Title Optimal mixture experiments / B.K. Sinha, N.K. Mandal, Manisha Pal, P. Das

Published New Delhi : Springer Verlag, [2014] ©2014

Click on the following:
Springer eBooks
Springer Mathematics and Statistics eBooks

Copies

Description 1 online resource Series Lecture notes in statistics ; volume 1028 Lecture notes in statistics (Springer-Verlag) ; volume 1028. Contents 880-01 Chapter 1. Mixture Models and Mixture Designs: Scope of the Monograph -- Chapter 2. Optimal Regression Designs -- Chapter 3. Parameter Estimation in Linear and Quadratic Mixture Models -- Chapter 4. Optimal Mixture Designs for Estimation of Natural Parameters in Scheffé's Model -- Chapter 5. Optimal Mixture Designs for Estimation of Natural Parameters in Scheffé's Model under Constrained Factor Space -- Chapter 6. Optimal Mixture Designs for Estimation of Natural Parameters in Other Mixture Models -- Chapter 7. Optimal Designs for Estimation of Optimum Mixture in Scheffé's Quadratic Model -- Chapter 8. More on Estimation of Optimum Mixture in Scheffé's Quadratic Model -- Chapter 9. Optimal Designs for Estimation of Optimum Mixture in Scheffé's Quadratic Model under Constrained Factor Space -- Chapter 10. Optimal Designs for Estimation of Optimum Mixture under Darroch-Waller and Log-Contrast Models -- Chapter 11. Applications of Mixture Experiments -- Chapter 12. Miscellaneous Topics: Robust mixtures, random regression coefficients, multiresponse experiments, mixture-amount models, blocking in mixture designs 880-01/(S Machine generated contents note: 1. Mixture Models and Mixture Designs: Scope of the Monograph -- 1.1. Introduction -- 1.2. Mixture Models -- 1.3. Mixture Designs -- 1.3.1. Simplex Lattice Designs -- 1.3.2. Simplex Centroid Designs -- 1.3.3. Axial Designs -- 1.4. Exact Versus Approximate or Continuous Designs -- 1.5. Applications of Mixture Methodology -- 1.6. Chapter-Wise Coverage of Topics -- References -- 2. Optimal Regression Designs -- 2.1. Introduction -- 2.2. Optimality Criteria -- 2.3. One Dimensional Polynomial Regression -- 2.4. Multi-factor First Degree Polynomial Fit Models -- 2.5. Multi-factor Second Degree Polynomial Fit Models -- References -- 3. Parameter Estimation in Linear and Quadratic Mixture Models -- 3.1. Introduction -- 3.2. Some Standard Mixture Designs and Estimation of, Parameters in Homogeneous Linear Mixture Models -- 3.3. Generalizations of Axial Design and Their Comparison -- 3.3.1. Generalized Axial Design of Type I (D1) -- 3.3.2. Generalized Axial Design of Type II (D2) -- 3.3.3. Generalized Axial Design of Type III (D3) -- 3.3.4. Comparison Between Generalized Axial Designs of Type II(D2) and Type III (D3) -- 3.4. Estimation of Parameters in Canonical Homogeneous Quadratic Mixture Model -- 3.5. Other Mixture Models -- 3.5.1. Estimation of Parameters in Becker's Homogeneous Model of Degree One in the Presence of Only Two-Component Synergistic Effects -- 3.5.2. Another Competing Design -- 3.5.3. Design Description and Estimability -- 3.5.4. Estimation of Parameters in Draper--St. John's, Model -- 3.6. Concluding Remarks -- References -- 4. Optimal Mixture Designs for Estimation of Natural Parameters in Scheffe's Models -- 4.1. Introduction -- 4.2. Optimum Designs for First and Second Degree Models -- 4.2.1. D- and I-Optimum Designs -- 4.2.2. φp-Optimum Designs -- 4.2.3. Kiefer-Optimal Designs -- 4.3. Polynomial Models of Degree Three and More -- 4.4. Mixture-Amount Model -- References -- 5. Optimal Mixture Designs for Estimation of Natural Parameters in Scheffe's Model Under Constrained Factor Space -- 5.1. Introduction -- 5.2. Optimum Designs -- 5.2.1. First-order designs -- 5.2.2. Second-order designs -- References -- 6. Optimal Mixture Designs for Estimation of Natural Parameters in Other Mixture Models -- 6.1. Introduction -- 6.2. Becker's Models -- 6.3. Darroch--Waller Model -- 6.4. Log-Contrast Model -- 6.5. Models with Inverse Terms -- References -- 7. Optimal Designs for Estimation of Optimum Mixture in Scheffe's Quadratic Model -- 7.1. Introduction -- 7.2. Estimation of Optimum Mixing Proportions -- 7.3. Optimum Mixture Designs Under Trace-Optimality Criterion -- 7.3.1. Case of Two Mixing Components -- 7.3.2. Case of Three Mixing Components -- 7.4. Optimum Mixture Designs via Equivalence Theory -- 7.4.1. Alternative Representation of Model -- 7.4.2. Case of Three Components -- 7.4.3. Case of Four Component Mixture -- 7.5. Optimum Mixture Designs with Unequal Apriori Moments -- 7.5.1. Case of Two Components -- 7.5.2. Case of Three Component Mixture -- References -- 8. More on Estimation of Optimum Mixture in Scheffe's Quadratic Model -- 8.1. Introduction -- 8.2. Optimum Mixture Designs Under Deficiency Criterion -- 8.2.1. Case of Two Mixing Components -- 8.2.2. Case of Three Components -- 8.3. Optimum Mixture Designs Under Minimax Criterion -- References -- 9. Optimal Designs for Estimation of Optimum Mixture in Scheffe's Quadratic Model Under Constrained Factor Space -- 9.1. Introduction -- 9.2. Optimum Mixture Designs Under Constraint on One Component -- 9.2.1. Case of Two Component Mixture Model -- 9.2.2. Case of Three Component Mixture Model -- 9.2.3. Heuristic Search for Optimum Design -- 9.2.4. Competitive Design -- 9.3. Optimum Designs Under Cost Constraint -- 9.3.1. Case of Two Components -- 9.3.2. Case of Three Components -- References -- 10. Optimal Designs for Estimation of Optimum Mixture Under Darroch--Waller and Log-Contrast Models -- 10.1. Introduction -- 10.2. Optimality Under Darroch--Waller Model -- 10.3. Optimality Under Log-Contrast Model -- References -- 11. Applications of Mixture Experiments -- 11.1. Introduction -- 11.2. Application in Replacement Series Intercropping Experiment -- 11.3. Preparation and Standardization of RTS Fruit Beverages -- 11.4. Application in Pharmaceutical Experiments -- 11.4.1. Optimum Design for Parameter Estimation -- 11.4.2. Optimum Design for Estimation of the Optimum Composition of M1 -- References -- 12. Miscellaneous Topics: Robust Mixtures, Random Regression Coefficients, Multi-response Experiments, Mixture---Amount Models, Blocking in Mixture Designs -- 12.1. Robust Mixture Designs -- 12.1.1. Preliminaries -- 12.1.2. V-Optimum Design -- 12.1.3. Minimum Bias Design -- 12.2. Optimum Mixture Designs for Random Coefficients Mixture Models -- 12.2.1. Preliminaries -- 12.2.2. Characterization -- 12.2.3. Darroch--Waller Model -- 12.3. Optimum Designs for Optimum Mixture in Some Variants of Scheffe's Quadratic Mixture Model -- 12.3.1. Preliminaries -- 12.3.2. Optimality in Mixture--Amount Model of Pal and Mandal -- 12.3.3. Optimality in Multi-response Mixture Model -- 12.3.4. Optimality in Multi-response Mixture--Amount Model -- 12.4. Mixture Designs in Blocks -- 12.4.1. Preliminaries -- 12.4.2. Orthogonal Mixture Designs Based on Symmetric Simplex Block Designs -- 12.4.3. Mixture Designs with Orthogonal Blocks Based on Mates of Latin Squares -- 12.4.4. D-Optimal Minimum Support Mixture Designs -- 12.4.5. Model and Estimators -- 12.4.6. Construction of Optimum Designs -- 12.4.7. Comparison with Other Designs -- References Summary The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé's quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments Bibliography Includes bibliographical references and indexes Notes Print version record Subject Optimal designs (Statistics) Statistics. Statistics as Topic statistics. MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Statistics Optimal designs (Statistics) Form Electronic book Author Mandal, N. K. (Nripes Kumar), author. Pal, Manisha, author Das, P. (Premadhis), author. ISBN 9788132217862 8132217861

  Permalink