A note on the robustness of Box–Behnken designs to the unavailability of data

Box–Behnken designs and central composite designs are efficient designs for fitting second order polynomials to response surfaces, because they use relatively small numbers of observations to estimate the parameters. In this paper we investigate the robustness of Box–Behnken designs to the unavailability of observations, in the sense of finding tmax, the maximum number of arbitrary rows in the design matrix that can be removed and still leave all of the parameters of interest estimable. The results are compared to the known results for the central composite designs found in MacEachern, Notz, Whittinghill & Zhu. The blocked Box–Behnken designs are equally as robust as those that are not blocked.