Compromise ascent directions for multiple-response applications

A process or system under study often requires the measurement of multiple responses. The optimization of multiple response variables has received considerable attention in the literature with the majority focusing on locating optimal operating conditions within the current experimental region and thus often occurs in the later stages of experimentation. This article focuses instead on the initial experiment and the location of additional experimental runs if the region of interest shifts. Considerable trade-off is often required in the multiple response context. In order to account for uncertainty in the model parameters and correlations among the responses, we propose the computation of Bayesian reliabilities to determine optimal factor settings for future experimental runs. The approach will be described in detail for two common design follow-up strategies: steepest ascent (descent) and shifting factor levels. Illustrative examples are provided for each application.