Weighted A-optimality criterion for generating robust mixture designs

Many experiments in research and development of industrial product formulations involve mixtures of ingredients. These are experiments in which the experimental factors are the ingredients of a mixture and the proportion of mixture ingredients cannot be varied independently. Mixture experiments usually involve constraints on the ingredient proportions of the mixture. In this paper, we propose a technique to generate robust A-optimal designs for mixture experiments using a genetic algorithm where the experimental region is an irregularly-shaped polyhedral region formed by constraints on the mixture ingredient proportions. Our approach seeks the design which minimizes the weighted average of the sum of the variances of the estimated coefficients across a set of potential mixture models that may occur due to initial model misspecification. This technique provides an alternative approach when the experimenter is uncertain about which final model should be selected. For illustration, examples with three ingredients are presented with comparisons of our GA designs to those obtained using PROC OPTEX that focuses only on a single model.