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Bayesian non-parametric simulation of hazard functions

In Bayesian non-parametric statistics, the extended gamma process can be used to model the class of monotonic hazard functions. However, numerical evaluations of the posterior process are very difficult to compute for realistic sample sizes. To overcome this, we use Monte Carlo methods introduced by Laud, Smith, and Damien (1996) to simulate from the posterior process. We show how these methods can be used to approximate the increasing failure rate of an item, given observed failures and censored times. We then use the results to compute the optimal maintenance schedule under a specified maintenance policy.