Supersaturated designs robust to two-factor interactions

A common assumption made in the study of supersaturated designs is the nonexistence of interaction effects. In this paper, however, we consider the constructions of supersaturated designs without this assumption. We propose and study a class of supersaturated designs, namely foldover supersaturated designs, for screening experiments. Such designs allow the identification of active main effects without making the assumption that two-factor interactions are negligible. We show that E(s²)-optimal foldover supersaturated designs can be obtained using [Formula presented]-optimal supersaturated designs. Further optimization of E(s²)-optimal foldover supersaturated designs is carried out by first minimizing the maximum correlation and then minimizing the frequency of the pairs of columns that attain the maximum correlation. Both theoretical and computational results are presented on the construction of optimal foldover supersaturated designs.