Software Reliability Modeling and Exponential Order Statistics

Properties of software failure times modelled as realizations of order statistics generated by independent but non-identically distributed exponential random variables are developed. Edgeworth and saddle point approximations to central order statistic densities so generated are developed using an exact integral representation of these densities. A comparison of Edgeworth and saddle point approximation with exact densities for two different population types is given. The accuracy of the saddle point approximation, even for very small population sizes (N = 6) and small samples'(n = 2) is excellent. The same technique is used to provide an exact integral representation of the probability that a particular fault appears in a sample of a given size. Some numerical comparisons of Rosen's (1972) approximation of inclusion probabilities with exact values are provided. His simple approximation appears to give excellent results as well. The intimate connection between successive sampling theory and EOS models for software reliability is documented.