Lower Bounds and Construction of Detecting Arrays

Abstract

Combinatorial testing has been widely used to generate test suites for detecting faults in various systems. As a type of fractional factorial design, detecting arrays have been proposed, out of the practical need for locating faults. In previous studies, the optimum detecting arrays in some cases have been determined through direct constructions and algorithmic methods. However, there are no practical lower bounds on the size of optimum detecting arrays for the general case. In this paper, we present two connections between detecting arrays and Sperner set systems that enables us to obtain lower bounds. An improved tabu search algorithm is developed for constructing mixed-level detecting arrays with a small number of rows. The performance of the algorithm is investigated by computational experiments. The experimental results show that the proposed algorithm can efficiently generate high-quality detecting arrays for different problem instances. Based on the lower bounds and algorithms presented in this study, several new optimum detecting arrays are obtained.