Practical extensions to NHPP application in repairable system reliability analysis

An overwhelming majority of publications on Nonhomogeneous Poisson Process (NHPP) considers just two monotonic forms of the NHPP's rate of occurrence of failures (ROCOF): the log-linear model the power law model. In this paper, we propose to capitalize on the fact that NHPP's ROCOF formally coincides with the hazard function of the underlying lifetime distribution. Therefore, the variety of parametric forms for the hazard functions of traditional lifetime distributions (lognormal, Gumbel, etc.) could be used as the models for the ROCOF of respective NHPPs. Moreover, the hazard function of a mixture of underlying distributions could be used to model the non-monotonic ROCOF. Parameter estimation of such ROCOF models reduces to the estimation of the cumulative hazard function of the underlying lifetime distribution. We use real-world automotive data to illustrate the point