The notion of a detecting array (DTA) was proposed, recently, by Colbourn and McClary in their research on software interaction tests. Roughly speaking, testing with a (d, t)-DTA (N , k, v) can locate d interaction faults and detect whether there are more than d interaction faults. In this paper, we establish a general lower bound on sizes of DTAs and explore an equivalence between optimal DTAs and super-simple orthogonal arrays (OAs). Taking advantage of this equivalence, a great number of DTAs are constructed, which are all optimal in the sense of their sizes. In particular, an optimal (2, t)-DTA (N , 5, v) of strength t = 2 or 3 is shown to exist whenever v ≥ 3 excepting (t, v) ∈ {(2, 3), (2, 6), (3, 4), (3, 6)}.

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Locating arrays are of interest in generating software test suites to cover all t-way component interactions and locate interaction faults in component-based systems. Recently, Tang, Colbourn and Yin made an investigation into optimal locating arrays in the case where a single fault is to be located. They pointed out that when two or more faults were considered, matters would become rather complicated. To handle those cases generally seems challenging, but is well worth further research. In this paper, we establish a lower bound on the size of locating arrays with at most two faults, and then prove that optimal locating arrays meeting this bound can be equivalently characterized in terms of orthogonal arrays with prescribed properties. Using this characterization, we develop a number of constructions of optimal locating arrays. Two infinite series of optimal locating arrays are then obtained.

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