A Construction of Variable Strength Covering Arrays

Covering arrays(CA)of strength t,mixed level or fixed level,have been applied to software testing to aim for a minimum coverage of all t-way interactions among components.The size of CA increases with the increase of strength interaction t,which increase the cost of software testing.However,it is quite often that some certain components have strong interactions,while others may have fewer or none.Hence,a better way to test software system is to identify the subsets of components which are involved in stronger interactions and apply high strength interaction testing only on these subsets.For this,in 2003,the notion of variable strength covering arrays was proposed by Cohen et al.to satisfy the need to vary the size of t in an individual test suite.In this paper,an effective deterministic construction of variable strength covering arrays is presented.Based on the construction,some series of variable strength covering arrays are then obtained,which are all optimal in the sense of their sizes.In the procedure,two classes of new difference matrices of strength 3 are also mentioned.