Introduction to Engineering Statistics and Lean Six Sigma

Theodore T. Allen

Introduction to Engineering Statistics and Lean Six SigmaStatistical Quality Control and Design of Experiments and Systems

Third Edition

Theodore T. AllenIndustrial 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

1st and 2nd edition: © Springer-Verlag London Limited 2006, 2010© Springer-Verlag London Ltd., part of Springer Nature 2019 The author(s) has/have asserted their right(s) to be identified as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988.This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer-Verlag London Ltd. part of Springer NatureThe registered company address is: The Campus, 4 Crinan Street, London, N1 9XW, United Kingdom

V

Dedicated to my wife and to my parents

Preface

There 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-fits 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 applica-tion from the theory needed to understand and evaluate the methods.

Second, many books teach methods without sufficiently clarifying the context in which the method could help to solve a real-world problem. Six sigma, statis-tics and operations-research experts have little trouble making the connections with practice. However, many other people do have this difficulty. Therefore, 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 sev-eral complete case studies conducted by myself and former students.

Third, 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 specific 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-fidence intervals, and defining relations) does have a bearing on these ques-tions. Yet the widely accepted view that the choice to apply a method is equivalent to purchasing a risky stock investment has not been sufficiently clarified. The theory in this book is mainly used to evaluate in advance the risks associated with specific 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 reflected in some of the alternative books. Therefore, this book constitutes an attempt to include more examples pertinent to service-sector jobs in accounting, education, call centers, health care, and software 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 artificial intelligence work and research. Both disciplines relate to formalized deci-sion processes and statistical concepts. Also, lean six sigma relates to more

VIIPreface

than half of procedures software in Minitab and JMP. Much of the remaining software methods in Minitab and JMP relate to human-not-in-the-loop deci-sion-making or machine learning.

In addition, this book can be viewed as attempt to build on and refocus mate-rial in other books and research articles, including: Harry and Schroeder (1999) and Pande et al. (2000) which comprehensively cover six sigma; Montgomery (2001) and Besterfield (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 tech-niques. 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 fill 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 apply-ing them to real-world problems. Professionals who have earned “black belt” and “master black belt” titles may find material more complete and intensive here than in other sources.

Rather than teaching methods as “correct” and fixed, 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 profits has been only partially explored. As a result, users of these methods too often 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 meth-ods 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 busi-nesses more competitive has increased the time and resources invested in developing and applying new statistical methods.

This 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 software that permits non-experts to make use of the related technologies. In addition, there is a push towards closer integration of optimization, marketing, and sta-tistical 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. The approach taken here is to minimize explanations requiring knowledge of these subjects, as far as pos-sible. This book is organized into three parts. For a single introductory course, the first few chapters in Parts One and Two could be used. More advanced courses could be built upon the remaining chapters. At The Ohio State Uni-versity, I use each part for a different 11 week course.

The second edition featured expanded treatment of lean manufacturing and design for six sigma (DFSS). Specifically, many lean methods are added to Chaps. 5 and 21 is entirely new. Also, there was additional design of exper-iments (DOE) related introductory material in Chap. 10. The 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.

The 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 Certified Quality Engineer (CQE) exam from ASQ. Second, motivation and change management are critical subjects for achiev-ing valuable results. They are also covered on the CQE exam. Third, reliability, maintenance, and product safety are covered in order to span the CQE body of knowledge more completely. Fourth, new material provides additional to software including Minitab.

In addition, the third edition provides more introductory material on anal-ysis of variance and multiple comparisons. Feedback from instructors sug-gested that more material be provided on these standard topics. The author

IXPreface

References

Besterfield D (2001) Quality control. Prentice Hall, ColumbusBox GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New

YorkBreyfogle FW (2003) Implementing six sigma: smarter solutions using statistical methods,

2nd edn. Wiley, New YorkDean A, Voss DT (1999) Design and analysis of experiments. Springer, BerlinFedorov V, Hackl P (1997) Model-oriented design of experiments. Springer, BerlinHarry MJ, Schroeder R (1999) Six Sigma, the breakthrough management strategy revolu-

tionizing the world’s top corporations. Bantam Doubleday Dell, New YorkMontgomery DC (2000) Design and analysis of experiments, 5th edn. Wiley, HobokenMontgomery DC (2001) Statistical quality control, 4th edn. Wiley, HobokenMyers RH, Montgomery DA (2001) Response surface methodology, 5th edn. Wiley, HobokenPande PS, Neuman RP, Cavanagh R (2000) The six sigma way: how GE, motorola, and other

top companies are honing their performance. McGraw-Hill, New YorkTaguchi G (1993) Taguchi methods: research and development. In: Konishi S (ed) Quality engi-

neering series, vol 1. The American Supplier Institute, LivoniaWu CFJ, Hamada M (2000) Experiments: planning, analysis, and parameter design optimization.

Wiley, New York

would like to thank the National Science Foundation for Support under grant #1409214. This support helped to create awareness of the results of lean six sigma to cybersecurity.

Theodore T. AllenColumbus, USA

Acknowledgements

I thank my wife, Emily, for being wonderful. I thank my sons, Andrew and Henry, for putting good efforts into their schooling. I also thank my par-ents, 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 includ-ing Kate Brown and Anthony Doyle provided valuable editing and comments. Discussions with Jack Feng were helpful in planning the third edition. In par-ticular, his knowledge and experiences relating to leadership and the ASQ Certified 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 technol-ogy 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 opti-mization 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 fidel-ity approaches to experimentation and optimization. I am grateful to James Brady for developing many of the real case studies and for playing the lead-ing 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 The Ohio State University played key roles in providing feedback, editing, refining, 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. These have included first and foremost

XIAcknowledgements

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 financially 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 The 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 Jeff 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Purpose of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Systems and Key Input Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Problem-Solving Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.1 What Is “Six Sigma”? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.2 What Is “Lean Manufacturing”? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.3 What Is the “Theory of Constraints (ToC)”? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.4 What Is “Theory of Constraints Lean Six Sigma (TLS)”? . . . . . . . . . . . . . . . . . . . 111.4 History of “Quality” and Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4.1 History of Management and Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.2 History of Documentation and Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.3 History of Statistics and Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.4 The Six Sigma Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.5 The Culture of Discipline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.6 Real Success Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.7 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.7.1 Inference and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.7.2 Inferential Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.7.3 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.7.4 Events and Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.8 Overview of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Part I Statistical Quality Control

2 Quality Control and Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2 Method Names as Buzzwords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3 Where Methods Fit into Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.4 Organizational Roles and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.5 Specifications: Nonconforming Versus Defective . . . . . . . . . . . . . . . . . . . . . . . 442.6 Standard Operating Procedures (SOPs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.6.1 Proposed SOP Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.6.2 Measurement SOPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

XIV Contents

3 Define Phase and Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2 Systems and Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Project Charters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3.1 Predicting Expected Profits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4 Strategies for Project Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.1 Bottleneck Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.4.2 Go-No-Go Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.5 Methods for Define Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.5.1 Pareto Charting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.5.2 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.6 Formal Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.7 Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4 Measure Phase and Statistical Charting . . . . . . . . . . . . . . . . . . . . . . . . . . 854.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.2 Evaluating Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.2.1 Types of Gauge R&R Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.2.2 Gauge R&R: Comparison with Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.2.3 Gauge R&R (Crossed) with Xbar & R Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.3 Measuring Quality Using SPC Charting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.3.1 Concepts: Common Causes and Assignable Causes . . . . . . . . . . . . . . . . . . . . . . 964.4 Commonality: Rational Subgroups, Control Limits, and Startup . . . . . . . . 984.5 Attribute Data: P-Charting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.6 Attribute Data: Demerit Charting and u-Charting . . . . . . . . . . . . . . . . . . . . . . 1054.7 Continuous Data: Xbar & R Charting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.7.1 Alternative Continuous Data Charting Methods . . . . . . . . . . . . . . . . . . . . . . . . . 1154.8 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5 Analyze Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.2 Lean Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.2.1 Process Mapping and Value Stream Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.2.2 5S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1325.2.3 Kanban . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.2.4 Poka-Yoke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.3 The Toyota Production System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.4 Process Flow and Spaghetti Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1365.5 Cause and Effect Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.6 Design of Experiments and Regression (Preview) . . . . . . . . . . . . . . . . . . . . . . 141

XVContents

5.7 Failure Mode and Effects Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1435.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1475.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

6 Improve or Design Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1616.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1626.2 Informal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1626.3 Quality Function Deployment (QFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1656.4 Formal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1706.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1736.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

7 Control or Verify Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1797.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1807.2 Control Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1817.3 Acceptance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1847.3.1 Single Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1847.3.2 Double Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.4 Documenting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1887.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1897.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

8 Advanced SQC Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1958.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1968.2 EWMA Charting for Continuous Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1968.3 Multivariate Charting Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2008.4 Multivariate Charting (Hotelling’s T2 Charts) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2048.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2088.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

9 SQC Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2129.2 Case Study: Printed Circuit Boards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2129.2.1 Experience of the First Team . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2139.2.2 Second Team Actions and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2169.3 Printed Circuitboard: Analyze, Improve, and Control Phases . . . . . . . . . . . 2189.4 Wire Harness Voids Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2219.4.1 Define Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2229.4.2 Measure Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2229.4.3 Analyze Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2249.4.4 Improve Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

XVI Contents

9.4.5 Control Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2259.5 Case Study Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2269.5.1 Project to Improve a Paper Air Wings System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2279.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2309.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

10 SQC Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23510.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23610.2 More on Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23610.3 Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23910.3.1 The Normal Probability Density Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24310.3.2 Defects Per Million Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24910.3.3 Independent, Identically Distributed and Charting . . . . . . . . . . . . . . . . . . . . . . . 25010.3.4 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25310.3.5 Advanced Topic: Deriving d2 and c4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25610.4 Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25710.4.1 The Geometric and Hypergeometric Distributions . . . . . . . . . . . . . . . . . . . . . . . 26010.5 Xbar Charts and Average Run Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26310.5.1 The Chance of a Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26310.5.2 Average Run Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26510.6 OC Curves and Average Sample Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26610.6.1 Single Sampling OC Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26710.6.2 Double Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26910.6.3 Double Sampling Average Sample Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27110.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27110.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

Part II Design of Experiments (DOE) and Regression

11 DOE: The Jewel of Quality Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . 27711.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27811.2 Design of Experiments Methods Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27811.3 The Two-Sample T-Test Methodology and the Word “Proven” . . . . . . . . . . . 28011.4 T-Test Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28311.5 Randomization Testing and Paired T-Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 28611.6 ANOVA for Two Sample T-Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29111.7 Full Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29411.8 Randomization and Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29511.9 Errors from DOE Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29711.10 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29811.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

XVIIContents

12 DOE: Screening Using Fractional Factorials . . . . . . . . . . . . . . . . . . . . . . 30712.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30812.2 Standard Screening Using Fractional Factorials . . . . . . . . . . . . . . . . . . . . . . . . 30812.3 Screening Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31712.4 Method Origins and Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32212.4.1 Origins of the Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32212.4.2 Alternatives to the Methods in This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32412.5 Standard Versus One-Factor-at-a-Time Experimentation . . . . . . . . . . . . . . . 32612.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32812.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

13 DOE: Response Surface Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33513.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33613.2 Design Matrices for Fitting RSM Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33613.3 One-Shot Response Surface Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33913.4 One-Shot RSM Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34313.5 Creating 3D Surface Plots in Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35213.6 Sequential Response Surface Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35213.7 Origin of RSM Designs and Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . 35913.7.1 Origins of the RSM Experimental Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35913.7.2 Decision Support Information (Optional) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36213.8 Appendix: Additional Response Surface Designs . . . . . . . . . . . . . . . . . . . . . . 36513.9 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36513.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

14 DOE: Robust Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37514.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37614.2 Expected Profits and Control-by-Noise Interactions . . . . . . . . . . . . . . . . . . . . 37714.3 Robust Design Based on Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . 38014.4 Extended Taguchi Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38714.5 Literature Review and Methods Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 39114.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39314.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

15 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39815.2 Single Variable Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39815.2.1 Demand Trend Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39915.2.2 The Least Squares Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40015.3 Preparing “Flat Files” and Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40115.4 Evaluating Models and DOE Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40215.4.1 Variance Inflation Factors and Correlation Matrices . . . . . . . . . . . . . . . . . . . . . . 403

XVIII Contents

15.4.2 Normal Probability Plots and Other “Residual Plots” . . . . . . . . . . . . . . . . . . . . . 40615.4.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41115.4.4 Calculating R2 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41215.5 Analysis of Variance Followed by Multiple T-Tests . . . . . . . . . . . . . . . . . . . . . . 41415.6 Regression Modeling Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41715.7 Categorical and Mixture Factors (Optional) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42215.7.1 Regression with Categorical Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42215.7.2 DOE with Categorical Inputs and Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42415.7.3 Recipe Factors or “Mixture Components” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42615.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42715.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

16 Advanced Regression and Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . 43516.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43616.2 Generic Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43616.2.1 Curve Fitting Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43716.3 Kriging Models and Computer Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 43816.3.1 Design of Experiments for Kriging Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43916.3.2 Fitting Kriging Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43916.3.3 Kriging Single Variable Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44116.4 Neural Nets for Regression Type Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44216.5 Logistic Regression and Discrete Choice Models . . . . . . . . . . . . . . . . . . . . . . . 44816.5.1 Design of Experiments for Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . 44916.5.2 Fitting Logit Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45016.6 Software: JMP and Minitab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45216.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45516.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

17 DOE and Regression Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45917.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46017.2 Case Study: The Rubber Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46017.2.1 The Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46017.2.2 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46117.2.3 The Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46117.3 The Application of Formal Improvement Systems Technology . . . . . . . . . . 46217.4 Case Study: Snap Tab Design Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46517.5 The Selection of the Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46917.6 General Procedure for Low Cost Response Surface Methods . . . . . . . . . . . 47017.7 The Engineering Design of Snap Fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47017.8 Concept Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47417.9 Additional Discussion of Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47617.10 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47817.11 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

XIXContents

18 DOE and Regression Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48118.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48218.2 Design of Experiments Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48218.3 Generating “Pseudo-Random” Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48418.3.1 Other Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48518.3.2 Correlated Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48818.3.3 Monte Carlo Simulation (Review) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48918.3.4 The Law of the Unconscious Statistician . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49018.4 Simulating T-Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49118.4.1 Sample Size Determination for T-Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49418.5 Simulating Standard Screening Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49618.6 Evaluating Response Surface Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49918.6.1 Taylor Series and Reasonable Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49918.6.2 Regression and Expected Prediction Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50118.6.3 The EIMSE Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50418.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50918.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

Part III Optimization and Management

19 Optimization and Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51719.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51819.2 Formal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51819.2.1 Heuristics and Rigorous Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52219.3 Stochastic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52419.4 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52619.4.1 Genetic Algorithms for Stochastic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 52619.4.2 Populations, Cross-over, and Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52719.4.3 An Elitist Genetic Algorithm with Immigration . . . . . . . . . . . . . . . . . . . . . . . . . . 52819.4.4 Test Stochastic Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53019.5 Variants on the Proposed Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53019.5.1 Fitness Proportionate Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53019.5.2 Ranking Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53119.5.3 Tournament Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53119.5.4 Elitist Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53119.5.5 Statistical Selection of the Elitist Subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53119.6 Appendix: C Code for “Toycoolga” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53119.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53619.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

XX Contents

20 Tolerance Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53920.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54020.2 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54120.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

21 Design for Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54321.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54421.2 Design for Six Sigma (DFSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54421.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54621.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

22 Lean Sigma Project Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55122.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55222.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55222.3 Reverse Engineering Six Sigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55322.4 Uncovering and Solving Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . 55522.5 Future Research Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55922.5.1 New Methods from Stochastic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55922.5.2 Meso-Analyses of Project Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56122.5.3 Test Beds and Optimal Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56322.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

23 Motivation and Change Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56723.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56823.2 Deming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56823.3 Job Design: The Motivating Potential Score . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57023.4 Elementary Human Factors Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57123.5 Change Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57223.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

24 Software Overview and Methods Review: Minitab . . . . . . . . . . . . . . 57524.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57624.2 Quality Data Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57724.3 Pareto Charting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57824.4 Control Charts: Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58324.5 Control Charts: Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58424.6 Acceptance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58724.7 Two Sample Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58724.8 ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58924.9 Multiple Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59024.10 Regular Fractional Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

XXIContents

24.11 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59524.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

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

ANOVA Analysis of Variance is a set of methods for testing whether factors affect system output dispersion (variance) or, alterna-tively, for guarding against Type I errors in regression

BBD Box Behnken designs are com-monly used approaches for structuring experimentation to permit fitting of second-order polynomials with prediction accuracy that is often acceptable

CCD Central composite designs are commonly used approaches to structure experimentation to permit fitting of second order polynomials with prediction accuracy that is often acceptable

DFSS Design for six sigma is a set of methods specifically designed for planning products such that they can be produced smoothly and with very high levels of quality

DOE Design of experiments methods are formal approaches for vary-ing input settings systematically and fitting models after data have been collected

EER Experimentwise Error Rate is a probability of Type I errors rele-vant to achieving a high level of evidence accounting for the fact that many effects might be tested simultaneously

EIMSE The Expected Integrated Mean Squared Error is a quantitative evaluation of an input pattern or “DOE matrix” to predict the likely errors in prediction that will occur, taking into account the effects of random errors and model misspecification or bias

Acronyms

FMEA Failure Mode and Effects Analy-sis is a technique for prioritizing critical output characteristics with regard to the need for addi-tional investments

GAs Genetic Algorithms are a set of methods for heuristically solv-ing optimization problems that share some traits in common with natural evolution

IER Individual Error Rate is a proba-bility of Type I errors relevant to achieving a relatively low level of evidence not accounting for the multiplicity of tests

ISO 9000: The International Standards 2000 Organization’s recent approach

for documenting and modeling business practices

KIV Key Input Variable is a control-lable parameter or factor whose setting is likely to affect at least one key output variable

KOV Key Output Variable is a system output of interest to stakeholders

LCRSM Low Cost Response Surface Methods are alternatives to standard RSM, generally requir-ing fewer test runs

OEMs Original Equipment Manufac-turers are the companies with well-known names that typically employ a large base of suppliers to make their products

OFAT One-Factor-at-a-Time is an experimental approach in which, at any given iteration, only a sin-gle factor or input has its settings varied with other factor settings held constant

XXIIIAcronyms

PRESS PRESS is a cross-validation- based estimate of the sum of squares errors relevant to the evaluation of a fitted model such as a linear regression fitted polynomial

QFD Quality Function Deployment are a set of methods that involve creating a large table or “house of quality” summarizing information about competitor system and customer prefer-ences

RDPM Robust Design Using Profit Max-imization is one approach to achieve Taguchi’s goals based on standard RSM experimenta-tion, i.e., an engineered system that delivers consistent quality

RSM Response Surface Methods are the category of DOE methods related to developing relatively accurate prediction models (com-pared with screening methods) and using them for optimization

SOPs Standard Operating Procedures are documented approaches intended to be used by an organ-ization for performing tasks

SPC Statistical Process Control is a collection of techniques tar-geted mainly at evaluating whether something unusual has occurred in recent operations

SQC Statistical Quality Control is a set of techniques intended to aid in the improvement of system quality

SSE Sum of Squared Errors is the additive sum of the squared residuals or error estimates in the context of a curve fitting method such as regression

TLS Theory of Constraints Lean Six Sigma which is the method of combining TOC, lean and six sigma

TOC Theory of Constraints is a method involving the identifi-cation and tuning of bottleneck subsystems

TPS The Toyota Production System is the way manufacturing is done at Toyota, which inspired lean production and Just In Time manufacturing

TTD Total Travel Distance is an approximate length that quanti-fies how far items or information pass through a facility

VIF Variance Inflation Factor is a number that evaluates whether an input pattern can support reliable fitting of a model form in question, i.e., it can help clar-ify whether a particular question can be answered using a given data source

VSM Value Stream Mapping is a var-iant of process mapping with added activities inspired by a desire to reduce waste and the Toyota Production System