D. H. Stamatis SIX SIGM A AND BEYOND Design of Experiments ST. LUCIE PRESS A CRC Press Company Boca Raton London New York Washington, D.C. © 2002 by CRC Press LLC SL3143_Frame_book Page 4 Tuesday, September 17, 2002 4:28 PM Library of Congress Cataloging-in-Publication Data Stamatis, D.H. Six sigma and beyond: foundations of excellent performance / Dean H. Stamatis. p. cm.—(Six Sigma and beyond series) Includes bibliographical references. ISBN 1-57444311-9 (v.1 : alk. paper) 1. Quality control—Statistical methods. 2. Production management—Statistical methods. 3. Industrial management. I. Title. II. Series. TS156 .S73 2001 658.5′62—dc21 2001041635 CIP This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. 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Visit the CRC Press Web site at www.crcpress.com © 2002 by CRC Press LLC St. Lucie Press is an imprint of CRC Press LLC No claim to original U.S. Government works International Standard Book Number 1-57444311-9 Library of Congress Card Number 2001041635 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Volume V: Design of Experiments: ISBN 157443143 © 2002 by CRC Press LLC SL3143_Frame_book Page 5 Tuesday, September 17, 2002 4:28 PM Dedication To my father, Χαραλαµπος (Charalambos) © 2002 by CRC Press LLC SL3143_Frame_book Page 7 Tuesday, September 17, 2002 4:28 PM Preface Like the other volumes in this series, this book started in a small way. The intention was to write a brief manual of sorts for those who would be doing some analytical work in the pursuit of the six sigma methodology. And that is how it began. It soon became obvious, however, that it did not seem possible to write a brief exposition of design of experiments (DOE) that anyone pursuing DOE would be happy with. So, here is another volume in the Six Sigma and Beyond series that concentrates on the DOE aspects of analytical work. The choice was made to describe it in a separate volume for three reasons. First, we believe that DOE is a general data analytic system that is close to the theoretical and inferential preoccupations and methods of scientific research. If science’s main job is to explain natural phenomena by discovering and studying the relations among variables, then DOE is a general and efficient method to help do this. Second, DOE and its rationale is one of the most important components of multivariate methods. Once DOE is mastered, all other methods become very easy to comprehend. Third, the strongest motivation for devoting a complete volume to this series is that, at present, the issue of quality is in the midst of a conceptual and technical revolution. The effects of this revolution are becoming apparent in the demands that producers and customers make on each other. The structure of this volume is fairly simple. There are two parts. Part I provides the foundations of DOE in the classical sense, and Part II provides the Taguchi approach to experimentation. The appendixes include a review of some of the mathematical concepts, tables and several formulas for calculations, as well as annotated computer commands for several software packages. Specifically, each chapter will cover the following: Chapter 1: The planning and managing of the “process” of experimentation Chapter 2: Considerations of experimental designs Chapter 3: Analysis of existing data Chapter 4: Analysis of means (ANOM) Chapter 5: Analysis of variance (ANOVA) Chapter 6: Factorial designs Chapter 7: Full factorials Chapter 8: Model building—utility of models with experiments Chapter 9: Fractional factorial designs Chapter 10: Three-level designs Chapter 11: Special topics in experimental design Chapter 12: Introduction to Taguchi and parameter design Chapter 13: A new attitude and approach © 2002 by CRC Press LLC SL3143_Frame_book Page 8 Tuesday, September 17, 2002 4:28 PM Chapter 14: Orthogonal and linear graphs Chapter 15: Parameter design Chapter 16: Taguchi and ANOVA Chapter 17: Case studies © 2002 by CRC Press LLC SL3143_Frame_FM Page 9 Wednesday, September 18, 2002 2:34 PM Acknowledgments As in the past, so many individuals have helped either directly or indirectly in this project that I am afraid I will forget to recognize someone. If I do, let me assure you that it is not because I did not value your comments, suggestions and opinions. Rather, it is because I am reaching the age which “senior moments” are to blame. Seriously, I am indeed thankful for all of you who lifted me up with your suggestions and encouraging words in the marathon to complete this series on six sigma. Specifically, I want to thank Dr. B. Price from Wayne State University, who introduced me to statistics, and Drs. R. Richey and D. Marcotte, also from Wayne State University, who guided me through the rough spots in understanding not only the beauty of statistics but also its power in application. Special thanks go to Dr. R.K. Roy, who was kind enough to provide the com- puterized case studies for Chapter 17 using the software Qualitek4; to Mr. L. Scott for helping and running the DOE on Design Ease; and to Cary Stamatis for his valuable help with the Excel spreadsheet in setting the OA and calculations for the examples. I want to also thank Dr. G. Taguchi for his comments on robust design during our extensive meeting in New Delhi, India. I have tried to incorporate some of his principles into this work. I want to also thank Mr. C. Taguchi for the fruitful discussions on linear graphs and his insight into robust design. I will not forget our lengthy discussions in Adelaide, Australia. Also, special thanks go to American Supplier Institute for giving me permission to use some of the orthogonal arrays and linear graphs used in Appendix A. My thanks and appreciation go to my wife Carla, who has put up with me during this project. Thanks also go to my students at Central Michigan University for their sugges- tions and comments for making this volume a better product. I am indebted also to my seminar participants for their comments and suggestions on how to make the material less “dry” and more “friendly.” I have tried to incorporate as many of their suggestions as possible. Finally, I want to thank the folks at CRC Press for the outstanding cooperation, direction and help they have shown me during this project. © 2002 by CRC Press LLC SL3143_Frame_book Page 11 Tuesday, September 17, 2002 4:28 PM About the Author D.H. Stamatis, Ph.D., ASQC-Fellow, CQE, CMfgE, is currently president of Contemporary Consultants in Southgate, Michigan. He received his B.S. and B.A. degrees in marketing from Wayne State University, his Master’s degree from Central Michigan University and his Ph.D. degree in instructional technology and busi- ness/statistics from Wayne State University. Dr. Stamatis is a certified quality engineer for the American Society of Quality Control, a certified manufacturing engineer for the Society of Manufacturing Engi- neers and a graduate of BSI’s ISO 9000 lead assessor training program. He is a specialist in management consulting, organizational development and quality science and has taught these subjects at Central Michigan University, the University of Michigan and Florida Institute of Technology. With more than 30 years of experience in management, quality training and consulting, Dr. Stamatis has served and consulted for numerous industries in the private and public sectors. His consulting extends across the United States, Southeast Asia, Japan, China, India and Europe. He has written more than 60 articles and presented many speeches at national and international conferences on quality. He is a contributing author to several books and the sole author of 20 books. In addition, he has performed more than 100 automotive-related audits and 25 pre-assessment ISO 9000 audits, and has helped several companies attain certification. He is an active member of the Detroit Engineering Society, the American Society for Training and Development, the American Marketing Association, the American Research Association and a fellow of the American Society for Quality Control. © 2002 by CRC Press LLC SL3143_Frame_bookTOC.fm Page 9 Wednesday, September 18, 2002 2:34 PM Contents PART I Traditional Experimental Design Introduction................................................................................................................3 Fundamental Concepts.....................................................................................3 Anatomy of an Experiment.............................................................................4 Factors.....................................................................................................5 Responses...............................................................................................5 Environmental Variables.........................................................................6 Principles of Conduct.......................................................................................7 Variation...........................................................................................................8 The Loss Function Concept...................................................................9 General Types of Designs....................................................................10 Logic of Hypothesis Testing................................................................12 Experimental Error.........................................................................................14 Expected Values....................................................................................15 Degrees of Freedom.......................................................................................17 Coding and Data Analysis.............................................................................18 Interaction.......................................................................................................20 Fixed, Random and Mixed Models...............................................................20 EMS Rules.....................................................................................................24 Example......................................................................................25 References......................................................................................................26 Selected Bibliography....................................................................................26 Chapter 1 Planning and Managing the Process of Experiment.....................................................................................29 Plan.................................................................................................................29 Do...................................................................................................................31 Study...............................................................................................................32 Act..................................................................................................................32 Getting Started with Experimental Design....................................................33 Recognition and Statement of the Problem.........................................33 How Might the Team Select or Clarify the Problem?.........................33 Choosing Factors and Levels......................................................33 Response Variable Selection.......................................................35 Experimental Design Choice......................................................36 © 2002 by CRC Press LLC SL3143_Frame_bookTOC.fm Page 10 Wednesday, September 18, 2002 2:34 PM Performing the Experiment........................................................37 Data Analysis..............................................................................37 Communicating the Results........................................................38 Chapter 2 Considerations of Experimental Designs..........................................41 Statistical Fundamentals................................................................................41 Variation and Variables.........................................................................41 Populations and Samples......................................................................42 Frequency Distributions.......................................................................42 Histograms and Frequency Curves......................................................42 Measures of Location.....................................................................................43 The Average or Mean.....................................................................................43 Median..................................................................................................44 Measures of Central Tendency......................................................................44 Measures of Dispersion.................................................................................44 Range....................................................................................................44 Variance................................................................................................46 Standard Deviation...............................................................................46 Shape of Distribution.....................................................................................46 The Normal Distribution......................................................................48 Characteristics of the Normal Distribution................................48 The Standardized Normal Distribution......................................50 Limitations of the Normal Distribution......................................52 The Distribution of Xbar............................................................52 Structure and Form of Experimental Designs...............................................54 Validity of Experimentation...........................................................................55 Design Types..................................................................................................56 Pre-Experimental Designs....................................................................56 True Experimental Designs..................................................................56 Quasi-Experimental Designs................................................................57 Interpretation of the Design Format....................................................58 References......................................................................................................65 Selected Bibliography....................................................................................66 Chapter 3 Analysis of Existing Data..................................................................69 Variance and Covariance................................................................................69 Simple Regression..........................................................................................71 A Fictitious Example............................................................................72 Test for Significance......................................................................................76 Multiple Regression.......................................................................................79 Regression Weights: b and b ...............................................................80 Calculation of the Squared Multiple Correlation Coefficient.......................83 Computer Programs.......................................................................................83 © 2002 by CRC Press LLC SL3143_Frame_bookTOC.fm Page 11 Wednesday, September 18, 2002 2:34 PM References......................................................................................................84 Selected Bibliography....................................................................................84 Chapter 4 Analysis of Means.............................................................................87 Hypothesis Testing.........................................................................................87 Statistical Hypothesis/Null Hypothesis.........................................................87 Tests of Hypothesis..............................................................................87 Hypothesis Testing Steps.....................................................................89 Selected Test Statistics for Large Samples..........................................92 Selected Tests for Small Samples........................................................93 Sample Size Considerations...........................................................................93 Data Collection Schemes and Design of Experiment.........................94 Characteristics of a Well Planned Data Collection or Experimental Program.....................................................................95 Analysis of Means (ANOM).........................................................................98 Sources of Variation Analysis (SVA)...........................................................100 Formulas for Sources of Variation.....................................................100 Other “Means” Tests....................................................................................104 Estimation Error and Confidence Intervals.................................................104 Confidence Interval Concept..............................................................105 Confidence Intervals for a Mean with Known Variance...................105 Confidence Intervals for Means When the Variance is Unknown....108 Confidence Intervals: Difference Between Two Means, Variance Unknown.............................................................................112 Independent Samples...................................................................................112 Dependent Samples............................................................................113 Selected Bibliography..................................................................................114 Chapter 5 Analysis of Variance (ANOVA).......................................................117 Assumptions of Analysis of Variance..........................................................119 Common Designs for Experiments.............................................................120 Complete Randomization for Background Conditions................................................................................122 The One-Way ANOVA................................................................................122 Two-Way ANOVA........................................................................................125 Randomized-Block Design for Background Conditions.............................127 Latin-Square Design for Background Conditions.......................................128 Other Designs...............................................................................................128 Types of ANOVA.........................................................................................129 Type I Problems.................................................................................129 Type II Problems................................................................................129 After ANOVA, What?..................................................................................130 Means Effects.....................................................................................130 © 2002 by CRC Press LLC