Supersaturated Designs for Main Effects and Two‐Factor Interactions

Supersaturated designs (SSDs), which use fewer runs than factors, are employed in screening experiments to identify large main effects (MEs), even when the experimental setting may also involve factors that interact. This paper introduces new SSD design criteria that account for two‐factor interactions (2FIs) and compares them with designs from existing SSD approaches. Overall, we found that several established and new SSD criteria perform well for screening both MEs and 2FIs when analyzed by the hierarchical garrote, a recently proposed regularization method, while an existing foldover‐based method is promising when paired with the Lasso. When MEs are large and sparse, these designs can effectively identify them, except when the SSD is too small or excessively supersaturated. In addition, reasonably sized SSDs can reliably identify large strong heredity 2FIs; however, weak heredity interactions cannot reliably detected by any design considered.