Opening with the basics of regression designs, this book reviews linear and quadratic Scheffé mixture models, applies the Darroch-Waller three-component quadratic mixture model to the general q-component model, discusses non-standard mixture designs and more.
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.
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.
"The aim of this book is to present different aspects regarding the optimality for mixture designs. ... At the end we find an up-to-date bibliography, an author index and a subject index. The book is very useful for both theoreticians and applied statisticians working especially in the field of mixture experiments using different mixture models." (T. Postelnicu, zbMATH 1308.62007, 2015)