Some theory and the construction of mixed-level supersaturated designs

Abstract

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 χ 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 χ 2( D) is obtained along with the sufficient and necessary condition for achieving it. The connections between χ 2( D) and other criteria are discussed. Especially, it is shown that χ 2( D) and the second power moment K 2( D) are in fact equivalent to each other and hence the two criteria, χ 2( D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs.