Abstract: Orthogonal minimally aliased response surface (OMARS) designs constitute a new family of three-level experimental designs for studying quantitative factors. Many experiments, however, also involve one or more two-level categorical factors. In this work, we derive necessary conditions for the existence of mixed-level OMARS designs, and present three construction methods based on integer programming. Like the original three-level OMARS designs, the new mixed-level designs are orthogonal main-effect plans in which the main effects are also orthogonal to the second-order effects. These properties distinguish the new designs from definitive screening designs with additional two-level categorical factors and other mixed-level designs recently presented in the literature. To demonstrate the flexibility of our construction methods, we provide 587 mixed-level OMARS designs in the online Supplementary Material.

Key words and phrases: Definitive screening design, foldover design, mixed integer programming, OMARS design, orthogonal array.