Separating interaction effects using locating and detecting arrays

The correctness and performance of complex engineered systems are often impacted by many factors, each of which has many possible levels. Performance can be affected not just by individual factor-level choices, but also by interactions among them. While covering arrays have been employed to produce combinatorial test suites in which every possible interaction of a specified number of factor levels arises in at least one test, in general they do not identify the specific interaction(s) that are significant. Locating and detecting arrays strengthen the requirements to permit the identification of a specified number of interactions of a specified size. Further, to cope with outliers or missing responses in data collected from real engineered systems, a further requirement of separation is introduced. In this paper, we examine two randomized methods for the construction of locating and detecting arrays, the first based on the Stein-Lovász-Johnson paradigm, and the second based on the Lovász Local Lemma. Each can be derandomized to yield efficient algorithms for construction, the first using a conditional expectation method, and the second using Moser-Tardos resampling. We apply these methods to produce upper bounds on sizes of locating and detecting arrays for various numbers of factors and levels, when one interaction of two factor levels is to be detected or located, for separation of up to four. We further compare the sizes obtained with those from more targeted (and more computationally intensive) heuristic methods.