Design of order-of-addition experiments

Abstract

Summary In an order-of-addition experiment, each treatment is a permutation of $m$ components. It is often unaffordable to test all the $m!$ possible treatments, and thus the design problem arises. We consider a flexible model that incorporates the order of each pair of components and can also account for the distance between the two components in every such pair. Under this model, the optimality of the uniform design measure is established, via the approximate theory, for a broad range of criteria. Coupled with an eigenanalysis, this result serves as a benchmark that paves the way for assessing the efficiency and robustness of any exact design. The closed-form construction of a class of robust optimal fractional designs that can also facilitate model selection is explored and illustrated.