Constructing 3-level foldover screening designs using cyclic generators

Most factors in chemical science and engineering are quantitative. Therefore, chemists and engineers are more familiar with the notion that factors should necessarily have three levels. Ref. [5] introduced a new class of 3-level screening designs which allows the assessment of curvature of the factor-response relationship. They called these designs definitive screening designs (DSDs). These DSDs are (i) saturated for estimating the intercept, the m main effects and the m quadratic effects; (ii) unlike resolution III designs, all main effects are orthogonal to 2-factor interactions; (iii) unlike resolution IV designs, 2-factor interactions are not fully aliased with one another; and (iv) unlike resolution III and IV designs, the quadratic effects can be estimated and are orthogonal to main effects and not fully aliased with 2-factor interactions; (v) when the design is sufficiently large, it allows efficient estimation of the full quadratic model in any three factors. This paper introduces a new class of DSD-like designs generated by cyclic generators. This new class can be used to study the presence of the second-order effects more efficiently.