| |
| |
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 | |