In the assessment and selection of supersaturated designs, the aliasing structure of interaction effects is usually ignored by traditional criteria such as $E(s^2)$-optimality. We introduce the Summary of Effect Aliasing Structure (SEAS) for assessing the aliasing structure of supersaturated designs, and other non-regular fractional factorial designs, that takes account of interaction terms and provides more detail than usual summaries such as (generalized) resolution and wordlength patterns. The new summary consists of three criteria, abbreviated as MAP: (1) Maximum dependency aliasing pattern; (2) Average square aliasing pattern; and (3) Pairwise dependency ratio. These criteria provided insight when traditional criteria fail to differentiate between designs. We theoretically study the relationship between the MAP criteria and traditional quantities, and demonstrate the use of SEAS for comparing some example supersaturated designs, including designs suggested in the literature. We also propose a variant of SEAS to measure the aliasing structure for individual columns of a design, and use it to choose assignments of factors to columns for an $E(s^2)$-optimal design.
翻译:在评估和选择超饱和设计时,互动效应的别名结构通常被传统的标准所忽略,如$E(s%2)美元-最佳度等传统标准所忽视。我们引入了效果外推结构摘要(SEAS),用于评估超饱和设计和其他非正常的分因子设计别名结构,其中考虑到互动术语,比通常的(一般的)分辨率和字长模式等摘要更为详细。新的摘要由三个标准组成,缩为MAP:(1) 最大依赖性别名模式;(2) 平均正方别名模式;和(3) 对称型依赖性依赖性比率。当传统标准无法区分设计时,这些标准提供了洞察力。我们理论上研究了超饱和设计标准标准与传统数量之间的关系,并展示了SEAS用于比较某些超饱和设计的例子,包括文献中建议的设计。我们还提出了SEAS的变式,以测量设计单列的别名结构,并使用它来选择将因数分配给$E(s_2)-optimal 设计栏。