A note on the optimal number of centre runs in a second phase design of response surface methods

Abstract

In searching for optimum conditions, the response surface methods comprise two phases. In the first phase, the method of the steepest ascent with a 2(k-p) design is used in searching for a region of improved response. The curvature of the response surface is checked in the second phase. For testing the evidence of curvature, a reasonable design is a 2(k-p) fractional factorial design augmented by centre runs. Using c-optimality criterion, the optimal number of centre runs is investigated. Incorporating c-efflciencies for the curvature test with D-efflciencies and G-efflciencies of CCDs for the quadratic response surfaces and then, adopting the Mini-Max principle, i.e. maximizing the worst efflciency, we propose robust centre runs with respect to the three optimality criteria to be chosen.