Optimal Slope Designs for Second Degree Kronecker Model Mixture Experiments

Abstract

The aim of this paper is to investigate some optimal slope mixture designs in the second degree Kronecker model for mixture experiments. The study is restricted to weighted centroid designs, with the second degree Kronecker model. For the selected maximal parameter subsystem in the model, a method is devised for identifying the ingredients ratio that leads to an optimal response. The study also seeks to establish equivalence relations for the existence of optimal designs for the various optimality criteria. To achieve this for the feasible weighted centroid designs the information matrix of the designs is obtained. Derivations of D-, A- and E-optimal weighted centroid designs are then obtained from the information matrix. Basically this would be limited to classical optimality criteria. Results on a quadratic subspace of H-invariant symmetric matrices containing the information matrices involved in the design problem was used to obtain optimal designs for mixture experiments analytically. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region.