Optimum Experimental Designs for Mixtures with Process Variables and Time Varying Responses

The optimum design of experiments for mixtures is increasingly well understood and some interesting optimum seeking procedures have recently been developed (Forlin et al. 2008). In my talk I will first review D-optimality for straightforward mixture models. I will then discuss results on blocking of mixture experiments and experiments in which there are both mixture and process variables.

The assumption in these results, as for example in Chapter 16 of Atkinson, Donev, and Tobias (2007), is that there is a single response. In the latter part of my talk I will discuss the design of experiments in which the response is a series of correlated observations. For D-optimality the General Equivalence Theorem leads to simply calculated methods for checking the optimality of designs and for improving those that are suboptimum. An important application is the scheduling of measurement times. In some cases different units should be subjected to distinct schedules of observation.