Theodore T. Allen-Introduction to engineering statistics and six sigma_ statistical quality control

Theodore T. Allen-Introduction to engineering statistics and six sigma_ statistical quality control

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Unformatted text preview: Introduction to Engineering Statistics and Six Sigma Theodore T. Allen Introduction to Engineering Statistics and Six Sigma Statistical Quality Control and Design of Experiments and Systems With 114 Figures 123 Theodore T. Allen, PhD Department of Industrial Welding and Systems Engineering The Ohio State University 210 Baker Systems 1971 Neil Avenue Colombus, OH 43210-1271 USA British Library Cataloguing in Publication Data Allen, Theodore T. Introduction to engineering statistics and six sigma: statistical quality control and design of experiments and systems 1. Engineering - Statistical methods 2. Six sigma (Quality control standard) I. Title 620’.0072 ISBN-10: 1852339551 Library of Congress Control Number: 2005934591 ISBN-10: 1-85233-955-1 ISBN-13: 978-1-85233-955-5 e-ISBN 1-84628-200-4 Printed on acid-free paper © Springer-Verlag London Limited 2006 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed in Germany 987654321 Springer Science+Business Media springer.com 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 benefits from applying methods under such headings as “statistical quality control” (SQC) and “design of experiments” (DOE). Some college-level books intertwine 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 sufficiently 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 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 several complete case studies conducted by myself and former students. Third, I feel that much of the “theory” in standard textbooks is rarely presented 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, confidence intervals, and defining 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 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 bioengineering 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 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. which comprehensively cover six sigma; Montgomery (2001) and Besterfield (2001), which focus on statistical quality control; Box and Draper viii Preface (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 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 applying 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 powerful 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 contribution 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, dramatic improvements have occurred in the ability to solve hard simulation and optimization problems, largely because of advances in computing speeds. It is 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. 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 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. The approach taken here is to minimize explanations requiring knowledge of these subjects, as far as possible. Preface ix 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 University, I use each part for a different 11 week course. References Box GEP, Draper NR (1987) Empirical Model-Building and Response Surfaces. Wiley, New York Besterfield D (2001) Quality Control. Prentice Hall, Columbus, OH 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 Heidelberg New York Fedorov V, Hackl P (1997) Model-Oriented Design of Experiments. Springer, Berlin Heidelberg New York Harry MJ, Schroeder R (1999) Six Sigma, The Breakthrough Management Strategy Revolutionizing The World’s Top Corporations. Bantam Doubleday Dell, New York Montgomery DC (2000) Design and Analysis of Experiments, 5th edn. John Wiley & Sons, Inc., Hoboken, NJ Montgomery DC (2001) Statistical Quality Control, 4th edn. John Wiley & Sons, Inc., Hoboken, NJ Myers RH, Montgomery DA (2001) Response Surface Methodology, 5th edn. John Wiley & Sons, Inc., Hoboken, NJ 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, MI Wu CFJ, Hamada M (2000) Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York Acknowledgments I thank my wife, Emily, for being wonderful. I thank my son, Andrew, for being extremely cute. 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, Sonya Humes and editors at Springer Verlag including Kate Brown and Anthony Doyle provided valuable editing and comments. 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 optimize 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 Chapter 14. Navara Chantarat played an important role in the design of experiments discoveries in Chapter 18. I thank Deng Huang for playing the leading role in our exploration of variable fidelity 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 (Chapter 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 Allen Miller, who has been a good boss and mentor, and also Richard Richardson and David Farson who have made the welding world accessible; it has been a pleasure xii Acknowledgments 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 University helped me to improve the book. Bruce Ankenman, Angela Dean, William Notz, Jason Hsu, and Tom Santner all contributed. 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 Chapter 13). Douglas Montgomery of Quality and Reliability Engineering 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 forcing the improvement of the examples and mitigation of the predominantly myopic, US-centered focus. Finally, I would like to thank six people who inspired me, perhaps unintentionally: 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 and teaches me many things. Contents List of Acronyms................................................................................................... xxi 1 Introduction ............................................................................................. 1 1.1 Purpose of this Book ...................................................................... 1 1.2 Systems and Key Input Variables................................................... 2 1.3 Problem-solving Methods .............................................................. 6 1.3.1 What Is “Six Sigma”? ....................................................... 7 1.4 History of “Quality” and Six Sigma ............................................. 10 1.4.1 History of Management and Quality............................... 10 1.4.2 History of Documentation and Quality ........................... 14 1.4.3 History of Statistics and Quality ..................................... 14 1.4.4 The Six Sigma Movement .............................................. 17 1.5 The Culture of Discipline ............................................................. 18 1.6 Real Success Stories..................................................................... 20 1.7 Overview of this Book ................................................................. 21 1.8 References .................................................................................... 22 1.9 Problems....................................................................................... 22 Part I Statistical Quality Control 2 Statistical Quality Control and Six Sigma ........................................... 29 2.1 Introduction .................................................................................. 29 2.2 Method Names as Buzzwords ...................................................... 30 2.3 Where Methods Fit into Projects.................................................. 31 2.4 Organizational Roles and Methods .............................................. 33 2.5 Specifications: Nonconforming vs Defective............................... 34 2.6 Standard Operating Procedures (SOPs)........................................ 36 2.6.1 Proposed SOP Process .................................................... 37 2.6.2 Measurement SOPs......................................................... 40 2.7 References .................................................................................... 40 2.8 Problems....................................................................................... 41 3 Define Phase and Strategy .................................................................... 45 3.1 Introduction .................................................................................. 45 xiv Contents 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Systems and Subsystems .............................................................. 46 Project Charters ............................................................................ 47 3.3.1 Predicting Expected Profits............................................. 50 Strategies for Project Definition................................................... 51 3.4.1 Bottleneck Subsystems ................................................... 51 3.4.2 Go-no-go Decisions ........................................................ 52 Methods for Define Phases........................................................... 53 3.5.1 Pareto Charting ............................................................... 53 3.5.2 Benchmarking................................................................. 56 Formal Meetings .......................................................................... 58 Significant Figures ....................................................................... 60 Chapter Summary......................................................................... 63 References .................................................................................... 65 Problems....................................................................................... 65 4 Measure Phase and Statistical Charting.............................................. 75 4.1 Introduction .................................................................................. 75 4.2 Evaluating Measurement Systems................................................ 76 4.2.1 Types of Gauge R&R Methods....................................... 77 4.2.2 Gauge R&R: Comparison with Standards ...................... 78 4.2.3 Gauge R&R (Crossed) with Xbar & R Analysis............. 81 4.3 Measuring Quality Using SPC Charting ...................................... 85 4.3.1 Concepts: Common Causes and Assignable Causes....... 86 4.4 Commonality: Rational Subgroups, Control Limits, and Startup. 87 4.5 Attribute Data: p-Charting............................................................ 89 4.6 Attribute Data: Demerit Charting and u-Charting ........................ 94 4.7 Continuous Data: Xbar & R Charting .......................................... 98 4.7.1 Alternative Continuous Data Charting Methods........... 104 4.8 Chapter Summary and Conclusions ........................................... 105 4.9 References .................................................................................. 107 4.10 Problems..................................................................................... 107 5 Analyze Phase ...................................................................................... 117 5.1 Introduction ................................................................................ 117 5.2 Process Mapping and Value Stream Mapping ........................... 117 5.2.1 The Toyota Production System.......
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