OPTIMAL DESIGNS FOR AN ADDITIVE QUADRATIC MIXTURE MODEL INVOLVING THE AMOUNT OF MIXTURE

This paper is concerned with D- and A-optimal designs for a quadratic additive model for experiments with mixtures, in which the response depends not only on the relative proportions but also on the actual amounts of the mixture com- ponents. It is found that the origin and vertices of the simplex are support points of these optimal designs, and when the number of mixture components increases, other support points shift gradually from barycentres of depth 1 to barycentres of higher depths. It is shown that the D-optimal designs have high eciency in terms of A-optimality, and vice versa.