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Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger

Springer Series in Statistics Alho/Spencer: Statistical Demography and Forecasting. Andersen/Borgan/Gill/Keiding: Statistical Models Based on Counting Processes. Atkinson/Riani: Robust Diagnostic Regression Analysis. Atkinson/Riani/Cerioli: Exploring Multivariate Data with the Forward Search. Berger: Statistical Decision Theory and Bayesian Analysis, 2nd edition. Borg/Groenen: Modern Multidimensional Scaling: Theory and Applications, 2nd edition. Brockwell/Davis: Time Series: Theory and Methods, 2nd edition. Bucklew: Introduction to Rare Event Simulation. Cappé/Moulines/Rydén: Inference in Hidden Markov Models. Chan/Tong: Chaos: A Statistical Perspective. Chen/Shao/Ibrahim: Monte Carlo Methods in Bayesian Computation. Coles: An Introduction to Statistical Modeling of Extreme Values. David/Edwards: Annotated Readings in the History of Statistics. Devroye/Lugosi: Combinatorial Methods in Density Estimation. Efromovich: Nonparametric Curve Estimation: Methods, Theory, and Applications. Eggermont/LaRiccia: Maximum Penalized Likelihood Estimation, Volume I: Density Fahrmeir/Tutz: Multivariate Statistical Modelling Based on Generalized Linear Fan/Yao: Nonlinear Time Series: Nonparametric and Parametric Methods. Farebrother: Fitting Linear Relationships: A History of the Calculus of Observations Federer: Statistical Design and Analysis for Intercropping Experiments, Volume I: Federer: Statistical Design and Analysis for Intercropping Experiments, Volume II: Estimation. Models, 2nd edition. 1750-1900. Two Crops. Three or More Crops. and Implementation Ferraty/Vieu: Nonparametric Functional Data Analysis: Models, Theory, Applications, Ghosh/Ramamoorthi: Bayesian Nonparametrics. Glaz/Naus/Wallenstein: Scan Statistics. Good: Permutation Tests: Parametric and Bootstrap Tests of Hypotheses, 3rd edition. Gouriéroux: ARCH Models and Financial Applications. Gu: Smoothing Spline ANOVA Models. Györfi/Kohler/Krzyz•ak/Walk: A Distribution-Free Theory of Nonparametric Regression. Haberman: Advanced Statistics, Volume I: Description of Populations. Hall: The Bootstrap and Edgeworth Expansion. Härdle: Smoothing Techniques: With Implementation in S. Harrell: Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. Hart: Nonparametric Smoothing and Lack-of-Fit Tests. Hastie/Tibshirani/Friedman: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Hedayat/Sloane/Stufken: Orthogonal Arrays: Theory and Applications. Heyde: Quasi-Likelihood and its Application: A General Approach to Optimal Parameter Estimation. (continued after index)

Rahul Mukerjee C.F. Jeff Wu A Modern Theory of Factorial Designs

Rahul Mukerjee Indian Institute of Management Calcutta Joka, Diamond Harbour Road Kolkata 700 104 India rmuk@iimcal.ac.in C.F. Jeff Wu School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332-0205 USA jeffwu@isye.gatech.edu Library of Congress Control Number: 2005939038 ISBN-10: 0-387-31991-3 ISBN-13: 978-0387-31991-9 Printed on acid-free paper. © 2006 Springer Science+Business Media, Inc. 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, Inc., 233 Springer 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, elec- tronic 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 in the United States of America. (MVY) 9 8 7 6 5 4 3 2 1 springer.com

To my father and wife, and to the memory of my mother, RM To my wife, CFJW

Springer Series in Statistics (continued from p. ii) Huet/Bouvier/Poursat/Jolivet: Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS and R Examples, 2nd edition. Ibrahim/Chen/Sinha: Bayesian Survival Analysis. Jolliffe: Principal Component Analysis, 2nd edition. Knottnerus: Sample Survey Theory: Some Pythagorean Perspectives. Kolen/Brennan: Test Equating: Methods and Practices. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume I. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume II. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume III. Küchler/Sørensen: Exponential Families of Stochastic Processes. Kutoyants: Statistical Influence for Ergodic Diffusion Processes. Lahiri: Resampling Methods for Dependent Data. Le Cam: Asymptotic Methods in Statistical Decision Theory. Le Cam/Yang: Asymptotics in Statistics: Some Basic Concepts, 2nd edition. Liu: Monte Carlo Strategies in Scientific Computing. Longford: Models for Uncertainty in Educational Testing. Manski: Partial Identification of Probability Distributions. Mielke/Berry: Permutation Methods: A Distance Function Approach. Molenberghs/Verbeke: Models for Discrete Longitudinal Data. Mukerjee/Wu: A Modern Theory of Factorial Designs. Nelsen: An Introduction to Copulas. 2nd edition Pan/Fang: Growth Curve Models and Statistical Diagnostics. Parzen/Tanabe/Kitagawa: Selected Papers of Hirotugu Akaike. Politis/Romano/Wolf: Subsampling. Ramsay/Silverman: Applied Functional Data Analysis: Methods and Case Studies. Ramsay/Silverman: Functional Data Analysis, 2nd edition. Rao/Toutenburg: Linear Models: Least Squares and Alternatives. Reinsel: Elements of Multivariate Time Series Analysis. 2nd edition. Rosenbaum: Observational Studies, 2nd edition. Rosenblatt: Gaussian and Non-Gaussian Linear Time Series and Random Fields. Särndal/Swensson/Wretman: Model Assisted Survey Sampling. Santner/Williams/Notz: The Design and Analysis of Computer Experiments. Schervish: Theory of Statistics. Shao/Tu: The Jackknife and Bootstrap. Simonoff: Smoothing Methods in Statistics. Singpurwalla and Wilson: Statistical Methods in Software Engineering: Reliability and Risk. Small: The Statistical Theory of Shape. Sprott: Statistical Inference in Science. Stein: Interpolation of Spatial Data: Some Theory for Kriging. Taniguchi/Kakizawa: Asymptotic Theory of Statistical Inference for Time Series. Tanner: Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd edition. Tillé: Sampling Algorithms. van der Laan: Unified Methods for Censored Longitudinal Data and Causality. van der Vaart/Wellner: Weak Convergence and Empirical Processes: With Applications to Statistics. Verbeke/Molenberghs: Linear Mixed Models for Longitudinal Data. Weerahandi: Exact Statistical Methods for Data Analysis. West/Harrison: Bayesian Forecasting and Dynamic Models, 2nd edition.

To my father and wife, and to the memory of my mother, RM To my wife, CFJW

Preface Factorial design has always played a prominent role in the theory and prac- tice of experimental design. It allows eﬃcient and economic experimentation with multiple input variables and has been successfully used in a wide range of applications. Much research has been done and texts have been written on factorial design in the 70 years since its inception. For economic reasons, fractional factorials have been extremely popular, especially when the number of factors is large and the runs are expensive. The ﬁrst and perhaps the most important issue faced by experimenters is the choice of a fractional factorial design. Given the long history of factorial design, an “optimality” theory for design selection should have emerged long ago. Surprisingly, the ﬁrst serious attempt in this direction was made only in the early sixties with the notion of resolution. It became apparent later that this notion was not discriminating as a criterion for design selection. Equally surprisingly, it took almost another 20 years to see the birth of the minimum aberration (MA) criterion, which has since become the major criterion for selecting fractional factorial designs. Once the importance of the MA criterion was recognized in the late eighties, research on the theory and algorithms for ﬁnding MA and related designs has grown rapidly in the last 15 years. Besides building and improving upon existing techniques in projective geometry and coding theory, such research has led to the development of novel techniques like complementary designs and eﬃcient search algorithms. Factorial designs with increasing complexity in the underlying structure (e.g., mixed-levels, blocking, split-plots, and ro- bust parameter design) have also received considerable attention. A detailed description of this history and an account of the nature and contents of the book appear in Chapter 1. In 2000, the present authors felt that the time was ripe to start planning and writing a modern book on factorial designs with the MA perspective. Such a book should contain the major theoretical tools and results, and tables of optimal or eﬃcient designs available in the literature. It took several visits by RM to CFJW at the Department of Statistics, University of Michigan, and later at the School of Industrial and Systems Engineering, Georgia Institute

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