  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.
