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EE EA Comprehensive Guide to Factorial Two-Level Experimentation AEE E Comprehensive Guide to Factorial Two-Level Experimentation Robert W. Mee A Comprehensive Guide to Factorial Two-Level Experimentation Robert W. Mee Department of Statistics, Operations, and Management Science The University of Tennessee 333 Stokely Management Center Knoxville, TN 37996-0532 USA ISBN 978-0-387-89102-6 e-ISBN 978-0-387-89103-3 DOI 10.1007/b105081 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009927712 © Springer Science+ Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) ASTM R is a registered trademark of ASTM International. AT&T R is a reg- istered trademark of AT&T in the United States and other countries. Baskin- Robbins R is a registered trademark of BR IP Holder LLC. JMP R and SAS R are registered trademarks of the SAS Institute, Inc. Kapton R is a registered trademark of DuPont. Minitab R is a registered trademark of Minitab, Inc. Design-Expert R is a registered trademark of Stat-Ease, Inc. MATLAB R is a registered trademark of The MathWorks, Inc. Web of Science R is a reg- istered tracemark of Thompson Reuters. The Isaiah quotation is from The Holy Bible, English Standard Version, copyright c 2001 by Crossway Bibles, a division of Good News Publishers. Used by permission. All rights reserved. Dedication To Cherol, my lovely wife and helpmate, and our children Joseph, Elizabeth and Evangeline To David Harville, thanks for the “license to learn” “All these things my hand has made, and so all these things came to be, declares the Lord. But this is the one to whom I will look: he who is humble and contrite in spirit and trembles at my word.” — Isaiah 66.2 Is the universe simply made up of numbers? Our eyes tell us everything is countable, action versus reaction, a swinging pendulum. And yet a tiny voice in each of us speaks to the opposite – that every blade of grass only masks the Uncountable, that every ray of light only clothes the Infinite. — Joseph Mee Nil sine Deo viii Being a student and professor is a great privilege. For 33 years I have learned about designed experiments from teachers, colleagues, and students alike. Beginning with Russell Heikes and Doug Montgomery at Georgia Tech, and David Harville and Oscar Kempthorne at Iowa State, I gained a solid foundation in the fascinating field of design and analysis of experiments. Both Dennis Lin and I came to the University of Tennessee (UT) in 1989, and Den- nis’s enthusiasm for research with two-level factorial designs helped reawaken my interest in the field. UT offered a 3-week Design of Experiments Institute at that time, and I gained a new appreciation for how practitioners learn to apply these tools from Richard Sanders, Bob McLean, and Mary Leitnaker. Tony Cooper, Doug Sanders, and Mike Urie challenged me with many ques- tions as students in a master’s-level design course I taught my first semester at UT; having such inquisitive students was a great incentive to understand more deeply. After Ram´on Le´on arrived at Tennessee, he included me in op- portunities to see how AT&T R presented robust parameter design methods to industry. At Ram´on’s initiative, we prepared and taught our own version of robust parameter design for an American Statistical Association workshop; that was a great learning experience. Other prominent statisticians extended invitations to me. Especially influential were Norman Draper’s invitation to a conference at Irsee, Germany and Jeff Wu’s recommendations to include me on early Spring Research Conference programs. Through the DAE (and other) conferences I have benefitted from contacts with so many colleagues that I can only name a few who have been the most influential: Hegang Chen, Ching- Shui Cheng, Shao-Wei Cheng, Sam Hedayat, Brad Jones, Max Morris, Bill Notz, Eric Schoen, David Steinberg, Boxin Tang, Dan Voss, and Hongquan Xu. Finally, many UT students have worked on projects involving two-level designs. Foremost of these have been Ph.D. students Robert Block, David Edwards, and Oksoun Yee. In addition, Rodney Bates, Anne Freeman, Dawn Heaney, Chris Krohn, Huo Li, Chris McCall, Marta Peralta, Anna Romanova, Yeak-Chong Wong, Regina Xiao, Ning Xue, Philip Yates, and Janna Young all completed M.S. independent study projects involving two-level designs that contributed to the results of this book. To this multitude of students, colleagues, and teachers, I say “Thanks.” A final thanks is due to the researchers and statisticians who provided me experiment details beyond that documented in their publications. This list includes George Bandurek, Mark Bond, Dennis Boos, Laurent Broudiscou, Hisham Choueiki and Clark Mount-Campbell, Steve Gilmour, Doug Hawkins and Joshua Yi, Eric Ho`ang, Adam Kramschuster, Aik Chong Lua, Cristina Martin, Eric Schoen, Wen Yang, and Stan Young. Preface Two-level factorial designs fascinated me when, as a senior at Georgia Tech, I was introduced to their clever structure and utility. Courses in design of ex- periments and response surface methodology persuaded me to pursue a career in Statistics. One year later, the eminently successful book Statistics for Ex- perimenters by Box, Hunter, and Hunter (BHH) (1978) was published. That book, more than any other, has enabled scientists and engineers to employ these useful designs. I recall loaning my copy of BHH to an engineering grad- uate student years ago, to introduce him to fractional factorial designs. To my surprise, it was the simpler 2k full factorial designs that captured this stu- dent’s interest. I had incorrectly assumed that he and other engineers would already be familiar with full factorial experiments. But that was not the case; the notion of experimenting with many factors simultaneously was completely new. Indeed, such an idea was truly novel in the 1920s, when Sir Ronald A. Fisher, the father of experimental design, wrote: No aphorism is more frequently repeated in connection with field tri- als, than that we must ask Nature few questions, or, ideally, one ques- tion, at a time. The writer is convinced that this view is wholly mis- taken. Nature, he suggests, will best respond to a logical and carefully thought out questionnaire; indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed. (Fisher, 1926) Two-level factorial and fractional factorial designs, Plackett–Burman de- signs, and two-level orthogonal arrays are now widely used. A search on Web of Science R in December 2008 yielded over 7000 articles mentioning factor- ial designs and nearly 500 more mentioning Plackett–Burman designs. While many of these factorial design applications involve factors with more than two levels, two-level factorial designs are the most common and are the easi- est to understand and analyze. Thus, while this book will be an introduction to 2k full factorial designs for some, its primary objectives go beyond an in- troduction. First, the purpose of this book is to help practitioners design and x Preface analyze two-level factorial designs correctly. As I reviewed published examples, I routinely found mistakes and misunderstandings, especially in the analysis. This book will help nonstatisticians plan and analyze factorial experiments correctly. The following chapters contain 50 analyses of actual data from two- level designs. By carefully studying these examples, how to properly analyze one’s own data will become clear. In the past, I thought intelligent software could automatically analyze the data. While it is true that statistical soft- ware packages such as JMP R , Design-Expert R , and Minitab R have made incredible strides in the last 10 years to facilitate the analysis of these designs, there are many details that distinguish one application from the next and ne- cessitate subtle changes to the analysis. Nothing will replace the requirement for an experienced user. The numerous analyses documented in this book are intended to help build the needed expertise. Beyond exposure to factorial designs and the knowledge to perform an analysis correctly, this book has the further objective of making new devel- opments accessible to practitioners. Over the last 30 years, the statistical literature regarding two-level factorial designs has exploded. General design of experiment books cannot cover such growth in the literature. My goal in writing this more focused book has been to sift through the hundreds of recent articles with new theory and methods, to decide what is most useful, and then to summarize and illustrate that useful material. This book’s comprehensiveness is unique. As a reference book, it will ben- efit both practitioners and statisticians. To aid the reader, the book is divided into three parts. For those with little or no exposure to factorial experimen- tation, Part I: Full Factorial Designs is the most relevant material. Chapter 1 introduces the reader to the advantages of factorial experiments, presents the basic regression models that become the foundation for the analysis, and concludes with a four-step strategy for planning these experiments.
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