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. - Highlights: • Review of dynamic extension of a minimal repair model (LEYP), introduced by Le Gat. • Derivation of likelihood function and comparison to NHPP model with heterogeneity. • Likelihood functions and conditional intensities are similar for the models. • ML estimation is considered for both models using a power law baseline. • A simulation study illustrates and confirms findings of the theoretical study