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In the assessment and selection of supersaturated designs, the aliasingstructure of interaction effects is usually ignored by traditional criteriasuch as $E(s^2)$-optimality. We introduce the Summary of Effect AliasingStructure (SEAS) for assessing the aliasing structure of supersaturateddesigns, and other non-regular fractional factorial designs, that takes accountof interaction terms and provides more detail than usual summaries such as(generalized) resolution and wordlength patterns. The new summary consists ofthree criteria, abbreviated as MAP: (1) Maximum dependency aliasing pattern;(2) Average square aliasing pattern; and (3) Pairwise dependency ratio. Thesecriteria provided insight when traditional criteria fail to differentiatebetween designs. We theoretically study the relationship between the MAPcriteria and traditional quantities, and demonstrate the use of SEAS forcomparing some example supersaturated designs, including designs suggested inthe literature. We also propose a variant of SEAS to measure the aliasingstructure for individual columns of a design, and use it to choose assignmentsof factors to columns for an $E(s^2)$-optimal design.

Summary of effect aliasing structure (SEAS): new descriptive statistics for factorial and supersaturated designs