Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process

For many applications of repairable systems, the minimal repair assumption, which leads to nonhomogeneous Poisson processes (NHPP), is not adequate. We review and study two extensions of the NHPP, the dynamic NHPP and the heterogeneous NHPP. Both extensions are motivated by specific aspects of potential applications. It has long been known, however, that the two paradigms are essentially indistinguishable in an analysis of failure data. We investigate the connection between the two approaches for extending NHPP models, both theoretically and numerically in a data example and a simulation study.