Simulation Designs for Quadratic Response Surface Models in the Presence of Model Misspecification
研究在仿真环境中估计二阶响应曲面模型时，如何选择实验设计以应对未拟合的三阶项带来的偏差，比较了四类设计（中心复合设计、Box-Behnken设计、三水平因子实验和小中心复合设计）与三种随机数分配策略，帮助用户选择合适方案。
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.