Response Surface Methodology : Process and Product Optimization Using Designed Experiments

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2009-01-14
  • Publisher: Wiley
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Identifying an appropriate response surface model from experimental data requires knowledge of statistical experimental design fundamentals, regression modeling techniques, and elementary optimization methods. This book integrates these three topics into a comprehensive, state-of-the-art presentation of response surface methodology (RSM). 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. Working with the most useful software packages, the authors bring an applied focus that emphasizes models useful in industry for product and process design and development.

Author Biography

Raymond H. Myers, PhD, is Professor Emeritus in the Department of Statistics at Virginia Polytechnic Institute and State University. He has over forty 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 Society, Dr. Myers has authored or coauthored numerous journal articles and books, including Generalized Linear Models: With Applications in Engineering and the Sciences, also published by Wiley.

Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery has over thirty years of academic and consulting experience and has devoted his research to engineering statistics, specifically the design and analysis of experiments. He has authored or coauthored numerous journal articles and twelve books, including Generalized Linear Models: With Applications in Engineering and the Sciences; Introduction to Linear Regression Analysis, Fourth Edition; and Introduction to Time Series Analysis and Forecasting, all published by Wiley.

Christine M. Anderson-Cook, PhD, is Project Leader a t the Los Alamos National Laboratory, New Mexico. Dr. Anderson-Cook has over ten years of academic and consulting experience and has written numerous journal articles on the topics of design of experiments and response surface methodology.

Table of Contents

Response Surface Methodology
Approximating Response Functions
The Sequential Nature of RSM
Objectives and Typical Applications of RSM
RSM and the Philosophy of Quality Improvement
Product Design and Formulation (Mixture Problems)
Robust Design and Process Robustness Studies
Useful References on RSM
Building Empirical Models
Linear Regression Models
Estimation of the Parameters in Linear Regression Models
Properties of the Least Squares Estimators and Estimation of
Hypothesis Testing in Multiple Regression
Test for Significance of Regression
Tests on Individual Regression Coefficients and Groups of Coefficients
Confidence Intervals in Multiple Regression
Confidence Intervals on the Individual Regression Coefficients, 38
A Joint Confidence Region on the Regression Coefficients
Confidence Interval on the Mean Response
Prediction of New Response Observations
Model Adequacy Checking
Residual Analysis
Scaling Residuals
Influence Diagnostics
Testing for Lack of Fit
Fitting a Second-Order Model
Qualitative Regressor Variables
Transformation of the Response Variable
Two-Level Factorial Designs
The Design
The Design, 1
The General Design
A Single Replicate of the Design
The Addition of Center Points to the Design
Blocking in the Factorial Design
Blocking in the Replicated Design
Confounding in the Design
Split-Plot Designs
Two-Level Fractional Factorial Designs
The One-Half Fraction of the Design
The One-Quarter Fraction of the Design
The General Fractional Factorial Design
Resolution III Designs
Resolution IV and V Designs
Fractional Factorial Split-Plot Designs
Process Improvement with Steepest Ascent
Determining the Path of Steepest Ascent
Development of the Procedure
Practical Application of the Method of Steepest Ascent
Consideration of Interaction and Curvature
What About a Second Phase?
What Happens Following Steepest Ascent?
Effect of Scale (Choosing Range of Factors)
Confidence Region for Direction of Steepest Ascent
Steepest Ascent Subject to a Linear Constraint
Steepest Ascent in a Split-Plot Experiment
The Analysis of Second-Order Response Surfaces
Second-Order Response Surface
Second-Order Approximating Function
The Nature of the Second-Order Function and Second-Order Surface
Illustration of Second-Order Response Surfaces
A Formal Analytical Approach to the Second-Order Model
Location of the Stationary Point
Nature of the Stationary Point (Canonical Analysis)
Ridge Systems
Role of Contour Plots
Ridge Analysis of the Response Surface
What Is the Value of Ridge Analysis?
Mathematical Development of Ridge Analysis
Sampling Properties of Response Surface Results
Standard Error of Predicted Response
Confidence Region on the Location of the Stationary Point
Use and Computation of the Confidence Region on the Location of the Stationary Point
Confidence Intervals on Eigenvalues in Canonical Analysis
Multiple Response Optimization
Further Comments Co
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