Generating systematic supersaturated designs

Practitioners are routinely faced with distinguishing between factors that have real effects and those whose apparent effects are due to random error. When there are many factors, the usual advice given is to run so-called main-effect designs (Resolution III designs in the orthogonal case), that require at least k + 1 runs for investigating k factors. This may be wasteful, however, if the goal is only to detect those active factors. This is particularly true when the number of factors is large. In such situations, a supersaturated design can often save considerable cost. A supersaturated design is a (fraction of a factorial) design composed of n observations where n < k + 1. When such a design is used, the abandonment of orthogonality is inevitable. This article examines the maximum number of factors that can be accommodated when the degree of the nonorthogonality is specified. Furthermore, interesting properties of systematic supersaturated designs are revealed. For example, such a design may be adequate to allow examination of many prespecified two-factor interactions. Comparisons are made with previous work, and it is shown that the designs given here are superior to other existing supersaturated designs. Data-analysis methods for such designs are discussed, and examples are provided.