Uniform order-of-addition designs

Abstract

The order-of-addition (OofA) experiment, whose response is affected by the addition order of components or materials, has received much attention recently. In this paper, based on suitable Hamming distance, we first establish the discrete discrepancy for any order-of-addition experiments from the viewpoint of uniformity and similarity. The lower bound of the discrete discrepancy under U-type designs is derived to serve as a benchmark of design optimality.In addition, we propose a new type of designs, called uniform order-of-addition (UOofA) designs, that achieve the lower bound of the discrete discrepancy. Some methods are provided to construct UOofA designs. The resulting designs have flexible run sizes and are suitable for sequential experiments. Furthermore, these designs under column permutations are efficient under the pairwise-order model.Such efficient UOofA designs, as well as their balance 性质 and projection 性质, are displayed in the S materials.