Uncertainty in counts and operating time in estimating Poisson occurrence rates

When quantifying a plant-specific Poisson event occurrence rate l in reliability or probabilistic risk analysis studies, it is sometimes the case that either the reported plant-specific number of events x or the operating time t (or both) are uncertain. We present a full hierarchical Bayesian MCMC method that can be used to obtain the required average posterior distribution of l which reflects the corresponding uncertainty in x and/or t. The method is easy to implement using existing WinBUGS software that is freely available from the Web. A real-data example from the commercial nuclear power industry is used to illustrate the method, and the corresponding WinBUGS code is provided and discussed.