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

Abstract

Mixing together two or more ingredients forms several products, for example, in building construction; concrete is formed by mixing, sand, water and cement. Many of mixture experiments involving m-ingredients, the respond is influenced by proportions in which the components are combined. This study investigates E-optimal designs; second degree Kronecker model for non-maximal parameter subsystem involving two and three ingredients, using Kiefer’s function serves as an optimality criterion. By employing the Kronecker model approach model proposed by Draper and Pukelsheim, coefficient matrices for non-maximal parameter subsystem is derived. Once the coefficient matrix is developed, information matrices and E-optimal weighted centroid designs associated to the parameter subsystem of interest for two and three, was then obtained. Optimal weights and design values were computed numerically using MATLAB. The results confirm that E-optimal weighted centroid designs exist for second-degree mixture models with two and three ingredients under non-maximal parameter subsystem.