Graphical tools for assessing the sensitivity of response surface designs to model misspecification

When comparing different designs for an experiment, optimality criteria and other measures often depend on the correctness of the assumed model. In this article we develop and illustrate an approach for comparing designs given the potential effect of bias due to an underspecified model. We illustrate this approach using graphical summaries of the expected mean squared error (EMSE) that allow assessment of the robustness of designs to model misspecification. For response surface designs in cuboidal regions, the excellent performance of the central composite designs when the quadratic model is correct is tempered when bias is present. The Box-Behnken designs demonstrate superiority in the presence of missing cubic terms. For a screening design scenario, the amount of bias present leads to different conclusions as to which design is best.