Modern Experimental Design

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1 Modern Experimental Design THOMAS P. RYAN Acworth, GA

3 Modern Experimental Design

5 Modern Experimental Design THOMAS P. RYAN Acworth, GA

6 Copyright C 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, , fax , or on the web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, , fax , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at , outside the United States at or fax Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at Library of Congress Cataloging-in-Publication Data: Ryan, Thomas P. Modern experimental design / by Thomas P. Ryan p. cm. Includes bibliographical references and index. ISBN Printed in the United States of America

7 Contents Preface xv 1 Introduction Experiments All Around Us Objectives for Experimental Designs Planned Experimentation versus Use of Observational Data Basic Design Concepts Randomization Replication versus Repeated Measurements Example Size of an Effect That Can be Detected Terminology Steps for the Design of Experiments Recognition and Statement of the Problem Selection of Factors and Levels Choice of Factors Choice of Levels Processes Should Ideally be in a State of Statistical Control Types of Experimental Designs Analysis of Means Missing Data Experimental Designs and Six Sigma Quasi-Experimental Design Summary 23 References 23 Exercises 26 v

8 vi contents 2 Completely Randomized Design Completely Randomized Design Model Example: One Factor, Two Levels Assumptions Examples: One Factor, More Than Two Levels Multiple Comparisons Unbalanced and Missing Data Computations Example Showing the Effect of Unequal Variances Analysis of Means ANOM for a Completely Randomized Design Example ANOM with Unequal Variances Applications Nonparametric ANOM ANOM for Attributes Data Software for Experimental Design Missing Values Summary 48 Appendix 49 References 49 Exercises 51 3 Designs that Incorporate Extraneous (Blocking) Factors Randomized Block Design Assumption Blocking an Out-of-Control Process Efficiency of a Randomized Block Design Example Critique ANOM Incomplete Block Designs Balanced Incomplete Block Designs Analysis Recovery of Interblock Information ANOM Partially Balanced Incomplete Block Designs Lattice Design Nonparametric Analysis for Incomplete Block Designs Other Incomplete Block Designs Latin Square Design Assumptions Model 74

9 contents vii Example Efficiency of a Latin Square Design Using Multiple Latin Squares ANOM Graeco Latin Square Design Model Degrees of Freedom Limitations on the Design Construction Sets of Graeco Latin Square Designs Application ANOM Youden Squares Model Lists of Youden Designs Using Replicated Youden Designs Analysis Missing Values Software Summary 90 References 91 Exercises 93 4 Full Factorial Designs with Two Levels The Nature of Factorial Designs The Deleterious Effects of Interactions Conditional Effects Sample Sizes for Conditional Effects Estimation Can We Transform Away Interactions? Effect Estimates Why Not One-Factor-at-a-Time Designs? ANOVA Table for Unreplicated Two-Factor Design? The 2 3 Design Built-in Replication Multiple Readings versus Replicates Reality versus Textbook Examples Factorial Design but not Factorial Model Bad Data in Factorial Designs ANOM Display Normal Probability Plot Methods Missing Data in Factorial Designs Resulting from Bad Data Proposed Solutions Inaccurate Levels in Factorial Designs Checking for Statistical Control Blocking 2 k Designs 142

10 viii contents 4.16 The Role of Expected Mean Squares in Experimental Design Hypothesis Tests with Only Random Factors in 2 k Designs? Avoid Them! Hierarchical versus Nonhierarchical Models Hard-to-Change Factors Software for Designs with Hard-to-Change Factors Factors Not Reset Detecting Dispersion Effects Software Summary 151 Appendix A Derivation of Conditional Main Effects 152 Appendix B Relationship Between Effect Estimates and Regression Coefficients: 153 Appendix C Precision of the Effect Estimates 153 Appendix D Expected Mean Squares for the Replicated 2 2 Design 153 Appendix E Expected Mean Squares, in General 155 References 157 Exercises Fractional Factorial Designs with Two Levels k 1 Designs Which Fraction? Effect Estimates and Regression Coefficients Alias Structure What if I Had Used the Other Fraction? k 2 Designs Basic Concepts Designs with k p = Normal Probability Plot Methods when k p = Other Graphical Methods Utility of Small Fractional Factorials vis-à-vis Normal Probability Plots Design Efficiency Retrieving a Lost Defining Relation Minimum Aberration Designs and Minimum Confounded Effects Designs Blocking Factorial Designs Blocking Fractional Factorial Designs Blocks of Size Foldover Designs Semifolding Conditional Effects Semifolding a 2 k 1 Design 210

11 contents ix General Strategy? Semifolding with Software John s 3/4 Designs Projective Properties of 2 k p Designs Small Fractions and Irregular Designs An Example of Sequential Experimentation Critique of Example Inadvertent Nonorthogonality Case Study Fractional Factorial Designs for Natural Subsets of Factors Relationship Between Fractional Factorials and Latin Squares Alternatives to Fractional Factorials Designs Attributed to Genichi Taguchi Missing and Bad Data Plackett Burman Designs Software Summary 233 References 234 Exercises Designs With More Than Two Levels k Designs Decomposing the A B Interaction Inference with Unreplicated 3 k Designs Conditional Effects k p Designs Understanding 3 k p Designs Constructing 3 k p Designs Alias Structure Constructing a Design Need for Mixed Number of Levels Replication of 3 k p Designs? Mixed Factorials Constructing Mixed Factorials Additional Examples Mixed Fractional Factorials Orthogonal Arrays with Mixed Levels Minimum Aberration Designs and Minimum Confounded Effects Designs Four or More Levels Software Catalog of Designs Summary 284 References 284 Exercises 286

12 x contents 7 Nested Designs Various Examples Software Shortcomings A Workaround Staggered Nested Designs Nested and Staggered Nested Designs with Factorial Structure Estimating Variance Components ANOM for Nested Designs? Summary 302 References 302 Exercises Robust Designs Taguchi Designs? Identification of Dispersion Effects Designs with Noise Factors Product Array, Combined Array, or Compound Array? Software Further Reading Summary 322 References 323 Exercises Split-Unit, Split-Lot, and Related Designs Split-Unit Design Split-Plot Mirror Image Pairs Designs Split-Unit Designs in Industry Split-Unit Designs with Fractional Factorials Blocking Split-Plot Designs Split-Unit Plackett-Burman Designs Examples of Split-Plot Designs for Hard-to-Change Factors Split-Split-Plot Designs Split-Lot Design Strip-Plot Design Applications of Strip-Block (Strip-Plot) Designs Commonalities and Differences Between these Designs Software Summary 351 References 351 Exercises 354

13 contents xi 10 Response Surface Designs Response Surface Experimentation: One Design or More Than One? Which Designs? Classical Response Surface Designs versus Alternatives Effect Estimates? Method of Steepest Ascent (Descent) Central Composite Designs CCD Variations Small Composite Designs Draper Lin Designs Additional Applications Properties of Space-Filling Designs Applications of Uniform Designs Box Behnken Designs Application Conditional Effects? Other Response Surface Designs Hybrid Designs Uniform Shell Designs Koshal Designs Hoke Designs Blocking Response Surface Designs Blocking Central Composite Designs Blocking Box Behnken Designs Blocking Other Response Surface Designs Comparison of Designs Analyzing the Fitted Surface Characterization of Stationary Points Confidence Regions on Stationary Points Ridge Analysis Ridge Analysis with Noise Factors Optimum Conditions and Regions of Operability Response Surface Designs for Computer Simulations ANOM with Response Surface Designs? Further Reading The Present and Future Direction of Response Surface Designs Software Catalogs of Designs Summary 408 References 409 Exercises 414

14 xii contents 11 Repeated Measures Designs One Factor The Example in Section More Than One Factor Crossover Designs Designs for Carryover Effects How Many Repeated Measures? Further Reading Software Summary 439 References 439 Exercises Multiple Responses Overlaying Contour Plots Seeking Multiple Response Optimization with Desirability Functions Weight and Importance Dual Response Optimization Designs Used with Multiple Responses Applications Multiple Response Optimization Variations The Importance of Analysis Software Summary 471 References 472 Exercises Miscellaneous Design Topics One-Factor-at-a-Time Designs Cotter Designs Rotation Designs Screening Designs Plackett Burman Designs Projection Properties of Plackett Burman Designs Applications Supersaturated Designs Applications Lesser-Known Screening Designs Design of Experiments for Analytic Studies Equileverage Designs One Factor, Two Levels Are Commonly Used Designs Equileverage? 502

15 contents xiii 13.7 Optimal Designs Alphabetic Optimality Applications of Optimal Designs Designs for Restricted Regions of Operability Space-Filling Designs Uniform Designs From Raw Form to Coded Form Sphere-Packing Designs Latin Hypercube Design Trend-Free Designs Cost-Minimizing Designs Mixture Designs Optimal Mixture Designs or Not? ANOM Design of Measurement Capability Studies Design of Computer Experiments Design of Experiments for Categorical Response Variables Weighing Designs and Calibration Designs Calibration Designs Weighing Designs Designs for Assessing the Capability of a System Designs for Nonlinear Models Model-Robust Designs Designs and Analyses for Non-normal Responses Design of Microarray Experiments Multi-Vari Plot Evolutionary Operation Software Summary 532 References 533 Exercises Tying It All Together Training for Experimental Design Use 544 References 545 Exercises 546 Answers to Selected Exercises 551 Appendix: Statistical Tables 565 Author Index 575 Subject Index 587

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