Finding Robust Response Surface Designs With Blocking Using a Model-Weighted A-Optimality Criterion

Abstract

This paper proposes a new approach to finding robust response surface designs that can accommodate potential model misspecifications. To achieve this, experimental designs that are robust across all potential models were considered prior to data collection. Blocking effects were combined into all possible models, and the set of all reduced models was obtained using the weak heredity principle. The objective of this study was to propose the use of the geometric mean of A-optimalities as a new weighted A-optimality criterion for finding robust response surface designs. Both a genetic algorithm (GA) and an exchange algorithm (EA) were employed to optimize the weighted A-optimality criterion and compared with the widely used central composite design. The weighted A-optimal designs generated by GA and EA in this study had higher Aw and A-efficiencies than CCD, and the Aw-optimal designs generated by the GA were as or more efficient than the EA.