Raymond H. Myers - Response Surface Methodology: Process and Product Optimization Using Designed Experiments

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

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Myers, Raymond H.

Response surface methodology : process and product optimization using designed experiments.

- - 3rd ed. / Raymond H. Myers, Douglas C. Montgomery, Christine M. Anderson-Cook. p. cm. - - (Wiley series in probability and statistics)

Includes bibliographical references and index.

ISBN 978-0-470-17446-3 (cloth)

1. Experimental design. 2. Response surfaces (Statistics). I. Montgomery, Douglas C. II. Anderson-Cook, Christine M. III. Title.

QA279.M94 2008

519.507- -dc22

2008019012

PREFACE

This book deals with the exploration and optimization of response surfaces. This is a problem faced by experimenters in many technical fields, where, in general, the response variable of interest is y and there is a set of predictor variables x1, x2, , xk. For example, y might be the viscosity of a polymer and x1, x2, and x3 might be the reaction time, the reactor temperature, and the catalyst feed rate in the process. In some systems the nature of the relationship between y and the xs might be known exactly, based on the underlying engineering, chemical, or physical principles. Then we could write a model of the form y = g(x1, x2, , xk) + , where represents the error in the system. This type of relationship is often called a mechanistic model. We consider the more common situation where the underlying mechanism is not fully understood, and the experimenter must approximate the unknown function g with an appropriate empirical modely = f(x1, x2, , xk) + . Usually the function f is a first-order or second-order polynomial. This empirical model is called a response surface model.

Identifying and fitting an appropriate response surface model from experimental data requires some knowledge of statistical experimental design fundamentals, regression modeling techniques, and elementary optimization methods. This book integrates all three of these topics into what has been popularly called response surface methodology (RSM).

We assume that the reader has some previous exposure to statistical methods and matrix algebra. Formal coursework in basic principles of experimental design and regression analysis would be helpful, but are not essential, because the important elements of these topics are presented early in the text. We have used this book in a graduate-level course on RSM for statisticians, engineers, and chemical/physical scientists. We have also used it in industrial short courses and seminars for individuals with a wide variety of technical backgrounds.

This third edition is a substantial revision of the book. We have rewritten many sections to incorporate new material, ideas, and examples, and to more fully explain some topics that were only briefly mentioned in previous editions. We have also woven the computer more tightly into the presentation, relying on JMP 7 and Design-Expert Version 7 for much of the computing, but also continuing to employ SAS for a few applications.

Chapters 1 through 4 contain the preliminary material essential to studying RSM. Chapter 1 is an introduction to the general field of RSM, describing typical applications such as (a) finding the levels of process variables that optimize a response of interest or (b) discovering what levels of these process variables will result in a product satisfying certain requirements or specifications on responses such as yield, molecular weight, purity, or viscosity. Chapter 2 is a summary of regression methods useful in response surface work, focusing on the basic ideas of least squares model fitting, diagnostic checking, and inference for the linear regression model. Chapters 3 and 4 describe two-level factorial and fractional factorial designs. These designs are essential for factor screening or identifying the correct set of process variables to use in the RSM study. They are also basic building blocks for many of the response surface designs discussed later in the text. Chapter 5 presents the method of steepest ascent, a simple but powerful optimization procedure used at the early stages of RSM to move the process from a region of relatively poor performance to one of greater potential. Chapter 6 introduces the analysis and optimization of a second-order response surface model. Both graphical and numerical techniques are presented. This chapter also includes techniques for the simultaneous optimization of several responses, a common problem in the application of RSM. Chapters 7 and 8 present detailed information on the choice of experimental designs for fitting response surface models. Chapter 7 is devoted to standard designs, including the central composite and BoxBehnken designs, and the important topic of blocking a response surface design. Chapter 8 covers small response surface designs, design optimality criteria, the use of computer-generated designs in RSM, and methods for evaluation of the prediction properties of response surface models constructed from various designs. We focus on variance dispersion graphs and fraction of design space plots, which are very important ways to summarize prediction properties. Chapter 9 contains more advanced RSM topics, including the use of mean square error as a design criterion, the effect of errors in controllable variables, RSM experiments for computer models, neural networks and RSM, split-plot type designs in a response surface setting, and the use of generalized linear models in the analysis of response surface experiments. Chapter 10 describes how the problem of robust parameter design originally proposed by Taguchi can be efficiently solved in the RSM framework. We show how RSM not only makes the original problem posed by Taguchi easier to solve, but also provides much more information to the analyst about process or system performance. This chapter also contains much information on robust parameter design and process robustness studies. Chapters 11 and 12 present techniques for designing and analyzing experiments that involve mixtures. A mixture experiment is a special type of response surface experiment in which the design factors are the components or ingredients of a mixture, and the response depends on the proportions of the ingredients that are present. Extensive sets of end-of-chapter problems are provided, along with a reference section.