I-Optimal Versus D-Optimal Split-Plot Response Surface Designs

Abstract

Response surface experiments often involve only quantitative factors, and the response is fit using a full quadratic model in these factors. The term response surface implies that interest in these studies is more on prediction than parameter estimation because the points on the fitted surface are predicted responses. When computing optimal designs for response surface experiments, it therefore makes sense to focus attention on the predictive capability of the designs. However, the most popular criterion for creating optimal experimental designs is the D-optimality criterion, which aims to minimize the variance of the factor effect estimates in an omnibus sense. Because I-optimal designs minimize the average variance of prediction over the region of experimentation, their focus is clearly on prediction. Therefore, the I-optimality criterion seems to be a more appropriate one than the D-optimality criterion for generating response surface designs. Here we introduce I-optimal design of split-plot response surface experiments. We show through several examples that I-optimal split-plot designs provide substantial benefits in terms of improved prediction compared with D-optimal split-plot designs, while also performing very well in terms of the precision of the factor effect estimates.