Simulation Designs for Quadratic Response Surface Models in the Presence of Model Misspecification

This article considers the selection of experimental designs for the estimation of second-order response surface metamodels in a simulation environment. Rather than construct designs based on the premise that the postulated model exactly represents the simulated response, as is the case in optimal design theory, we assume that the estimation process may be biased by the presence of unfitted third-order terms. We therefore seek to specify experimental plans that address the bias due to possible model misspecification as well as traditional variance considerations. The performance measure used for this "fit-protect" scenario is Box and Draper's design criterion of average mean squared error of predicted response. Four important classes of response surface experimental plans are examined: (1) central composite designs, (2) Box-Behnken plans, (3) three-level factorial experiments, and (4) small central composite designs. Each design class is studied in conjunction with three pseudorandom number assignment strategies: (1) the use of a unique set of streams at each design point; (2) the assignment of a common stream set to all experimental points: and (3) the simultaneous use of common and antithetic streams through design blocking. Comparisons of both design classes and assignment strategies are presented to assist the user in the selection of an appropriate experimental strategy.