Optimal mixed-level supersaturated design

A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, E(f(NOD)) criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of E(f(NOD)) which can serve as a benchmark of design optimality is obtained. It is shown that the existing E(s(2)) and ave chi(2) criteria (for two- and three-level supersaturated designs respectively) are in fact special cases of this criterion. Furthermore, a construction method for mixed-level supersaturated designs is proposed and some properties of the resulting designs are investigated.