A comparison of supersaturated designs and orthogonal arrays

The purpose of a screening experiment is to accurately and cost-efficiently identify the few most influential factors from among the many studied. Two types of screening experiments use orthogonal arrays (OAs) and supersaturated designs (SSDs), respectively. The first requires the number of runs <i>n</i> to be a multiple of 4 and greater than the number of factors <i>k</i>, while the second is a bolder approach wherein <i>n</i>&lt;<i>k</i>. In this study, we compare the performance of OAs with SSDs, using both simulation and a method based on the probability of perfect sign recovery under the Lasso. Our findings indicate that for the scenarios considered, OAs that were far from saturation had similar performance to those that were only slightly above saturation, slightly supersaturated designs required effects between 1.5 and 2 times larger than those for the OAs in order to have similar screening performance, and very supersaturated designs were clearly less effective than the OAs even when detecting effects up to three times as large.