Some theory and the construction of mixed-level supersaturated designs

Supersaturated design is a form of fractional factorial design and has recently received much interest because of its potential in factor screening experiments. This paper mainly concerns the existing criteria for mixed-level designs, i.e. the chi(2) (D) criterion (for design D) proposed by Yamada and Matsui (J. Statist. Plann. Inference 104 (2002) 459), the E(f(NOD)) Criterion proposed by Fang et al. (Metrika 58 (2003b) 279) and the minimum moment aberration (MMA) proposed by Xu (Statist. Sinica 13 (2003) 691). A lower bound of X 2 (D) is obtained along with the sufficient and necessary condition for achieving it. The connections between chi(2) (D) and other criteria are discussed. Especially, it is shown that chi(2) (D) and the second power moment chi(2)(D) are in fact equivalent to each other and hence the two criteria, chi(2) (D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs. (C) 2004 Elsevier B.V. All rights reserved.