Optimal Designs for Mixture-Process Experiments Involving Continuous and Categorical Noise Variables

Abstract

Mixture experiments in a robust parameter design (RPD) setting are commonly encountered in industry. The objective of a mixture-process RPD problem is to find levels for the controllable variables that result in a product that has a desirable mean response and that has small variability in the response transmitted from the noise variables. We consider statistical designs for experiments involving mixture variables, continuous noise variables, and categorical noise variables. We show how to construct designs for the RPD problem in the case of a mixture-process experiment with both continuous and categorical noise variables that simultaneously optimize the scaled prediction variances for the mean model and the slope model.