Some flexible families of intensities for non‐homogeneous Poisson process models and their Bayes inference

Non‐homogeneous Poisson processes are useful for modeling repairable system reliability. An NHPP is specified in terms of a non‐negative failure rate or intensity function. Standard parametric forms such as the well‐known power law process intensity are constant, increasing without bound or decreasing to zero. These provide limited flexibility in modeling. For example, under them the failure rate of a system cannot increase or decrease to a positive, finite constant. In this article we consider a variety of more flexible (and yet tractable) families of intensities built on the notion of switching in time between two simple constituent intensities. We consider the problem of Bayesian inference in these families based on Markov chain Monte Carlo posterior samples. Examples are provided.