Response Surface Methodology : Process and Product Optimization Using Designed Experiments

by Myers, Raymond H.; Montgomery, Douglas C.; Anderson-Cook, Christine M.

• ISBN13: 9780470174463
• ISBN10: 0470174463
• Edition: 3rd
• Format: Hardcover
• Copyright: 2009-01-14
• Publisher: Wiley

Summary

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

Preface

Introduction

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

Exercises

Two-Level Factorial Designs

Introduction

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

Exercises

Two-Level Fractional Factorial Designs

Introduction

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

Summary

Exercises

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

Exercises

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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