On inconsistency of estimators of parameters of non-homogeneous Poisson process models for software reliability

Non-homogeneous Poisson Process (NHPP) models form a significant subclass of the many software reliability models proposed in the literature. We prove an important limitation of NHPP models for which the expected number of failures in infinite testing is finite. Specifically, the parameters of those models cannot be estimated consistently as the testing time approaches infinity. We also discuss certain parameter-based asymptotic properties of the maximum likelihood estimators of the model parameters and some logical implications of NHPP model assumptions.