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Abstract:
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Covering arrays are commonly used in software testing since testing all possible combinations is often impossible. A t-covering array covers all factor level combinations of any t factors, but even testing all t factor combinations can be infeasible. An ?-bad covering array covers only (1-?)% of the factor levels combinations required for a t-covering array. Some theoretical bounds for constructions of this type exist, but an explicit construction method is lacking. This work presents a construction method that results in a higher coverage than a given known result. These results hold for any fixed number of factor levels and any strength t, where no systematic method had previously existed. The calculation of the exact value of ? and a second more general construction are presented. When the cost of running more experiments is high relative to the cost of missing an error or initial results are needed quickly, these designs are preferred over traditional t-covering arrays due to their high coverage obtained in a small number of runs. Follow up experiments can be done using a known construction method to obtain full t-coverage starting from an ?-bad array for some cases.
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