Optimum mixture designs under constraints on mixing components

TLDR: In this article, Mandal et al. derived a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions for estimating the optimum proportion of mixture components when the factor space is constrained.

Abstract: Scheffe (1958, 1963) first introduced models and designs suitable for a mixture experiment where the mean response is assumed to depend only on the relative proportions of the ingredients or components. Extensive literature on optimum designs for the estimation of parameters of different mixture models is available. The specific problem of characterization of optimal designs for estimating the op- timum proportion of mixture components has been recently considered by Pal and Mandal (2006, 2008) as also by Mandal and Pal (2008) using different optimality criteria. Generalizing the work of Pal and Mandal (2006), who had dealt with the trace criterion and adopted a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions, Mandal et al. (2008) relaxed the invariance property of the second order moments of the op- timum mixing proportions. In this paper, optimum designs are derived for the problem of estimating the optimum proportion of mixture components when the factor space is constrained.