Analysis on $$s^{n-m}$$ s n - m designs with general minimum lower-order confounding

Abstract

An optimal design should minimize the confounding among factor effects, especially the lower-order effects, such as main effects and two-factor interaction effects. Based on the aliased component-number pattern, general minimum lower-order confounding (GMC) criterion can provide the confounding information among factors of designs in a more elaborate and explicit manner. In this paper, we extend GMC theory to s-level regular designs, where s is a prime or prime power. For an \(s^{n-m}\) design D with \(N=s^{n-m}\) runs, the confounding of design D is given by complementary set. Further, according to the factor number n, we discuss two cases: (i) \(N/s<n\le (N-1)/(s-1)\), and (ii) \((N/s+1)/2<n\le N/s\). We not only provide the lower-order confounding information among component effects of D, but also obtain three necessary conditions for design D to have GMC.