Constructing orthogonal minimally aliased response surface designs using circulant weighing matrices

In chemical and engineering sciences, most factors are quantitative, benefiting from investigation at three distinct levels when studying quadratic or non-linear relationships. Consequently, definitive screening designs (DSDs), a class of 3-level foldover designs introduced by Jones and Nachtsheim (2011), have gained prominence over traditional 2-level designs such as fractional factorial and Plackett–Burman designs. This article extends the framework of conference matrix-based DSDs by introducing a new class of circulant weighing matrix-based screening designs, offering greater design flexibility. Like DSDs and the orthogonal minimally aliased response surface (OMARS) designs recently proposed by Núñez Ares and Goos (2020), these new designs preserve orthogonality among main effects and between main and second-order effects (i.e., quadratic effects and two-factor interactions), while ensuring the absence of full aliasing among second-order effects. We refer to these designs as OMARS designs to highlight their ability to support both factor screening and response surface exploration in a single step. We present a comprehensive catalog of 149 new OMARS designs with desirable projection capability, accommodating up to 50 factors.