Optimal designs for estimating the parameters in weighted power-mean-mixture models

Abstract

In the mixing of fluids, a mixture may be viewed conceptually as a hypothetical collection of fluid clusters. In this context, a mixture model is defined by prescriptions for (a) estimating fluid cluster properties and (b) combining them to yield an overall mixture property. A particular flexible form is obtained from using generalized weighted-power-means with the weighting based on global mole fractions equation image. Optimal designs for estimating the parameters in Scheffé S- and K-polynomials are well known. In this paper, we present optimal designs for estimating the parameters in the generalized weighted-power-mean mixture models, which may be nonlinear in the pure and binary interaction parameters. We illustrate the practical value of applying optimal designs for mixture variables through design efficiencies. The designs are derived for modeling viscosity from three-component mixtures.