A statistical engineering strategy for mixture problems with process variables

ABSTRACT

Experimenting with both mixture components and process variables, especially when there is likely to be interaction between these two sets of variables, is discussed. We consider both design and analysis questions within the context of addressing an actual mixture/process problem. We focus on a strategy for attacking such problems, as opposed to finding the best possible design or best possible model for a given set of data. In this sense, a statistical engineering framework is used. In particular, when we consider the potential of fitting parsimonious linear additive or nonlinear models as opposed to larger linearized models, we find potential to reduce the size of experimental designs. It is difficult in practice to know what type of model will best fit the resulting data. Therefore, an integrated, sequential design and analysis strategy is recommended. Using two published data sets and one new data set, we find that in some cases nonlinear models, or linear additive models —with no process/mixture interaction terms, enable reduction of experimentation on the order of 50%. In other cases, additive or nonlinear models will not suffice. We therefore provide guidelines as to when such an approach is likely to succeed, and propose an overall strategy for these types of problems.

KEYWORDS:

• mixture experiments
• design of experiments
• process improvement
• empirical modeling
• statistical thinking