Are Nonhomogeneous Poisson Process Models Preferable to General-Order Statistics Models for Software Reliability Estimation?

Abstract

As alternatives to general order statistics (GOS) models, several nonhomogeneous Poisson process (NHPP) models have been proposed in the literature for software reliability estimation. It has been known that an NHPP model in which the expected number of events (μ) over (0, ∞) is finite (called an NHPP-I process) is a Poisson mixture of GOS processes. We find that the underlying GOS model better fits the data in the sense that it has a larger likelihood than the NHPP-I model. Also, among unbiased estimators for an NHPP-I model, if an estimator is optimal for estimating a related feature of the underlying GOS model, then it is also optimal for the NHPP-I estimation problem. We conducted a simulation study to compare maximum likelihood estimators for one NHPP-I model and for its corresponding GOS model. The results show for small μ and small debugging time the estimators for NHPP-I model are unreliable. For longer debugging time the estimators for the two models behave similarly. These results and certain logical issues suggest that compared to an NHPP-I model, its underlying GOS model may better serve for analyzing software failure data.