Mixed-level screening designs based on skew-symmetric conference matrices

Screening is an important step of experimental design. It aims to identify a few active factors, among a large number of potential factors. In this paper, we propose two classes of mixedlevel screening designs with desirable design properties; such as, low correlations between any two design columns, high design efficiencies (e.g., D- or A-efficiencies), and orthogonality between main effects and two-factor interactions. Conference matrices with skew-symmetric structure play an important role in the proposed construction. Two new construction methods for conference matrices with skew-symmetric structure, recursive and algebraic constructions, are provided. It is shown that the proposed mixed-level screening designs have all desirable design properties and do not require any computer search.