Description
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 ASA and the Institute of Industrial Engineers, and an Honorary Member of 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 ASQ.
Chapter
2 Building Empirical Models
2.1 Linear Regression Models
2.2 Estimation of the Parameters in Linear Regression Models
2.3 Properties of the Least Squares Estimators and Estimation of 𝝈2
2.4 Hypothesis Testing in Multiple Regression
2.4.1 Test for Significance of Regression
2.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients
2.5 Confidence Intervals in Multiple Regression
2.5.1 Confidence Intervals on the Individual Regression Coefficients
2.5.2 A Joint Confidence Region on the Regression Coefficients
2.5.3 Confidence Interval on the Mean Response
2.6 Prediction of New Response Observations
2.7 Model Adequacy Checking
2.7.3 Influence Diagnostics
2.7.4 Testing for Lack of Fit
2.8 Fitting a Second-Order Model
2.9 Qualitative Regressor Variables
2.10 Transformation of the Response Variable
3 Two-Level Factorial Designs
3.4 The General 2k Design
3.5 A Single Replicate of the 2k Design
3.6 2k Designs are Optimal Designs
3.7 The Addition of Center Points to the 2k Design
3.8 Blocking in the 2k Factorial Design
3.8.1 Blocking in the Replicated Design
3.8.2 Confounding in the 2k Design
4 Two-Level Fractional Factorial Designs
4.2 The One-Half Fraction of the 2k Design
4.3 The One-Quarter Fraction of the 2k Design
4.4 The General 2k−p Fractional Factorial Design
4.5 Resolution III Designs
4.6 Resolution IV and V Designs
4.7 Alias Structures in Fractional Factorial and Other Designs
4.8 Nonregular Fractional Factorial Designs
4.8.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs
4.8.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs
4.8.3 Analysis of Nonregular Fractional Factorial Designs
4.9 Fractional Factorial Split-Plot Designs
5 Process Improvement with Steepest Ascent
5.1 Determining the Path of Steepest Ascent
5.1.1 Development of the Procedure
5.1.2 Practical Application of the Method of Steepest Ascent
5.2 Consideration of Interaction and Curvature
5.2.1 What About a Second Phase?
5.2.2 What Happens Following Steepest Ascent?
5.3 Effect of Scale (Choosing Range of Factors)
5.4 Confidence Region for Direction of Steepest Ascent
5.5 Steepest Ascent Subject to a Linear Constraint
5.6 Steepest Ascent in a Split-Plot Experiment
6 The Analysis of Second-Order Response Surfaces
6.1 Second-Order Response Surface
6.2 Second-Order Approximating Function
6.2.1 The Nature of the Second-Order Function and Second-Order Surface
6.2.2 Illustration of Second-Order Response Surfaces
6.3 A Formal Analytical Approach to the Second-Order Model
6.3.1 Location of the Stationary Point
6.3.2 Nature of the Stationary Point (Canonical Analysis)
6.3.4 Role of Contour Plots
6.4 Ridge Analysis of the Response Surface
6.4.1 Benefits of Ridge Analysis
6.4.2 Mathematical Development of Ridge Analysis
6.5 Sampling Properties of Response Surface Results
6.5.1 Standard Error of Predicted Response
6.5.2 Confidence Region on the Location of the Stationary Point
6.5.3 Use and Computation of the Confidence Region on the Location of the Stationary Point
6.5.4 Confidence Intervals on Eigenvalues in Canonical Analysis
6.6 Further Comments Concerning Response Surface Analysis
7 Multiple Response Optimization
7.1 Balancing Multiple Objectives
7.2 Strategies for Multiple Response Optimization
7.2.1 Overlaying Contour Plots
7.2.2 Constrained Optimization
7.2.3 Desirability Functions
7.2.4 Pareto Front Optimization
7.2.5 Other Options for Optimization
7.3 A Sequential Process for Optimization—DMRCS
7.4 Incorporating Uncertainty of Response Predictions into Optimization
8 Design of Experiments for Fitting Response Surfaces—I
8.1 Desirable Properties of Response Surface Designs
8.2 Operability Region, Region of Interest, and Metrics for Desirable Properties
8.2.1 Metrics for Desirable Properties
8.2.2 Model Inadequacy and Model Bias
8.3 Design of Experiments for First-Order Models and First-Order Models with Interactions
8.3.1 The First-Order Orthogonal Design
8.3.2 Orthogonal Designs for Models Containing Interaction
8.3.3 Other First-Order Orthogonal Designs—The Simplex Design
8.3.4 Definitive Screening Designs
8.3.5 Another Variance Property—Prediction Variance
8.4 Designs for Fitting Second-Order Models
8.4.1 The Class of Central Composite Designs
8.4.2 Design Moments and Property of Rotatability
8.4.3 Rotatability and the CCD
8.4.4 More on Prediction Variance—Scaled, Unscaled, and Estimated
8.4.5 The Face-Centered Cube in Cuboidal Regions
8.4.6 Choosing between Spherical and Cuboidal Regions
8.4.7 The Box–Behnken Design
8.4.8 Definitive Screening Designs for Fitting Second-Order Models
8.4.9 Orthogonal Blocking in Second-Order Designs
9 Experimental Designs for Fitting Response Surfaces—II
9.1 Designs that Require a Relatively Small Run Size
9.1.4 The Small Composite Design
9.1.5 Some Saturated or Near-Saturated Cuboidal Designs
9.2 General Criteria for Constructing, Evaluating, and Comparing Designed Experiments
9.2.1 Practical Design Optimality
9.2.2 Use of Design Efficiencies for Comparison of Standard Second-Order Designs
9.2.3 Graphical Procedure for Evaluating the Prediction Capability of an RSM Design
9.3 Computer-Generated Designs in RSM
9.3.1 Important Relationship Between Prediction Variance and Design Augmentation for D-Optimality
9.3.2 Algorithms for Computer-Generated Designs
9.3.3 Comparison of D-, G-, and I-Optimal Designs
9.3.4 Illustrations Involving Computer-Generated Design
9.3.5 Computer-Generated Designs Involving Qualitative Variables
9.4 Multiple Objective Computer-Generated Designs for RSM
9.4.1 Pareto Front Optimization for Selecting a Design
9.4.2 Pareto Aggregating Point Exchange Algorithm
9.4.3 Using DMRCS for Design Optimization
9.5 Some Final Comments Concerning Design Optimality and Computer-Generated Design
10 Advanced Topics in Response Surface Methodology
10.1 Effects of Model BIAS on the Fitted Model and Design
10.2 A Design Criterion Involving Bias and Variance
10.2.1 The Case of a First-Order Fitted Model and Cuboidal Region
10.2.2 Minimum Bias Designs for a Spherical Region of Interest
10.2.3 Simultaneous Consideration of Bias and Variance
10.2.4 How Important Is Bias?
10.3 Errors in Control of Design Levels
10.4 Experiments with Computer Models
10.4.1 Design for Computer Experiments
10.4.2 Analysis for Computer Experiments
10.4.3 Combining Information from Physical and Computer Experiments
10.5 Minimum Bias Estimation of Response Surface Models
10.7 Split-Plot Designs for Second-Order Models
10.8 RSM for Non-normal Responses—Generalized Linear Models
10.8.1 Model Framework: The Link Function
10.8.2 The Canonical Link Function
10.8.3 Estimation of Model Coefficients
10.8.4 Properties of Model Coefficients
10.8.8 Diagnostic Plots and Other Aspects of the GLM
11 Robust Parameter Design and Process Robustness Studies
11.2 What is Parameter Design?
11.2.1 Examples of Noise Variables
11.2.2 An Example of Robust Product Design
11.3 The Taguchi Approach
11.3.1 Crossed Array Designs and Signal-to-Noise Ratios
11.4 The Response Surface Approach
11.4.1 The Role of the Control×Noise Interaction
11.4.2 A Model Containing Both Control and Noise Variables
11.4.3 Generalization of Mean and Variance Modeling
11.4.4 Analysis Procedures Associated with the Two Response Surfaces
11.4.5 Estimation of the Process Variance
11.4.6 Direct Variance Modeling
11.4.7 Use of Generalized Linear Models
11.5 Experimental Designs For RPD and Process Robustness Studies
11.5.1 Combined Array Designs
11.5.2 Second-Order Designs
11.5.3 Other Aspects of Design
11.6 Dispersion Effects in highly Fractionated Designs
11.6.1 The Use of Residuals
11.6.2 Further Diagnostic Information from Residuals
11.6.3 Further Comments Concerning Variance Modeling
12 Experiments with Mixtures
12.2 Simplex Designs and Canonical Mixture Polynomials
12.2.1 Simplex Lattice Designs
12.2.2 The Simplex-Centroid Design and Its Associated Polynomial
12.2.3 Augmentation of Simplex Designs with Axial Runs
12.3 Response Trace Plots
12.4 Reparameterizing Canonical Mixture Models to Contain a Constant Term (𝜷0)
13 Other Mixture Design and Analysis Techniques
13.1 Constraints on the Component Proportions
13.1.1 Lower-Bound Constraints on the Component Proportions
13.1.2 Upper-Bound Constraints on the Component Proportions
13.1.3 Active Upper- and Lower-Bound Constraints
13.1.4 Multicomponent Constraints
13.2 Mixture Experiments Using Ratios of Components
13.3 Process Variables in Mixture Experiments
13.3.1 Mixture-Process Model and Design Basics
13.3.2 Split-Plot Designs for Mixture-Process Experiments
13.3.3 Robust Parameter Designs for Mixture-Process Experiments
13.4 Screening Mixture Components
Appendix 1 Moment Matrix of a Rotatable Design
Appendix 2 Rotatability of a Second-Order Equiradial Design
WILEY SERIES IN PROBABILITY AND STATISTICS
Response Surface Methodology
：Process and Product Optimization Using Designed Experiments
( Wiley Series in Probability and Statistics )
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
