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Response Surface Methodology: Process and Product Optimization Using Designed Experiments / Edition 1

Response Surface Methodology: Process and Product Optimization Using Designed Experiments / Edition 1


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Using a practical approach, it discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques. Features numerous authentic application examples and problems. Illustrates how computers can be a useful aid in problem solving. Includes a disk containing computer programs for a response surface methodology simulation exercise and concerning mixtures.

Product Details

ISBN-13: 9780471581000
Publisher: Wiley
Publication date: 01/28/1995
Series: Wiley Series in Probability and Statistics Series , #286
Edition description: Older Edition
Pages: 728
Product dimensions: 6.42(w) x 9.76(h) x 1.53(d)

About the Author

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.

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Table of Contents

1.1Response Surface Methodology1
1.2Product Design and Formulation (Mixture Problems)14
1.3Robust Design and Process Robustness Studies15
1.4Useful References on RSM16
2Building Empirical Models17
2.1Linear Regression Models17
2.2Estimation of the Parameters in Linear Regression Models18
2.3Properties of the Least Squares Estimators and Estimation of [sigma superscript 2]25
2.4Hypothesis Testing in Multiple Regression29
2.5Confidence Intervals in Multiple Regression37
2.6Prediction of New Response Observations41
2.7Model Adequacy Checking43
2.8Fitting a Second-Order Model56
2.9Qualitative Regressor Variables65
2.10Transformation of the Response Variable68
3Two-Level Factorial Designs85
3.2The 2[superscript 2] Design85
3.3The 2[superscript 3] Design100
3.4The General 2[superscript k] Design111
3.5A Single Replicate of the 2[superscript k] Design112
3.6The Addition of Center Points to the 2[superscript k] Design128
3.7Blocking in the 2[superscript k] Factorial Design134
4Two-Level Fractional Factorial Designs155
4.2The One-Half Fraction of the 2[superscript k] Design156
4.3The One-Quarter Fraction of the 2[superscript k] Design170
4.4The General 2[superscript k-p] Fractional Factorial Design178
4.5Resolution III Designs183
4.6Resolution IV and V Designs192
5Process Improvement with Steepest Ascent203
5.1Determining the Path of Steepest Ascent205
5.2Consideration of Interaction and Curvature213
5.3Effect of Scale (Choosing Range of Factors)218
5.4Confidence Region for Direction of Steepest Ascent220
5.5Steepest Ascent Subject to a Linear Constraint224
6The Analysis of Second-Order Response Surfaces235
6.1Second-Order Response Surface235
6.2Second-Order Approximating Function235
6.3A Formal Analytical Approach to the Second-Order Model241
6.4Ridge Analysis of the Response Surface254
6.5Sampling Properties of Response Surface Results262
6.6Multiple Response Optimization273
6.7Further Comments Concerning Response Surface Analysis286
7Experimental Designs for Fitting Response Surfaces--I303
7.1Desirable Properties of Response Surface Designs303
7.2Operability Region, Region of Interest, and Model Inadequacy304
7.3Design of Experiments for First-Order Models307
7.4Designs for Fitting Second-Order Models321
8Experimental Designs for Fitting Response Surfaces--II377
8.1Designs That Require a Relatively Small Run Size378
8.2General Criteria for Constructing, Evaluating, and Comparing Experimental Designs390
8.3Computer-Generated Designs in RSM413
8.4Some Final Comments Concerning Design Optimality and Computer-Generated Design428
9.Advanced Response Surface Topics--I437
9.1Effects of Model Bias on the Fitted Model and Design437
9.2A Design Criterion Involving Bias and Variance441
9.3RSM in the Presence of Qualitative Variables456
9.4Errors in Control of Design Levels478
9.5Experiments with Computer Models481
9.6Minimum Bias Estimation of Response Surface Models485
9.7Neural Networks489
10.Advanced Response Surface Topics--II500
10.1RSM for Nonnormal Responses--Generalized Linear Models501
10.2Restrictions in Randomization in RSM521
11Robust Parameter Design and Process Robustness Studies536
11.2What Is Parameter Design?536
11.3The Taguchi Approach539
11.4The Response Surface Approach552
11.5Experimental Designs for RPD and Process Robustness Studies586
11.6Dispersion Effects in Highly Fractionated Designs591
12Experiments with Mixtures614
12.2Simplex Designs and Canonical Mixture Polynomials618
12.3Response Trace Plots638
12.4Reparameterizing Canonical Mixture Models to Contain a Constant Term ([beta subscript 0])639
13Other Mixture Design and Analysis Techniques652
13.1Constraints on the Component Proportions652
13.2Mixture Experiments Using Ratios of Components685
13.3Process Variables in Mixture Experiments690
13.4Screening Mixture Components701
14Continuous Process Improvement with Evolutionary Operation715
14.2An Example of EVOP716
14.3EVOP Using Software721
14.4Simplex EVOP725
14.5Some Practical Advice About Using EVOP727
Appendix 1.Variable Selection and Model Building in Regression742
Appendix 2.Multicollinearity and Biased Estimation in Regression759
Appendix 3.Robust Regression770
Appendix 4.Some Mathematical Insights into Ridge Analysis778
Appendix 5.Moment Matrix of a Rotatable Design779
Appendix 6.Rotatability of a Second-Order Equiradial Design784
Appendix 7.Relationship Between D-Optimality and the Volume of a Joint Confidence Ellipsoid on [beta]787
Appendix 8.Relationship Between the Maximum Prediction Variance in a Region and the Number of Parameters789
Appendix 9.The Development of Equation (8.21)790
Appendix 10.Determination of Data Augmentation Result (Choice of x[subscript r + 1] for the Sequential Development of a D-Optimal Design)791

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