Experiments E-Book

C. F. Jeff Wu

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 1051

Veröffentlichungsjahr: 2011

Beschreibung

Praise for the First Edition:

"If you . . . want an up-to-date, definitive reference written by authors who have contributed much to this field, then this book is an essential addition to your library."
—Journal of the American Statistical Association

Fully updated to reflect the major progress in the use of statistically designed experiments for product and process improvement, Experiments, Second Edition introduces some of the newest discoveries—and sheds further light on existing ones—on the design and analysis of experiments and their applications in system optimization, robustness, and treatment comparison. Maintaining the same easy-to-follow style as the previous edition while also including modern updates, this book continues to present a new and integrated system of experimental design and analysis that can be applied across various fields of research including engineering, medicine, and the physical sciences.

The authors modernize accepted methodologies while refining many cutting-edge topics including robust parameter design, reliability improvement, analysis of non-normal data, analysis of experiments with complex aliasing, multilevel designs, minimum aberration designs, and orthogonal arrays. Along with a new chapter that focuses on regression analysis, the Second Edition features expanded and new coverage of additional topics, including:

• Expected mean squares and sample size determination

• One-way and two-way ANOVA with random effects

• Split-plot designs

• ANOVA treatment of factorial effects

• Response surface modeling for related factors

Drawing on examples from their combined years of working with industrial clients, the authors present many cutting-edge topics in a single, easily accessible source. Extensive case studies, including goals, data, and experimental designs, are also included, and the book's data sets can be found on a related FTP site, along with additional supplemental material. Chapter summaries provide a succinct outline of discussed methods, and extensive appendices direct readers to resources for further study.

Experiments, Second Edition is an excellent book for design of experiments courses at the upper-undergraduate and graduate levels. It is also a valuable resource for practicing engineers and statisticians.

Leseprobe

Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc. Hoboken, New JerseyPublished simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Wu, Chien-Fu Jeff.

Experiments: planning, analysis, and optimization / C. F. Jeff Wu, Michael S. Hamada. – 2nd ed.

p. cm.

Includes index.

ISBN 978-0-471-69946-0 (cloth)

1. Experimental design. I. Hamada, Michael, 1955– II. Title.

QA279.W7 2009519.5’7—dc22

2008049909

To my parents and Jung Hee, Christina, and Alexandra

M. S. H.

To my mother and family

C. F. J. W.

Preface to the Second Edition

Nearly a decade has passed since the publication of the first edition. Many instructors have used the first edition to teach master’s and Ph.D. students. Based on their feedback and our own teaching experience, it became clear that we needed to revise the book to make it more accessible to a larger audience, including upper-level undergraduates. To this end, we have expanded and reorganized the early chapters in the second edition. For example, our book now provides a self-contained presentation of regression analysis (Sections 1.4–1.8), which prepares those students who have not previously taken a regression course. We have found that such a foundation is needed because most of the data analyses in this book are based on regression or regression-like models. Consequently, this additional material will make it easier to adopt the book for courses that do not have a regression analysis prerequisite.

In the early chapters, we have provided more explanation and details to clarify the calculations required in the various data analyses considered. The ideas, derivations, and data analysis illustrations are presented at a more leisurely pace than in the first edition. For example, first edition Chapter 1 has been expanded into second edition Chapters 1 and 2. Consequently, second edition Chapters 3–14 correspond to first edition Chapters 2–13. We have also reorganized second edition Chapters 3–5 in a more logical order to teach with. For example, analysis methods for location effects that focus on the mean response are presented first and separated from analysis methods for dispersion effects that consider the response variance. This allows instructors to skip the material on dispersion analysis if it suits the needs of their classes. In this edition, we have also removed material that did not fit in the chapters and corrected errors in a few calculations and plots.

To aid the reader, we have marked more difficult sections and exercises by a “*”; they can be skipped unless the reader is particularly interested in the topic. Note that the starred sections and exercises are more difficult than those in the same chapter and are not necessarily more difficult than those in other chapters.

The second edition presents a number of new topics, which include:

• expected mean squares and sample size determination (Section 2.4),

• one-way ANOVA with random effects (Section 2.5),

• two-way ANOVA with random effects (Section 3.4) with application to measurement system assessment,

• split-plot designs (Section 3.9),

• ANOVA treatment of factorial effects (Section 4.5) to bridge the main analysis method of Chapters 1–3 with the factorial effect based analysis method in Chapter 4,

• a response surface modeling method for related factors (Section 7.9.3), which allows expanded prediction capability for two related factors that are both quantitative,

• more details on the Method II frequentist analysis method for analyzing experiments with complex aliasing (Section 9.4),

• more discussion of the use of compound noise factors in robust parameter design (Section 11.8.1),

• more discussion and illustration of Bayesian approach to analyzing GLMs and other models for nonnormal data (Sections 14.5–14.6).

In addition, ANOVA derivations are given in Section 3.8 on balanced incomplete block designs, and more details are given on optimal designs in Section 5.4.2. In this edition, we have also rewritten extensively, updated the references throughout the book, and have sparingly pointed the reader to some recent and important papers in the literature on various topics in the later chapters. All data sets, sample lecture notes, and a sample syllabus can be accessed on the book’s FTP site:

ftp://ftp.wiley.com/public/sci tech med/experiments-planning/

Solutions to selected exercises are available to instructors from the authors.

The preparation of this edition has benefited from the comments and assistance of many colleagues and former students, including Nagesh Adiga, Derek Bingham, Ying Hung, V. Roshan Joseph, Lulu Kang, Rahul Mukerjee, Peter Z. Qian, Matthias Tan, Huizhi Xie, Kenny Qian Ye, and Yu Zhu. Tirthankar Dasgupta played a major role in the preparation and writing of new sections in the early chapters; Xinwei Deng provided meticulous support throughout the preparation of the manuscript. We are grateful to all of them. Without their support and interest, this revision could not have been completed.

C. F. Jeff WuMichael S. Hamada

Atlanta, Georgia

Los Alamos, New Mexico

June 2009

Preface to the First Edition

(Note that the chapter numbering used below refers to first edition chapters.)

Statistical experimental design and analysis is an indispensable tool for experimenters and one of the core topics in a statistics curriculum. Because of its importance in the development of modern statistics, many textbooks and several classics have been written on the subject, including the influential 1978 book Statistics for Experimenters by Box, Hunter, and Hunter. There have been many new methodological developments since 1978 and thus are not covered in standard texts. The writing of this book was motivated in part by the desire to make these modern ideas and methods accessible to a larger readership in a reader friendly fashion.

Among the new methodologies, robust parameter design stands out as an innovative statistical/engineering approach to off-line quality and productivity improvement. It attempts to improve a process or product by making it less sensitive to noise variation through statistically designed experiments. Another important development in theoretical experimental design is the widespread use of the minimum aberration criterion for optimal assignment of factors to columns of a design table. This criterion is more powerful than the maximum resolution criterion for choosing fractional factorial designs. The third development is the increasing use of designs with complex aliasing in conducting economical experiments. It turns out that many of these designs can be used for the estimation of interactions, which is contrary to the prevailing practice that they be used for estimating the main effects only. The fourth development is the widespread use of Generalized Linear Models (GLMs) and Bayesian methods for analyzing nonnormal data. Many experimental responses are nonnormally distributed, such as binomial and Poisson counts as well as ordinal frequencies, or have lifetime distributions and are observed with censoring that arises in reliability and survival studies. With the advent of modern computing, these tools have been incorporated in texts on medical statistics and social statistics. They should also be made available to experimenters in science and engineering. There are also other experimental methodologies that originated more than 20 years ago but have received scant attention in standard application-oriented texts. These include mixed two- and four-level designs, the method of collapsing for generating orthogonal main-effect plans, Plackett–Burman designs, and mixed-level orthogonal arrays. The main goal of writing this book is to fill in these gaps and present a new and integrated system of experimental design and analysis, which may help in defining a new fashion of teaching and for conducting research on this subject.

The intended readership of this book includes general practitioners as well as specialists. As a textbook, it covers standard material like analysis of variance (ANOVA), two- and three-level factorial and fractional factorial designs and response surface methodologies. For reading most of the book, the only prerequisite is an undergraduate level course on statistical methods and a basic knowledge of regression analysis. Because of the multitude of topics covered in the book, it can be used for a variety of courses. The material contained here has been taught at the Department of Statistics and the Department of Industrial and Operations Engineering at the University of Michigan to undergraduate seniors, master’s, and doctoral students. To help instructors choose which material to use from the book, a separate “Suggestions of Topics for Instructors” follows this preface.

Some highlights and new material in the book are outlined as follows. Chapters 1 and 2 contain standard material on analysis of variance, one-way and multi-way layout, randomized block designs, Latin squares, balanced incomplete block designs, and analysis of covariance. Chapter 3 addresses two-level factorial designs and provides new material in Sections 3.13–3.17 on the use of formal tests of effect significance in addition to the informal tests based on normal and half-normal plots. Chapter 4, on two-level fractional factorial designs, uses the minimum aberration criterion for selecting optimal fractions and emphasizes the use of follow-up experiments to resolve the ambiguities in aliased effects. In Chapter 5, which deals with three-level designs, the linear-quadratic system and the variable selection strategy for handling and analyzing interaction effects are new. A new strategy for handling multiple responses is also presented. Most of the material in Chapter 6 on mixed two- and four-level designs and the method of sliding levels is new. Chapter 7, on nonregular designs, is the only theoretical chapter in the book. It emphasizes statistical properties and applications of the designs rather than their construction and mathematical structure. For practitioners, only the collections of tables in its appendices and some discussions in the sections on their statistical properties may be of interest. Chapter 7 paves the way for the new material in Chapter 8. Both frequentist and Bayesian analysis strategies are presented. The latter employs Gibbs sampling for efficient model search. Supersaturated designs are also briefly discussed. Chapter 9 contains a standard treatment of response surface methodologies. Chapters 10 and 11 present robust parameter design. The former deals with problems with a simple response while the latter deals with those with a signal–response relationship. The three important aspects of parameter design are considered: choice of performance measures, planning techniques, and modeling and analysis strategies. Chapter 12 is concerned with experiments for reliability improvement. Both failure time data and degradation data are considered. Chapter 13 is concerned with experiments with nonnormal responses. Several approaches to analysis are considered, including generalized linear models and Bayesian methods.

The book has some interesting features not commonly found in experimental design texts. Each of Chapters 3 to 13 starts with one or more case studies, which include the goal of the investigation, the data, the experimental plan, and the factors and their levels. It is then followed by sections devoted to the description of experimental plans (i.e., experimental designs). Required theory or methodology for the experimental designs are developed in these sections. They are followed by sections on modeling and analysis strategies. The chapter then returns to the original data, analyzes it using the strategies just outlined, and discusses the implications of the analysis results to the original case studies. The book contains more than 80 experiments, mostly based on actual case studies; of these, 30 sets are analyzed in the text and more than 50 are given in the exercises. Each chapter ends with a practical summary which provides an easy guide to the methods covered in that chapter and is particularly useful for readers who want to find a specific tool but do not have the patience to go through the whole chapter. The book takes a novel approach to design tables. Many tables are new and based on recent research in experimental design theory and algorithms. For regular designs, only the design generators are given. Full designs can be easily generated by the readers from these generators. The collections of clear effects are given in these tables, however, because it would require some effort, especially for the less mathematically oriented readers, to derive them. The complete layouts of the orthogonal arrays are given in Chapter 8 for the convenience of the readers. With our emphasis on methodologies and applications, mathematical derivations are given sparingly. Unless the derivation itself is crucial to the understanding of the methodology, we omit it and refer to the original source.

The majority of the writing of this book was done at the University of Michigan. Most of the authors’ research that is cited in the book was done at the University of Michigan with support from the National Science Foundation (1994–1999) and at the University of Waterloo (1988–1995) with support from the Natural Sciences and Engineering Research Council of Canada and the GM/NSERC Chair in Quality and Productivity. We have benefited from the comments and assistance of many colleagues and former students, including Julie Bérubé, Derek Bingham, Ching-Shui Cheng, Hugh Chipman, David Fenscik, Xiaoli Hou, Longcheen Huwang, Bill Meeker, Randy Sitter, Huaiqing Wu, Hongquan Xu, Qian Ye, Runchu Zhang, and Yu Zhu. Shao-Wei Cheng played a pivotal supporting role as the book was completed; Jock MacKay read the first draft of the entire book and made numerous penetrating and critical comments; Jung-Chao Wang provided invaluable assistance in the preparation of tables for Chapter 8. We are grateful to all of them. Without their efforts and interest, this book could not have been completed.

C. F. Jeff WuMichael S. Hamada

Ann Arbor, Michigan

Los Alamos, New Mexico

Suggestions of Topics for Instructors

One term for senior and master’s students in Statistics, Engineering, Physical, Life and Social Sciences (with no background in regression analysis):

Chapters 1, 2, 3 (some of 3.4, 3.8, 3.9, 3.11 can be skipped), 4 (except 4.5, 4.13, 4.14), 5; optional material from Chapters 11 (11.1–11.5, part of 11.6–11.9), 6 (6.1–6.6), 8 (8.1–8.5), 9 (9.1–9.4), 10 (10.1–10.3, 10.5, 10.7). For students with a background in regression analysis, Sections 1.4–1.8 can be skipped or briefly reviewed.

One term for a joint master’s and Ph.D. course in Statistics/Biostatistics:

Chapters 1 (1.1–1.3), 2 (except 2.4), 3 (3.4 and 3.9 may be skipped), 4 (except 4.13–4.14), 5, 6 (6.7–6.8 may be skipped), 10 (10.4 and 10.8 may be skipped), 11 (11.1–11.6, part of 11.7–11.9); optional material from Chapters 7 (7.1–7.5, 7.9), 8 (8.1–8.5), 9 (except 9.5). Coverage of Chapters 1 to 3 can be accelerated for those with a background in ANOVA.

Two-term sequence for master’s and Ph.D. students in Statistics/Biostatistics:

First term: Chapters 1 to 3 (can be accelerated if ANOVA is a prerequisite), Chapters 4 (4.13–4.14 may be skipped), 5, 6, 7.

Second term: Chapters 8 (the more theoretical material may be skipped), 9 (9.5 may be skipped), 10 (10.8 may be skipped), 11, 12 (12.6 may be skipped), 13 (13.5 may be skipped), 14 (14.5–14.6, 14.8–14.9 may be skipped).

One-term advanced topics course for Ph.D. students with background in introductory graduate experimental design course:

Selected topics from Chapters 5 to 14 depending on the interest and back ground of the students.

One-term course on theoretical experimental design for Ph.D. students in Statistics and Mathematics:

Sections 1.3, 3.6–3.9, 4.2–4.3, 4.6–4.7, 4.15, 5.2–5.6, 6.3–6.4, 6.8, 7.2–7.3, 7.7–7.8, Chapter 8, 9.6, 10.4, 10.7–10.8, 11.6–11.8, 12.6.

List of Experiments and Data Sets

CHAPTER 1Table 1.1.Breast Cancer Mortality DataTable 1.10.Rainfall DataTable 1.11.Brain and Body Weight DataTable 1.12.Long Jump DataTable 1.13.Ericksen DataTable 1.14.Gasoline Consumption DataCHAPTER 2Table 2.1.Reflectance Data, Pulp ExperimentTable 2.5.Strength Data, Composite ExperimentTable 2.8.Adapted Muzzle Velocity DataTable 2.9.Summary Data, Airsprayer ExperimentTable 2.10.Packing Machine DataTable 2.11.Blood Pressure DataCHAPTER 3Table 3.1.Residual Chlorine Readings, Sewage ExperimentTable 3.4.Strength Data, Girder ExperimentTable 3.8.Torque Data, Bolt ExperimentTable 3.12.Sensory Data, Measurement System Assessment StudyTable 3.17.Weight Loss Data, Wear ExperimentTable 3.23.Wear Data, Tire ExperimentTable 3.29.Water Resistance Data, Wood ExperimentTable 3.34.Data Starch ExperimentTable 3.40.Design Matrix and Response Data, Drill ExperimentTable 3.41.Strength Data, Original Girder ExperimentTable 3.43.Yield Data, Chemical Reaction ExperimentTable 3.44.Strength Data, Revised Composite ExperimentTable 3.45.Yield Data, Tomato ExperimentTable 3.46.Worsted Yarn DataTable 3.48.Data, Resistor ExperimentTable 3.49.Data, Blood Pressure ExperimentTable 3.50.Throughput DataTable 3.51.Muzzle Velocity DataTable 3.52.Corrosion Resistances of Steel Bars, Steel ExperimentTable 3.53.Data, Thickness Gauge StudyTable 3.54.Data, CMM StudyCHAPTER 4Table 4.1.Design Matrix and Thickness Data, Adapted Epitaxial Layer Growth ExperimentTable 4.10.Design Matrix and Thickness Data, Original Epitaxial Layer Growth ExperimentTable 4.14.Planning Matrix and Response Data, Spring ExperimentTable 4.15.Food ExperimentTable 4.16.Task Efficiency ExperimentTable 4.17.Design Matrix and Roughness Data, Drive Shaft ExperimentTable 4.18.Metal Alloy Crack ExperimenCHAPTER 5Table 5.2.Design Matrix and Free Height Data, Leaf Spring ExperimentTable 5.10.Yield ExperimentTable 5.11.Design Matrix and Tensile Strength Data, Spot Welding ExperimentTable 5.12.Design Matrix and Response Data, Stamping ExperimentTable 5.13.Design Matrix and Closing Effort Data, Hatchback ExperimentCHAPTER 6Table 6.2.Design Matrix and Response Data, Seat-Belt ExperimentTable 6.14.Design Matrix and Response Data, Confirmatory Seat-Belt ExperimentTable 6.15.Design Matrix and Response Data, Ultrasonic Bonding ExperimentTable 6.16.Design Matrix and Response Data, Control Valve ExperimentTable 6.17.Design Matrix and Response Data, Core Drill ExperimentTable 6.18.Design Matrix and Response Data, Casting ExperimentCHAPTER 7Table 7.2.Design Matrix and Lifetime Data, Router Bit ExperimentTable 7.6.Design Matrix, Paint ExperimentTable 7.7.Thickness Data, Paint ExperimentTable 7.11.Design Matrix and Covariates, Light Bulb ExperimentTable 7.13.Appearance Data, Light Bulb ExperimentTable 7.18.Design Matrix and Response Data, Reel Motor ExperimentTable 7.19.Design Matrix and Response Data, Plastic-Forming ExperimentTable 7.21.Design Matrix and Response Data, Weatherstrip ExperimentCHAPTER 8Table 8.2.Design Matrix and Lifetime Data, Cast Fatigue ExperimentTable 8.4.Design Matrix and Response Data, Blood Glucose ExperimentTable 8.11.A 10-Factor 12-Run Experiment with Six Added RunsCHAPTER 9Table 9.2.Design Matrix and Response Data, Plackett–Burman Desig Example ExperimentTable 9.5.Supersaturated Design Matrix and Adhesion Data, Epoxy ExperimentTable 9.6.Original Epoxy Experiment Based on 28-Run Plackett–Burman DesignTable 9.8.Design Matrix and Lifetime Data, Heat Exchanger ExperimentTable 9.12.Design Matrix, Window Forming ExperimentTable 9.13.Pre-Etch Line-Width Data, Window Forming ExperimentTable 9.14.Post-Etch Line-Width Data, Window Forming ExperimentTable 9.16.Design Matrix and Strength Data, Ceramics ExperimentTable 9.17.Design Matrix and Response Data, Wood Pulp ExperimentCHAPTER 10Table 10.2.Design Matrix and Response Data, Ranitidine ExperimentTable 10.3.Design Matrix and Yield Data for First-Order DesignTable 10.5.Design Matrix and Yield Data for Second-Order DesignTable 10.9.Design Matrix, Ranitidine Screening ExperimentTable 10.12.Design Matrix and Response Data, Final Second-Order Ranitidine ExperimentTable 10.14.Runs Along the First Steepest Ascent DirectionTable 10.15.Central Composite DesignTable 10.17.Design Matrix and Response Data, Amphetamine ExperimentTable 10.18.Design Matrix and Response Data, Whiteware ExperimentTable 10.19.Design Matrix and Response Data, Drill ExperimentTable 10.20.Design Matrix and Response Data, Ammonia ExperimentTable 10.21.Design Matrix and Response Data, TAB Laser ExperimentTable 10.22.Design Matrix and Response Data, Cement ExperimentTable 10.23.Design Matrix, Bulking Process ExperimentCHAPTER 11Table 11.2.Cross Array and Thickness Data, Layer Growth ExperimentTable 11.4.Cross Array and Height Data, Leaf Spring ExperimentTable 11.11.Cross Array and Dishing Data, Gear ExperimentTable 11.12.Cross Array and Percent Shrinkage Data, Injection Molding ExperimentTable 11.13.Cross Array and Tar Value Data, Chemical Process ExperimentTable 11.14.Single Array and Response Data, Injection Molding ExperimentCHAPTER 12Table 12.3.Control Array, Injection Molding ExperimentTable 12.4.Response Data, Injection Molding ExperimentTable 12.11.Design Matrix and Weight Data, Coating ExperimentTable 12.13.Control Array, Drive Shaft ExperimentTable 12.14.Response Data, Drive Shaft ExperimentTable 12.16.Control Array, Surface Machining ExperimentTable 12.17.Single Array for Signal and Noise Factors, Surface Machining ExperimentTable 12.18.Response Data, Surface Machining ExperimentTable 12.20.Control Array and Fitted Parameters, Engine Idling ExperimentCHAPTER 13Table 13.1.Design Matrix and Failure Time Data, Light ExperimentTable 13.3.Design Matrix, Thermostat ExperimentTable 13.4.Failure Time Data, Thermostat ExperimentTable 13.6.Cross Array and Failure Time Data (with Censoring Time of 3000), Drill Bit ExperimentTable 13.13.Design Matrix and Failure Time Data, Ball Bearing ExperimentTable 13.14.Design Matrix and Lifetime Data (×103 Cycles, Censored at 2000), Transmission Shaft ExperimentTable 13.15.Original Window Size Data (WNO Indicates Window not Opened), Window Forming ExperimentTable 13.16.Design Matrix and Lifetime Data, Threading Machine ExperimentCHAPTER 14Table 14.1.Design Matrix and Defect Counts, Wave Soldering ExperimentTable 14.7.Cross Array and Frequencies (good (I), ok (II), poor (III)), Foam Molding ExperimentTable 14.9.Design Matrix and Response Data, Windshield Molding ExperimentTable 14.10.Design Matrix and Response Data, Arc Welding ExperimentTable 14.11.Design Matrix and Response Data, Flywheel Balancing ExperimentTable 14.12.Design Matrix and Flow Mark Count Data, Glove Compartment ExperimentTable 14.13.Design Matrix and Off-Grade Tile Count (Out of 100), Tile ExperimentTable 14.14.Poppy Counts, Weed Infestation ExperimentTable 14.15.Larvae Counts, Larvae Control ExperimentTable 14.16.Unsuccessful Germination Counts (Out ofSeeds), Wheat ExperimentTable 14.17.Window Size Data, Window Forming ExperimentTable 14.18.Design and Max Peel Strength Data, Sealing Process Experiment