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

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