Some Investigations on Designs for Mixture Experiments with Process Variable

Abstract

In mixture experiments, the response is assumed to depend on the relative proportions of the ingredients present in the mixture and not on total amount of the mixture. When these experiments are conducted with variables that do not form any portion of the mixture, the levels changed could affect the blending properties of the ingredients are called mixture experiments with process variables. Different models used in various situations for the analysis of mixture experiments with process variables have been discussed. Two methods of construction of mixture experiments with process variables have been developed. In the first method, an efficient response surface design with orthogonal blocks is taken. The mixture designs have been obtained by projecting a suitable unconstrained design (response surface design) onto the hyper-plane defined by the constraints (Prescott in Commun Stat Theory Methods, 29:2229–2253, 2000). The second method is developed by modifying the method given by Wu and Ding (J Stat Plan Infer 71:331–348, 1998) for response surface designs for qualitative and quantitative factors.