A RESOLUTION RANK CRITERION FOR SUPERSATURATED DESIGNS

Hadamard matrices are found to be useful in constructing supersaturated designs. In this paper, we study a special form of supersaturated designs using Hadamard matrices. Properties of such a supersaturated design are discussed. It is shown that the popular E(s 2 ) criterion is in general inadequate to measure the goodness of a supersaturated design. A new criterion based upon the projection property, called resolution rank (r-rank), is proposed. Furthermore, an upper bound for r-rank is given for practical use. When the number of factors is large and a small number of runs is desired, a supersaturated design can save considerable cost. A two-level supersaturated design is a fraction of a factorial design with n observations in which the number of factors k is larger than n − 1. The usefulness of such a supersaturated design relies upon the realism of effect sparsity, namely, that the number of dominant active factors is small. The goal is to identify these active factors with so-called screening experimentation. (A brief review of early work on supersaturated de- signs is available from Lin (1991).) Apart from some ad hoc procedures and computer-generated designs, the construction problem has not been addressed until very recently (see Lin (1993a) and (1995), Wu (1993), and Tang and Wu (1997)). Most of these supersaturated designs were constructed based on Hadamard matrices. In this paper, a special form of supersaturated designs using Hadamard matrices is studied. Further- more, a criterion based upon the projection property called resolution rank is proposed to further differentiate among designs.