Bayesian non-parametric specification of bathtub shaped hazard rate functions

Hazard rate functions of natural and manufactured systems often show a bathtub shaped failure rate. A high early rate of failures is followed by an extended period of useful working life where failures are rare, and finally the failure rate increases as the system reaches the end of its life. Parametric modelling of such hazard rate functions can lead to unnecessarily restrictive assumptions on the function shape, however the most common non-parametric estimator (the Kaplan-Meier estimator) does not allow specification of the requirement that it be bathtub shaped. In this paper we extend the Lo and Weng (1989) approach and specify four nonparametric bathtub hazard rate functions drawn from Gamma Process Priors. We implement and demonstrate simulation for these four models.