Confident visualisation techniques in the analysis of mixture experiments

Abstract

When characterising the results from a mixture experiment, the practitioner often wishes to find a set of component blends that optimise the expected value of the response variable, y. Often the experimenter would start out with some best guess or reference blend and create an experiment varying the components around this blend. The question of interest addressed here is whether there are any candidate blends that yield an improvement in the long-run mean response over that of the reference blend. If so, how much is this improvement? Here, we discuss methods for visualisation of the amount of improvement over the reference blend with simultaneous confidence bounds utilising pseudocomponents, especially for experiments where the number of components is greater than three. We then modify this technique to create variance profile plots to assess the impact of our choice for the reference blend. This technique is useful for any model that is linear in its parameters and for any experimental region that can be created utilising pseudocomponents. Two examples are presented in this article to illustrate how this technique is useful in practice.