Optimal mixture designs for four components in two orthogonal blocks

Abstract

Abstract A D-optimal mixture design for four flours mixed into doughs in various proportions is given in Draper et al. (Technometrics 35(3) (1993) 268–276). The design consists of 18 runs in two orthogonal blocks of 9 runs each. In this paper, we present another design which is A-optimal and different from the D-optimal design. Then we compare the A-optimal design with the D-optimal design using two other criteria. It is shown that the A-optimal design performs better than the D-optimal design in the sense of having the smaller (1) maximum characteristic root for the variance-covariance matrix of the estimators of parameters and (2) maximum value for the variance of the predicted response.