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

Bayesian non-parametric specification of bathtub shaped hazard rate functions