Optimal test distributions for software failure cost estimation

We generalize the input domain based software reliability measures by E.C. Nelson (1973) and by S.N. Weiss and E.J. Weyuker (1988), introducing expected failure costs under the operational distribution as a measure for software unreliability. This approach incorporates in the reliability concept a distinction between different degrees of failure severity. It is shown how to estimate the proposed quantity by means of random testing, using the Importance Sampling technique from Rare Event Simulation. A test input distribution that yields an unbiased estimator with minimum variance is determined. The practical application of the presented method is outlined, and a detailed numerical example is given