Constructing large orthogonal minimally aliased response surface designs by concatenating two definitive screening designs

Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each other nor with the quadratic effects and the two-factor interactions. Complete catalogs of OMARS designs with up to five factors have been obtained using an enumeration algorithm. However, the algorithm is computationally demanding for designs with many factors and runs. To overcome this issue, we propose a construction method for large OMARS designs that concatenates two definitive screening designs and improves the statistical features of its parent designs. The concatenation employs an algorithm that minimizes the aliasing among the second-order effects using foldover techniques and column permutations for one of the parent designs. We study the properties of the new OMARS designs and compare them with alternative designs in the literature.正交最小混叠响应面（Orthogonal Minimally Aliased Response Surface, OMARS）设计可通过数量经济的试验次数，开展三水平定量因子的相关研究。在该类设计中，因子的线性效应既不会彼此混叠，也不会与二次效应及两因子交互作用产生混叠。研究人员已基于枚举算法，构建出因子数不超过5的OMARS设计完整目录。然而，当设计涉及较多因子与试验次数时，该枚举算法的计算复杂度极高。为解决该问题，本文提出一种适用于大型OMARS设计的构造方法：将两款确定性筛选设计（Definitive Screening Design, DSD）进行拼接，并对其中一款亲本设计的统计特性进行优化。该拼接过程采用一种算法，通过折叠技术与列置换最小化二阶效应间的混叠程度。本文对新型OMARS设计的特性展开研究，并将其与现有文献中的其他同类设计进行对比分析。