorical Inputs and Outputs...... 424 15.7.3 Recipe Factors or “Mixture Components”...... 426 15.8 Chapter Summary ...... 427 15.9 Problems...... 427 References...... 433

16 Advanced Regression and Alternatives...... 435 16.1 Introduction...... 436 16.2 Generic Curve Fitting ...... 436 16.2.1 Curve Fitting Example...... 437 16.3 Kriging Models and Computer Experiments ...... 438 16.3.1 Design of Experiments for Kriging Models ...... 439 16.3.2 Fitting Kriging Models...... 439 16.3.3 Kriging Single Variable Example...... 441 16.4 Neural Nets for Regression Type Problems...... 442 16.5 Logistic Regression and Discrete Choice Models...... 448 16.5.1 Design of Experiments for Logistic Regression ...... 449 16.5.2 Fitting Logit Models...... 450 16.6 Software: JMP and Minitab...... 452 16.7 Chapter Summary ...... 455 16.8 Problems...... 455 References...... 456

17 DOE and Regression Case Studies ...... 459 17.1 Introduction...... 460 17.2 Case Study: The Rubber Machine...... 460 17.2.1 The Situation...... 460 17.2.2 Background Information...... 461 17.2.3 The Problem Statement...... 461 17.3 The Application of Formal Improvement Systems Technology...... 462 17.4 Case Study: Snap Tab Design Improvement...... 465 17.5 The Selection of the Factors...... 469 17.6 General Procedure for Low Cost Response Surface Methods ...... 470 17.7 The Engineering Design of Snap Fits...... 470 17.8 Concept Review...... 474 17.9 Additional Discussion of Randomization ...... 476 17.10 Chapter Summary ...... 478 17.11 Problems...... 478 References...... 480 XIX Contents

18 DOE and Regression Theory...... 481 18.1 Introduction...... 482 18.2 Design of Experiments Criteria...... 482 18.3 Generating “Pseudo-Random” Numbers...... 484 18.3.1 Other Distributions...... 485 18.3.2 Correlated Random Variables ...... 488 18.3.3 Monte Carlo Simulation (Review)...... 489 18.3.4 The Law of the Unconscious Statistician ...... 490 18.4 Simulating T-Testing...... 491 18.4.1 Sample Size Determination for T-Testing...... 494 18.5 Simulating Standard Screening Methods...... 496 18.6 Evaluating Response Surface Methods...... 499 18.6.1 Taylor Series and Reasonable Assumptions...... 499 18.6.2 Regression and Expected Prediction Errors...... 501 18.6.3 The EIMSE Formula...... 504 18.7 Chapter Summary ...... 509 18.8 Problems...... 510 References...... 512

Part III Optimization and Management

19 Optimization and Strategy...... 517 19.1 Introduction...... 518 19.2 Formal Optimization...... 518 19.2.1 Heuristics and Rigorous Methods...... 522 19.3 Stochastic Optimization...... 524 19.4 Genetic Algorithms...... 526 19.4.1 Genetic Algorithms for Stochastic Optimization...... 526 19.4.2 Populations, Cross-over, and Mutation...... 527 19.4.3 An Elitist Genetic Algorithm with Immigration ...... 528 19.4.4 Test Stochastic Optimization Problems...... 530 19.5 Variants on the Proposed Methods...... 530 19.5.1 Fitness Proportionate Selection...... 530 19.5.2 Ranking Selection...... 531 19.5.3 Tournament Selection...... 531 19.5.4 Elitist Selection...... 531 19.5.5 Statistical Selection of the Elitist Subset...... 531 19.6 Appendix: C Code for “Toycoolga”...... 531 19.7 Chapter Summary ...... 536 19.8 Problems...... 536 References...... 537 XX Contents

20 Tolerance Design...... 539 20.1 Introduction...... 540 20.2 Chapter Summary ...... 541 20.3 Problems...... 542 Reference...... 542

21 Design for Six Sigma...... 543 21.1 Introduction...... 544 21.2 Design for Six Sigma (DFSS)...... 544 21.3 Implementation ...... 546 21.4 Problems...... 549 References...... 550

22 Lean Sigma Project Design...... 551 22.1 Introduction...... 552 22.2 Literature Review...... 552 22.3 Reverse Engineering Six Sigma...... 553 22.4 Uncovering and Solving Optimization Problems...... 555 22.5 Future Research Opportunities...... 559 22.5.1 New Methods from Stochastic Optimization...... 559 22.5.2 Meso-Analyses of Project Databases...... 561 22.5.3 Test Beds and Optimal Strategies...... 563 22.6 Problems...... 564 References...... 565

23 Motivation and Change Management...... 567 23.1 Introduction...... 568 23.2 Deming...... 568 23.3 Job Design: The Motivating Potential Score...... 570 23.4 Elementary Human Factors Engineering...... 571 23.5 Change Management...... 572 23.6 Problems...... 573 References...... 574

24 Software Overview and Methods Review: Minitab...... 575 24.1 Introduction...... 576 24.2 Quality Data Visualization...... 577 24.3 Pareto Charting...... 578 24.4 Control Charts: Variables...... 583 24.5 Control Charts: Attributes...... 584 24.6 Acceptance Sampling...... 587 24.7 Two Sample Comparisons...... 587 24.8 ANOVA...... 589 24.9 Multiple Comparisons...... 590 24.10 Regular Fractional Factorials...... 591 XXI Contents

24.11 Regression...... 595 24.12 Problems...... 597 Reference...... 600

Supplementary Information ...... 601 Problem Solutions...... 602 Glossary...... 621 Index ...... 625 Acronyms

ANOVA Analysis of Variance is a set of FMEA Failure Mode and Effects Analy- methods for testing whether sis is a technique for prioritizing factors affect system output critical output characteristics dispersion (variance) or, alterna- with regard to the need for addi- tively, for guarding against Type tional investments I errors in regression GAs Genetic Algorithms are a set of BBD Box Behnken designs are com- methods for heuristically solv- monly used approaches for ing optimization problems that structuring experimentation to share some traits in common permit fitting of second-order with natural evolution polynomials with prediction accuracy that is often acceptable IER Individual Error Rate is a probability of Type I errors relevant to CCD Central composite designs are achieving a relatively low level of commonly used approaches to evidence not accounting for the structure experimentation to multiplicity of tests permit fitting of second order ISO 9000: The International Standards polynomials with prediction 2000 Organization’s recent approach accuracy that is often acceptable for documenting and modeling business practices DFSS Design for six sigma is a set of methods specifically designed KIV Key Input Variable is a control- for planning products such that lable parameter or factor whose they can be produced smoothly setting is likely to affect at least and with very high levels of one key output variable quality KOV Key Output Variable is a system DOE Design of experiments methods output of interest to stakeholders are formal approaches for vary- ing input settings systematically LCRSM Low Cost Response Surface and fitting models after data Methods are alternatives to have been collected standard RSM, generally requiring fewer test runs EER Experimentwise Error Rate is a probability of Type I errors rele- OEMs Original Equipment Manufac- vant to achieving a high level of turers are the companies with evidence accounting for the fact well-known names that typically that many effects might be tested employ a large base of suppliers simultaneously to make their products EIMSE The Expected Integrated Mean OFAT One-Factor-at-a-Time is an Squared Error is a quantitative experimental approach in which, evaluation of an input pattern at any given iteration, only a sin- or “DOE matrix” to predict the gle factor or input has its settings likely errors in prediction that varied with other factor settings will occur, taking into account held constant the effects of random errors and model misspecification or bias XXIII Acronyms

PRESS PRESS is a cross-validation- SSE Sum of Squared Errors is the based estimate of the sum of additive sum of the squared squares errors relevant to the residuals or error estimates in evaluation of a fitted model the context of a curve fitting such as a linear regression fitted method such as regression polynomial TLS Theory of Constraints Lean Six QFD Quality Function Deployment Sigma which is the method of are a set of methods that combining TOC, lean and six involve creating a large table or sigma “house of quality” summarizing TOC Theory of Constraints is a information about competitor method involving the identifi- system and customer prefer- cation and tuning of bottleneck ences subsystems TPS The Toyota Production System is RDPM Robust Design Using Profit Max- the way manufacturing is done imization is one approach to at Toyota, which inspired lean achieve Taguchi’s goals based production and Just In Time on standard RSM experimenta- manufacturing tion, i.e., an engineered system TTD Total Travel Distance is an that delivers consistent quality approximate length that quanti- RSM Response Surface Methods are fies how far items or information the category of DOE methods pass through a facility related to developing relatively accurate prediction models (com- VIF Variance Inflation Factor is a pared with screening methods) number that evaluates whether and using them for optimization an input pattern can support reliable fitting of a model form SOPs Standard Operating Procedures in question, i.e., it can help clar- are documented approaches ify whether a particular question intended to be used by an organ- can be answered using a given ization for performing tasks data source SPC Statistical Process Control is a VSM Value Stream Mapping is a var- collection of techniques tar- iant of process mapping with geted mainly at evaluating added activities inspired by a whether something unusual has desire to reduce waste and the occurred in recent operations Toyota Production System SQC Statistical Quality Control is a set of techniques intended to aid in the improvement of system quality