A Graphical Approach for Evaluating Mixture Designs

Single‐valued criteria such as A‐, D‐, G‐ and V‐optimality are used often in constructing and evaluating so‐called ‘optimal’ experimental designs. These criteria are especially popular with mixture experiments where the shape of the design region can become complicated by the imposition of additional constraints on the ingredient proportions. Although such criteria provide a valuable and reasonable basis for generating designs, the resulting designs are optimal only in the strict sense of the particular criterion used. Often, these criteria fail to convey the true nature of the design's support of the fitted model in terms of the variance of the prediction equation over the region of interest. Thus, a graphical approach is presented that allows the user to critique a given design's support for the fitted model in terms of prediction variance. This paper extends the graphical techniques advocated by others for investigating response surface designs to the particular case of mixture designs. The procedures are illustrated with a well‐known mixture experiment.