Blocked nonregular two-level factorial designs

This article discusses the optimal blocking criteria for nonregular two-level designs. We extend the optimal blocking criteria of Cheng and Wu to nonregular designs by adapting the G- and G ₂-minimum aberration criteria discussed by Tang and Deng. To define word-length pattern for nonregular designs, we extend the notion of "word" to nonregular designs through a polynomial representation of factorial designs. We define treatment resolution and block resolution for evaluating the degrees of aliasing and confounding. We propose four new criteria, which we use to search for optimal blocking schemes of 12-run, 16-run, and 20-run two-level orthogonal arrays.