Universally Optimal Designs for Symmetric Models in Order-of-Addition Experiments
本文提出顺序添加实验的对称线性模型通用形式，证明常用模型等价于它，并发现特定强度的分量正交阵列是通用最优设计，还给出了构造方法和数值验证。
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 paper, 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.