A family of orthogonal main effects screening designs for mixed-level factors

There is limited literature on screening when some factors are at three levels and others are at two levels. This topic has seen renewed interest of late following the introduction of the definitive screening design structure by Jones and Nachtsheim 2011 and Xiao et al. 2012. Two well-known examples are Taguchi’s L ₁₈ and L ₃₆ designs. However, these designs are limited in two ways. First, they only allow for either 18 or 36 runs, which is restrictive. Second, they provide no protection against bias of the main effects due to active two-factor interactions. In this article, we introduce a family of orthogonal, mixed-level screening designs in multiples of eight runs. Our 16-run design can accommodate up to four continuous three-level factors and up to eight two-level factors. The three-level factors must be continuous, whereas the two-level factors can be either continuous or categorical. All of our designs supply substantial bias protection of the main effects estimates due to active two-factor interactions.