1st Edition
Robust Response Surfaces, Regression, and Positive Data Analyses
Although widely used in science and technology for experimental data generating, modeling, and optimization, the response surface methodology (RSM) has many limitations. Showing how robust response surface methodology (RRSM) can overcome these limitations, Robust Response Surfaces, Regression, and Positive Data Analyses presents RRS designs, along with the relevant regression and positive data analysis techniques. It explains how to use RRSM in experimental designs and regression analysis.
The book addresses problems of RRS designs, such as rotatability, slope-rotatability, weak rotatability, and optimality. It describes methods for estimating model parameters as well as positive data analysis techniques. The author illustrates the concepts and methods with real examples of lifetime responses, resistivity, replicated measures, and more.
The range of topics and applications gives the book broad appeal both to theoreticians and practicing professionals. The book helps quality engineers, scientists in any area, medical practitioners, demographers, economists, and statisticians understand the theory and applications of RRSM. It can also be used in a second course on the design of experiments.
INTRODUCTION
The Problem and the Perspective
A Brief Review of the Literature
Scope of the Present Textbook
Robust Rotatable Designs
Summary of the Work Done
Concluding Remarks
ROBUST FIRST-ORDER DESIGNS
Introduction and Summary
First-Order Correlated Model
Robust First-Order Designs
Robust First-Order Designs for Intra-Class Structure
Robust First-Order Designs for Inter-Class Structure
Robust First-Order Designs for Generalized Inter-Class Structure
Robust First-Order Designs for Compound Symmetry Structure
Robust First-Order Designs for Tri-Diagonal Structure
Robust First-Order Designs for Auto Correlated Structure
Concluding Remarks
ROBUST SECOND-ORDER DESIGNS
Introduction and Summary
Second-Order Correlated Model
Robust Second-Order Rotatability
Robust Second-Order Designs for Intra-Class Structure
Robust Second-Order Designs for Inter-Class Structure
Robust Second-Order Designs for Compound Symmetry Structure
Robust Second-Order Designs for Tri-Diagonal Structure
Robust Second-Order Designs for Auto Correlated Structure
Concluding Remarks
LIFETIME IMPROVEMENT ROBUST FIRST-ORDER DESIGNS
Introduction and Summary
Location-Scale Lifetime First-Order Correlated Model
Lifetime Improvement (LI) Robust First-Order Designs
LI Robust First-Order Designs for Intra-Class Structure
LI Robust First-Order Designs for Inter-Class Structure
LI Robust First-Order Designs for Compound Symmetry Structure
LI Robust First-Order Designs for Tri-Diagonal Structure
LI Robust First-Order Designs for Autocorrelated Structure
Concluding Remarks
LIFETIME IMPROVEMENT ROBUST SECOND-ORDER DESIGNS
Introduction and Summary
Location-Scale Lifetime Second-Order Correlated Model
Lifetime Improvement Robust Second-Order Rotatability
LI Robust Second-Order Designs for Intra-Class Structure
LI Robust Second-Order Designs for Inter-Class Structure
LI Robust Second-Order Designs for Compound Symmetry Structure
LI Robust Second-Order Designs for Tri-Diagonal Structure
LI Robust Second-Order Designs for Autocorrelated Structure
Concluding Remarks
WEAKLY ROBUST ROTATABLE DESIGNS
Introduction and Summary
Deviation from Rotatability
Weakly Robust First-Order Rotatable Designs
Weakly Robust Second-Order Rotatable Designs
Concluding Remarks
Appendix
ROBUST SECOND-ORDER SLOPE-ROTATABILITY
Introduction and Summary
Robust Second-Order Slope-Rotatability Conditions
Robust Second-Order Slope-Rotatable Designs
Modified Robust Second-Order Slope-Rotatability Conditions
Robust Second-Order Slope-Rotatable Designs for Intra-Class Structure
Robust Second-Order Modified Slope-Rotatable Designs for Intra-Class Structure
Illustration
Concluding Remarks
ROBUST SECOND-ORDER SLOPE-ROTATABILITY OVER ALL DIRECTIONS
Introduction and Summary
Estimation of Derivatives
Robust Second-Order Slope-Rotatability over All Directions
Robust Second-Order Slope-Rotatable Designs over All Directions for
Concluding Remarks
ROBUST SECOND-ORDER SLOPE-ROTATABLE DESIGNS WITH MAXIMUM DIRECTIONAL VARIANCE AND D-OPTIMAL SLOPE
Introduction and Summary
Robust Balanced Designs
Robust Second-Order Slope-Rotatability with Maximum Directional Variance
Robust Second-Order Slope-Rotatable Designs with Maximum Directional Variance
D-Optimal Robust Second-Order Slope-Rotatability
D-Optimal Robust Second-Order Slope-Rotatability Conditions
D-Optimal Robust Second-Order Slope-Rotatable Designs
Conel Uding Remarks
WEAKLY ROBUST SECOND-ORDER SLOPE-ROTATABLE DESIGNS
Introduction and Summary
Robust Second-Order Slope-Rotatability Measures
Illustrations
Concluding Remarks
REGRESSION ANALYSIS FOR CORRELATED OBSERVATIONS
Introduction and Summary
Regression Model with Correlated Errors
Estimation of Regression Parameters for
Inference on Regression Parameters for
Regression Diagnostics with Correlated Errors
Index of Fit
Illustration
Location-Scale Lifetime Regression Model
Estimation of Regression Parameters for Location-Scale Lifetime Model with
Illustration
Concluding Remarks
APPLICATIONS OF CORRELATED REGRESSION ANALYSES
Introduction and Summary
Analysis of a Randomized Block Design with Correlated Errors
A Reinforced Randomized Block Design with Correlated Errors
POSITIVE DATA ANALYSES
Introduction and Summary
Log-Normal and Gamma Model with Constant Variance
Log-Normal and Gamma Model with Non-Constant Variance
Discrepancy in Regression Estimate between the Two Models for Constant Variance
Discrepancy in Regression Estimates between the Two Models for Non-Constant Variance
Discrepancy in Fitting between the Two Models for Non-Constant Variance
Concluding Remarks
APPLICATIONS OF LOG-NORMAL AND GAMMA MODELS
Introduction and Summary
Lifetime Data Analysis Based on Log-Normal Model
Resistivity Data Analysis Based on Log-Normal and Gamma Model
Multiple Responses Data Analysis Based on Gamma Model
Human Biochemical Parameters Relationships
Active Factors on Human Body Mass Index
The Role of Iodine in the Thyroid Status of Mother and Her Neonates
Effects of Wine Drinking on Liver Biochemical Parameters
Risk Factors of Diabetes Mellitus to Pima India Mothers
Personal Characteristics and Dietary Impacts on Plasma Concentrations
Infant Mortality in India
Concluding Remarks
Biography
Rabindra Nath Das
"… this book stands [as the] first of its kind … The author explains well the utilization of RRS methods in experimental designs and regression analysis. The author ingeniously furthers the explanation on the problem of RRS designs … This book elucidates these methods to both theoreticians and researchers besides practical users, like engineers in quality control, … demographers, hydro-geologists, economists, statisticians, biological and physical scientists, and environmental and agricultural scientists …"
—Zentralblatt MATH 1306
