E-Optimal Designs For Maximal Parameter Subsystem Second-Degree Kronecker Model Mixture Experiments

Abstract

Many products are formed by mixing together two or more ingredients, for example, in building construction; concrete is formed by mixing sand, water and cement. Many practical problems are associated with investigation of mixture of m ingredients which are assumed to influence the response through the proportions in which they are blended together. Second degree Kronecker model put forward by Draper and Pukelsheim is applied in the study. This study investigates E-optimal designs, second degree Kronecker model, maximal parameter subsystem for two, three and four ingredients, where Kiefer’s function serves as optimality criteria. The consideration was restricted to weighted centroid design for completeness results. By employing the Kronecker model approach, coefficient matrices and a set of feasible weighted centroid designs for maximal parameters subsystem is obtained. Once the coefficient matrix is developed, information matrices associated to the parameter subsystem of interest for two, three, and four is then obtained. E-optimal weighted centroid designs based on maximal parameter subsystem for the corresponding two, three, four ingredients is derived. Also optimal weights and values for the weighted centroid designs were numerically obtained using Matlab software. Results based on maximal parameter subsystem, second degree mixture model with two, three and four ingredient for E-optimal weighted centroid design for information matrix......