Universally Optimal Designs for Symmetric Models in Order-of-Addition Experiments

Recently, a lot of models for order-of-addition (OofA) experiments have been proposed, as well as the corresponding designs. However, most of those researches are under specific models and/or specific criteria, and a general framework is lacked. In this article, we propose a general form of linear models for OofA experiments, called the symmetric linear models. We show that almost all popularly-used linear models for OofA experiments are equivalent to symmetric linear models, and we further prove that the component orthogonal arrays (COAs) of particular strengths are the corresponding universally optimal OofA designs. Conversely, under some particular cases, the optimal OofA designs must be COAs. Furthermore, we propose a systematic method for constructing COAs of strength 3, and provide some specific constructions of COAs of strengths 2, 4 and higher. Numerical results show that COAs perform well under various criteria. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.