An upper bound on software testing effectiveness

Failure patterns describe typical ways in which inputs revealing program failure are distributed across the input domain-in many cases, clustered together in contiguous regions. Based on these observations several debug testing methods have been developed. We examine the upper bound of debug testing effectiveness improvements possible through making assumptions about the shape, size and orientation of failure patterns. We consider the bounds for testing strategies with respect to minimizing the F-measure, maximizing the P-measure, and maximizing the E-measure. Surprisingly, we find that the empirically measured effectiveness of some existing methods that are not based on these assumptions is close to the theoretical upper bound of these strategies. The assumptions made to obtain the upper bound, and its further implications, are also examined.