Praise for the Third Edition:

"This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM."

- Zentralblatt Math

Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM.

With multiple revised sections with new topics and expanded coverage, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition includes:

• Many updates on topics such as optimal designs, optimization techniques, robust parameter design, methods for design evaluation, computer-generated designs, multiple response optimization, and non-normal responses
• Additional coverage on topics such as experiments with computer models, definitive screening designs, and data measured with error
• Expanded integration of examples and experiments, which present up-to-date software applications, such as JMP®, SAS, and Design-Expert®, throughout
• An extensive references section to help readers stay up-to-date with leading research in the field of RSM

An ideal textbook for upper-undergraduate and graduate-level courses in statistics, engineering, and chemical/physical sciences, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition is also a useful reference for applied statisticians and engineers in disciplines such as quality, process, and chemistry.

Raymond H. Myers, PhD, is Professor Emeritus in the Department of Statistics at Virginia Polytechnic Institute and State University. He has more than 40 years of academic experience in the areas of experimental design and analysis, response surface analysis, and designs for nonlinear models. A Fellow of the American Statistical Association (ASA) and the American Society for Quality (ASQ), Dr. Myers has authored numerous journal articles and books, including Generalized Linear Models: with Applications in Engineering and the Sciences, Second Edition, also published by Wiley.

Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Arizona State University Foundation Professor of Engineering. Dr. Montgomery has more than 30 years of academic and consulting experience and his research interest includes the design and analysis of experiments. He is a Fellow of the ASA and the Institute of Industrial Engineers, and an Honorary Member of the ASQ. He has authored numerous journal articles and books, including Design and Analysis of Experiments, Eighth Edition; Generalized Linear Models: with Applications in Engineering and the Sciences, Second Edition; Introduction to Introduction to Linear Regression Analysis, Fifth Edition; and Introduction to Time Series Analysis and Forecasting, Second Edition, all published by Wiley.

Christine M. Anderson-Cook, PhD, is a Research Scientist and Project Leader in the Statistical Sciences Group at the Los Alamos National Laboratory, New Mexico. Dr. Anderson-Cook has over 20 years of academic and consulting experience, and has written numerous journal articles on the topics of design of experiments, response surface methodology and reliability. She is a Fellow of the ASA and the ASQ.

Praise for the Third Edition:

This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM.

- Zentralblatt Math

Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM.

With multiple revised sections with new topics and expanded coverage, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition includes:

• Many updates on topics such as optimal designs, optimization techniques, robust parameter design, methods for design evaluation, computer-generated designs, multiple response optimization, and non-normal responses
• Additional coverage on topics such as experiments with computer models, definitive screening designs, and data measured with error
• Expanded integration of examples and experiments, which present up-to-date software applications, such as JMP®, SAS, and Design-Expert®, throughout
• An extensive references section to help readers stay up-to-date with leading research in the field of RSM

An ideal textbook for upper-undergraduate and graduate-level courses in statistics, engineering, and chemical/physical sciences, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition is also a useful reference for applied statisticians and engineers in disciplines such as quality, process, and chemistry.

Preface xiii

1 Introduction 1

1.1 Response Surface Methodology, 1

1.1.1 Approximating Response Functions, 2

1.1.2 The Sequential Nature of RSM, 7

1.1.3 Objectives and Typical Applications of RSM, 9

1.1.4 RSM and the Philosophy of Quality Improvement, 11

1.2 Product Design and Formulation (Mixture Problems), 11

1.3 Robust Design and Process Robustness Studies, 12

1.4 Useful References on RSM, 12

2 Building Empirical Models 13

2.1 Linear Regression Models, 13

2.2 Estimation of the Parameters in Linear Regression Models, 14

2.3 Properties of the Least Squares Estimators and Estimation of 2, 22

2.4 Hypothesis Testing in Multiple Regression, 24

2.4.1 Test for Significance of Regression, 24

2.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients, 27

2.5 Confidence Intervals in Multiple Regression, 31

2.5.1 Confidence Intervals on the Individual Regression Coefficients ß, 32

2.5.2 A Joint Confidence Region on the Regression Coefficients ß, 32

2.5.3 Confidence Interval on the Mean Response, 33

2.6 Prediction of New Response Observations, 35

2.7 Model Adequacy Checking, 36

2.7.1 Residual Analysis, 36

2.7.2 Scaling Residuals, 38

2.7.3 Influence Diagnostics, 42

2.7.4 Testing for Lack of Fit, 43

2.8 Fitting a Second-Order Model, 47

2.9 Qualitative Regressor Variables, 55

2.10 Transformation of the Response Variable, 61

Exercises, 66

3 Two-Level Factorial Designs 81

3.1 Introduction, 81

3.2 The 22 Design, 82

3.3 The 23 Design, 94

3.4 The General 2k Design, 103

3.5 A Single Replicate of the 2k Design, 108

3.6 2k Designs are Optimal Designs, 125

3.7 The Addition of Center Points to the 2k Design, 130

3.8 …