Title Experimental design for formulation / Wendell F. Smith

Published Philadelphia, Pa. : Society for Industrial and Applied Mathematics ; Alexandria, Va. : American Statistical Association, [2005] ©2005

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Description xix, 367 pages : illustrations ; 26 cm Series ASA-SIAM series on statistics and applied probability ASA-SIAM series on statistics and applied probability. Contents Machine derived contents note: 2 Mixture Space 9 -- 3 Models for a Mixture Setting 15 -- 3.1 Model Assumptions 16 -- 3.2 Linear Models 19 -- 3.2.1 Intercept Forms 21 -- 3.3 Quadratic M odels 23 -- 3.3.1 Intercept Forms 25 -- 3.4 Cubic and Quartic Scheff6 Models 27 -- 3.4.1 Special Forms 29 -- 3.5 Choosing a Model 31 -- II Design 33 -- 4 Designs for Simplex-Shaped Regions 35 -- 4.1 Constraints and Subspaces 35 -- 4.2 Some Design Considerations 45 -- 4.3 Three designs 47 -- 4.3.1 Simplex Lattice Designs 47 -- 4.3.2 Simplex Centroid Designs 50 -- 4.3.3 Simplex-Screening Designs 52 -- 4.4 Designs for Three Components 55 -- 4.5 Coding Mixture Variables 57 -- 5 Designs for Non-Simplex-Shaped Regions 61 -- 5.1 Strategy Overview 62 -- 5.2 Algorithm Overview 65 -- 5.3 Creating a Candidate List 67 -- 5.3.1 XVERT 67 -- 5.3.2 CONSIM 70 -- 5.4 Choosing Design Points 72 -- 5.4.1 Designs Based on Classical Two-Level Screening Designs 73 -- 5.4.2 D-Optimality Criterion 76 -- 5.4.3 A-Optimality Criterion 84 -- D esign Study 87 -- 6 Design Evaluation 95 -- 6.1 Properties of the Least-Squares Estimators 95 -- 6.2 Leverage 100 -- 7 Blocking Mixture Experiments 119 -- 7.1 Symmetrically Shaped Design Regions 119 -- 7.2 Asymmetrically Shaped Design Regions 131 -- Appendix 7A. Mates for Latin Squares of Order 4 and 5 146 -- III Analysis 151 -- 8 Building Models in a Mixture Setting 153 -- 8.1 Partitioning Total Variability. Sequential Sums of Squares 156 -- 8.2 The ANOVA Table. Partial Sums of Squares 165 -- 8.3 Summary Statistics 172 -- 8.3.1 The R2 Statistic 172 -- 8.3.2 The Adjusted R2 Statistic 175 -- 8.3.3 PRESS and R2 for Prediction 176 -- C ase Study 179 -- 9 Model Evaluation 183 -- 9.1 Scaling Residuals 183 -- 9.2 Plotting Residuals 186 -- 9.2.1 Checking Assumptions 187 -- 9.2.2 Outlier Detection 192 -- 9.3 Measuring Influence 193 -- 9.3.1 Cook's Distance 194 -- 9.3.2 DFFITS 198 -- 9.3.3 DFBETAS 199 -- Case Study 202 -- 10 Model Revision 205 -- 10.1 Remedial Measures for Outliers 205 -- 10.2 Variable Selection 218 -- 10.3 Partial Quadratic Mixture Models 227 -- 10.4 Transformation of the Response 235 -- C ase Study 249 -- 11 Effects 257 -- 11.1 Orthogonal Effects 57 -- 1 1.2 Cox Effects 261 -- I1.3 Piepel Effects 264 -- 11.4 Calculating/Displaying Effects 267 -- 11.5 Inferences 269 -- Case Study 271 -- 12 Optimization 277 -- 12.1 Graphical Optimization 279 -- 12.2 Numerical. Optimization 281 -- 12.3 Propagation ofError 290 -- IV Special Topics 297 -- 13 Including Process Variables 299 -- 13. 1 Models 299 -- 13.2 Designs 303 -- 13.3 Collecting Data 308 -- 13.4 Analysis 310 -- 13.5 Related Applications 314 -- Case Study 3 15 -- 14 Collinearity 325 -- 14.1 Definition and Impact 325 -- 14.2 Warnings and Diagnostics 332 -- 14.3 Dealing with Collinearity 341 -- Case Study 347 Bibliography Includes bibliographical references (pages 351-361) and index Subject Experimental design. Author Society for Industrial and Applied Mathematics. LC no. 2004065317 ISBN 0898715806 paperback

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