E-OPTIMAL DESIGNS FOR SECOND-DEGREE KRONECKER

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 mixtures of m ingredients, assumed to influence the response through the proportions in which they are blended together. Second degree Kronecker model put forward by Draper and Pukelsheim isapplied in the study.This study investigate E-optimal designs in the second degree Kronecker model for maximal and non-maximal parameter subsystem for m≥2 ingredients, where Kiefer’s function serves as optimality criteria. The consideration is restricted to weighted centroid design for completeness of results. By employing the Kronecker model approach, coefficient matrices and a set of feasible weighted centroid designs for maximal and non-maximal subsystem of parameters is obtained. Once the coefficient matrix is developed, information matrices associated to the parameter subsystem of interest for two, three, four and generalization to m ingredients is obtained. E-optimal weighted centroid designs based on maximal and non-maximal parameter subsystem for the corresponding two, three, four and m ingredients is derived. A general formula also for the computation of smallest eigenvalues is obtained. In addition optimal, weights and values for the weighted centroid designs are numerically obtained using Matlab software. Results based on non-maximal and maximal parameter subsystem, second degree mixture model with m≥2 ingredient for E-optimal weighted centroid design for K’θ hence exist.