Pseudo-Bayesian AA-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model

In the analysis of experiments with mixture, quadratic models have been widely used. Several authors considered finding optimum designs for the estimation of the parameters of the model. The optimum designs for the estimation of optimum mixing proportions in Scheffé’s quadratic mixture model has been studied by Pal and Mandal (2006) and Mandal et al., 2008a and Mandal et al., 2008b using a pseudo-Bayesian approach. In this paper, we consider an additive quadratic mixture model, proposed by Darroch and Waller (1985), when the amount of mixture is taken into account, and obtain the AA-optimal designs for the estimation of optimum proportions, adopting the approach of Pal and Mandal (2006). We show that, besides other support points, the origin and the vertices of the simplex are necessarily the support points of the optimum design.