Mixture-process variable experiments with noise variables

In a mixture experiment, the design factors are mixture components whose proportions are varied, and the response variables are assumed to depend only on these component proportions. In addition to the mixture components, the experimenter may be interested in other variables that can be varied independently of one another and of the mixture components. We consider the case where one or more of these variables is a noise variable, or a variable that cannot be controlled in practice. We develop models for these robust mixture formulation problems. We then derive mean and variance functions and illustrate their use in formulation optimization. Cases of uncorrelated and correlated noise variables are addressed.