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El. knyga: Robust Response Surfaces, Regression, and Positive Data Analyses

(The University of Burdwan, India)
  • Formatas: 336 pages
  • Išleidimo metai: 21-May-2014
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466506800
Kitos knygos pagal šią temą:
Robust Response Surfaces, Regression, and Positive Data AnalysesDidesnis paveikslėlis
  • Formatas: 336 pages
  • Išleidimo metai: 21-May-2014
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466506800
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"The present book initiates the concept of robust response surface designs, along with the relevant regression and positive data analysis techniques. Response surface methodology (RSM), well-known in literature, is widely used in every field of science and technology such as Biology, Natural (Physical/Chemical), Environmental, Medical, Agricultural, Quality engineering etc. RSM is the most popular experimental data generating, modeling and optimization technique in every field of science. It is a particular case of robust response surface methodology (RRSM). RSM has many limitations, and RRSM aims to overcome many of such limitations. Thus, RRSM will be much better than RSM. It is intended for anyone who knows basic concepts of experimental designs and regression analysis. This is the first unique book on RRSM. Every chapter is unique regarding its contents, presentation and organization. Problems on robust response surface designs such as rotatability, slope-rotatability, weak rotatability, optimality, and along with the method of estimation of model parameters, positive data analysis techniques are considered in this book. Some real examples on lifetime responses, resistivity, replicated measures, medical, demography, hydrogeology data etc., are analysed. Some examples (considered in this book) on design of experiments do not satisfy the classical assumptions of response surface methodology."--

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.

Recenzijos

" 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

List of Figures
xiii
List of Tables
xv
Preface xix
Author xxiii
1 Introduction
1(14)
1.1 The Problem And Perspective
1(2)
1.2 A Brief Review Of The Literature
3(3)
1.3 Existing Literature In The Direction Of Present Research Monograph
6(1)
1.4 Robust Regression Designs
7(2)
1.5 Summary Of The Research Monograph
9(4)
1.6 Concluding Remarks
13(2)
2 Robust First-Order Designs
15(30)
2.1 Introduction And Overview
16(1)
2.2 First-Order Correlated Model
16(4)
2.2.1 Model
16(1)
2.2.2 Analysis And rotatability
17(1)
2.2.3 Robust rotatable and optimum designs
18(2)
2.3 Robust First-Order Designs For Intra-Class Structure
20(1)
2.3.1 Comparison between rford And Ford
21(1)
2.4 Robust First-Order Designs For Inter-Class Structure
21(5)
2.4.1 Optimum Robust First-Order Designs Under Inter-Class Structure
23(1)
2.4.2 Rford And D-ORFOD under inter-class structure
24(2)
2.5 Robust First-Order Designs For Generalized Inter-Class Structure
26(1)
2.6 Robust First-Order Designs For Compound Symmetry Structure
27(3)
2.6.1 Optimum robust first-order designs under compound symmetry structure
28(1)
2.6.2 Rford and D-ORFOD under compound symmetry structure
29(1)
2.7 Robust First-Order Designs For Tri-Diagonal Structure
30(3)
2.7.1 Optimum robust first-order designs under tri-diagonal structure
31(1)
2.7.2 Rford and D-ORFOD under tri-diagonal structure
31(2)
2.8 Robust First-Order Designs For Autocorrelated Structure
33(7)
2.8.1 Optimum robust designs under autocorrelated structure
34(1)
2.8.2 RFORD and nearly D-ORFOD under autocorrelated structure
35(5)
2.9 Concluding Remarks
40(5)
3 Robust Second-Order Designs
45(32)
3.1 Introduction And Overview
46(1)
3.2 Second-Order Correlated Model
46(2)
3.2.1 Model
46(1)
3.2.2 Analysis
47(1)
3.3 Robust Second-Order Rotatability
48(4)
3.3.1 Robust second-order rotatability conditions
48(2)
3.3.2 Robust second-order rotatable non-singularity condition
50(1)
3.3.3 Robust second-order rotatable and optimum designs
51(1)
3.4 Robust Second-Order Designs For Intra-Class Structure
52(2)
3.4.1 Second-order rotatability conditions under intra-class structure
52(1)
3.4.2 Non-singularity condition under intra-class structure
53(1)
3.4.3 Estimated response variance under intra-class structure
53(1)
3.4.4 Optimum RSORD under intra-class Structure
54(1)
3.5 Robust Second-Order Designs For Inter-Class Structure
54(9)
3.5.1 Second-order rotatability conditions under inter-class structure
55(2)
3.5.2 RSORD construction methods under inter-class structure
57(6)
3.6 Robust Second-Order Designs For Compound Symmetry Structure
63(3)
3.6.1 Second-order rotatability conditions under compound symmetry structure
63(3)
3.6.2 RSORD construction for compound symmetry structure
66(1)
3.7 Robust Second-Order Designs For Tri-Diagonal Structure
66(5)
3.7.1 Second-order rotatability conditions under tri-diagonal structure
66(1)
3.7.2 RSORD construction for tri-diagonal structure
67(4)
3.8 Robust Second-Order Designs For Autocorrelated Structure
71(4)
3.8.1 Second-order rotatability conditions for autocorrelated structure
71(2)
3.8.2 RSORD construction for autocorrelated structure
73(2)
3.9 Concluding Remarks
75(2)
4 Robust Regression Designs For Non-Normal Distributions
77(12)
4.1 Introduction And Overview
77(1)
4.2 Correlated Error Models For Non-Normal Distributions
78(3)
4.2.1 Correlated error models for log-normal distribution
79(1)
4.2.2 Correlated error models for exponential distribution
80(1)
4.3 Robust First-Order Designs For Log-Normal And Exponential Distributions
81(2)
4.4 Robust First-Order Designs For Two Non-Normal Distributions
83(4)
4.4.1 Compound symmetry correlation structure
83(2)
4.4.2 Inter-class correlation structure
85(1)
4.4.3 Intra-class correlation structure
85(1)
4.4.4 Tri-diagonal correlation structure
86(1)
4.5 Robust Second-Order Designs For Two Non-Normal Distributions
87(1)
4.6 Concluding Remarks
88(1)
5 Weakly Robust Rotatable Designs
89(20)
5.1 Introduction And Overview
89(1)
5.2 Deviation From Rotatability
90(1)
5.3 Weakly Robust First-Order Rotatable Designs
91(5)
5.3.1 Robust first-order rotatability measure based on dispersion matrix
91(1)
5.3.2 Robust first-order rotatability measure based on moment matrix
92(2)
5.3.3 Comparison between robust first-order rotatable and weakly robust rotatable designs
94(2)
5.4 Weakly Robust Second-Order Rotatable Designs
96(10)
5.4.1 Robust second-order rotatability measure based on moment matrix
97(2)
5.4.2 Robust second-order rotatability measure based on polar transformation
99(2)
5.4.3 Comparison between robust second-order rotatable and weakly robust rotatable designs
101(1)
5.4.4 Illustrations
102(3)
5.4.5 Comparison between two robust second-order rotatability measures Qk(d) and Pk(d)
105(1)
5.5 Concluding Remarks
106(3)
6 Robust Second-Order Slope Rotatability
109(16)
6.1 Introduction And Overview
109(2)
6.2 Second-Order Slope-Rotatability With Uncorrelated Errors
111(1)
6.2.1 Second-order slope-rotatability conditions for uncorrelated errors
111(1)
6.2.2 Modified second-order slope-rotatability conditions for uncorrelated errors
111(1)
6.3 Robust Second-Order Slope Rotatability Conditions
112(3)
6.4 Modified Second-Order Slope Rotatable Design With Correlated Errors
115(2)
6.5 Robust Second-Order Slope Rotatable-And Modified Slope Rotatable Designs Under Intra-Class Structure
117(1)
6.6 Illustrations
118(6)
6.7 Concluding Remarks
124(1)
7 Optimal Robust Second-Order Slope Rotatable Designs
125(18)
7.1 Introduction And Summary
125(2)
7.2 Estimation Of Derivatives
127(1)
7.3 Robust Second-Order Slope-Rotatability Over All Directions
128(3)
7.4 Robust Second-Order Symmetric Balanced Design
131(1)
7.5 Robust Slope-Rotatability With Equal Maximum Directional Variance
132(4)
7.6 D-Optimal Robust Second-Order Slope-Rotatable Designs
136(1)
7.7 Robust Slope Rotatable Designs Over All Directions, With Equal Maximum Directional Variance And D-Optimal Slope
137(4)
7.8 Concluding Remarks
141(2)
8 Robust Second-Order Slope-Rotatability Measures
143(12)
8.1 Introduction And Overview
143(1)
8.2 Robust Second-Order Slope-Rotatability Measures
144(5)
8.2.1 Robust second-order slope-rotatability measure along axial directions
144(4)
8.2.2 Robust second-order slope-rotatability measure over all directions
148(1)
8.2.3 Robust second-order slope-rotatability measure with equal maximum directional variance
149(1)
8.3 Illustrations Of Robust Slope-Rotatability Measures
149(4)
8.4 Concluding Remarks
153(2)
9 Regression Analyses With Correlated Errors And Applications
155(40)
9.1 Introduction And Summary
156(2)
9.2 Regression Analyses With Compound Symmetry Error Structure
158(16)
9.2.1 Correlated error regression models
158(1)
9.2.2 Regression parameter estimation with OSES
159(2)
9.2.3 Hypotheses testing of regression parameters with CSES
161(1)
9.2.4 Confidence ellipsoid of regression parameters with CSES
162(1)
9.2.5 Index of fit with CSES
163(1)
9.2.6 Illustration of regression analysis with CSES
163(3)
9.2.7 Randomized block design with CSES
166(1)
9.2.7.1 Background of an RBD with CSES
166(1)
9.2.7.2 Randomized block design model with CSES
167(1)
9.2.7.3 Analysis of an RBD with CSES
168(2)
9.2.7.4 Confidence ellipsoid of treatment contrasts with CSES
170(1)
9.2.7.5 Multiple comparison of treatment contrasts with CSES
171(1)
9.2.7.6 Illustration of an RBD with CSES
172(2)
9.3 Regression Analyses With Compound Autocorrelated Error Structure
174(19)
9.3.1 Estimation of regression parameters with CAES
174(3)
9.3.2 Hypothesis testing of regression parameters with CAES
177(1)
9.3.3 Confidence ellipsoid of regression parameters with CAES
178(1)
9.3.4 Index of fit with CAES
179(1)
9.3.5 Illustration of regression analysis with CAES
179(3)
9.3.6 Randomized block design with CAES
182(1)
9.3.6.1 A reinforced RBD with CAES
182(2)
9.3.6.2 An RBD model with CAES
184(1)
9.3.6.3 A reinforced RBD analysis with CAES
185(4)
9.3.6.4 Confidence ellipsoid of treatment contrasts with CAES
189(1)
9.3.6.5 Multiple comparison of treatment contrasts with CAES
190(1)
9.3.6.6 Illustration of a reinforced RBD with CAES
191(2)
9.4 Concluding Remarks
193(2)
10 Positive Data Analyses Via Log-Normal And Gamma Models
195(76)
10.1 Introduction And Overview
196(2)
10.2 Discrepancy In Regression Estimates Between Log-Normal And Gamma Models For Constant Variance
198(12)
10.2.1 Log-normal and gamma models for constant variance
198(1)
10.2.2 Log-normal and gamma models for non-constant variance
199(1)
10.2.3 Motivating example
200(2)
10.2.4 Examples of different regression estimates
202(5)
10.2.5 Discussion about discrepancy
207(3)
10.3 Discrepancy Of Regression Parameters Between Log-Normal And Gamma Models For Non-Constant Variance
210(7)
10.4 Discrepancy In Fitting Between Log-Normal And Gamma Models
217(7)
10.5 Replicated Responses Analysis In Quality Engineering
224(8)
10.5.1 Background of replicated response analyses
224(1)
10.5.2 Taguchi approach and dual-response approach with its extension in GLMs
225(2)
10.5.3 Illustrations with two real examples
227(5)
10.6 Resistivity Of Urea Formaldehyde Resin Improvement
232(7)
10.6.1 Resin experiment background
233(1)
10.6.2 Urea formaldehyde resin experiment data
234(1)
10.6.2.1 Resistivity analysis of urea formaldehyde resin data
234(2)
10.6.2.2 Non-volatile solid analysis of urea formaldehyde resin data
236(1)
10.6.2.3 Viscosity analysis of urea formaldehyde resin data
236(1)
10.6.2.4 Acid value analysis of urea formaldehyde resin data
236(1)
10.6.2.5 Petroleum ether tolerance value analysis of urea formaldehyde resin data
237(2)
10.7 Determinants Of Indian Infant And Child Mortality
239(10)
10.7.1 Infant and child mortality background
240(1)
10.7.2 Infant survival time data, analysis, and interpretation
241(6)
10.7.3 Child survival time data, analysis, and interpretation
247(2)
10.8 An Application Of Gamma Models In-Hydrology
249(10)
10.8.1 Background of drinking groundwater quality characteristics
249(2)
10.8.2 Description, analyses, and interpretation of groundwater data
251(1)
10.8.2.1 Analysis of chemical oxygen demand (COD)
251(1)
10.8.2.2 Analysis of total alkalinity (TAK)
252(2)
10.8.2.3 Analysis of total hardness (THD)
254(1)
10.8.2.4 Analysis of dissolved oxygen (DO)
255(1)
10.8.2.5 Analysis of electrical conductivity (EC)
256(1)
10.8.2.6 Analysis of chloride content (CLD)
257(2)
10.9 An Application Of Log-Normal And Gamma Models In Medical Science
259(10)
10.9.1 Background of human blood biochemical parameters
260(1)
10.9.2 Description, analysis, and interpretations of human blood biochemical parameters
260(1)
10.9.2.1 Analysis of fasting serum insulin (FI)
261(1)
10.9.2.2 Analysis of total cholesterol (TC)
261(2)
10.9.2.3 Analysis of serum triglycerides (STG)
263(1)
10.9.2.4 Analysis of low-density lipoprotein (LDL)
264(2)
10.9.2.5 Analysis-of high-density lipoprotein (HDL)
266(1)
10.9.2.6 Analysis of fasting plasma glucose level (PGL)
267(2)
10.10 Concluding Remarks R
269(2)
11 General Conclusions And Discussions
271(6)
Appendix 277(12)
Bibliography 289(18)
Index 307
Rabindra Nath Das
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