Variance Dispersion Properties of Second-Order Response Surface Designs

Summary: Often, second-order response surface designs are chosen on the basis of a single-valued criterion such as D- or G-optimality. While such criteria provide a useful basis for selecting designs, they often fail to convey the true nature of the design's support of the fitted model in terms of prediction properties over a region of interest. As an alternative to a single-valued criterion, we propose variance dispersion graphs to compare various second-order response surface designs. This graphical procedure is used to examine the relative strengths and weaknesses of such popular designs as the central composite, Box-Behnken, and small composite. Areas in the region of interest where prediction is relatively good and relatively poor are discussed, and designs which have good overall performance are highlighted. A summary comparison of such saturates or near-saturates designs as the hybrid, Box-Draper, and Notz designs is given together with recommendations concerning the proper choice among these designs. Finally, we show how the use of the D-optimality criterion can lead to misleading results when the user is truly interested in response surface prediction.