Stratum order-of-addition designs

Abstract Order-of-addition experiments are widely employed in many fields of science and industry to study how the order of components being added influences the response. Although several classes of attractive order-of-addition designs have been proposed in recent years, the performance of these designs often relies on prespecified models and their run sizes are typically large unless the number of components is very small. In this paper, we put forward a model-free approach, called stratum order-of-addition designs, for order-of-addition experiments. By achieving stratum orthogonality of various strengths, the proposed designs are not only economical in run size, but also robust to model uncertainty. Theoretical justifications for these designs are established under a broad class of models for order-of-addition experiments. In addition, several deterministic methods are developed for constructing such designs with flexible run sizes. Numerical studies demonstrate that the proposed designs are competitive under many model-based and model-free criteria, as compared with existing designs in the literature.