Uncertainty in counts and operating time in estimating Poisson occurrence rates

When quantifying a plant-specific Poisson event occurrence rate λ in PRA 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 Bayesian Markov chain Monte Carlo method that can be used to obtain the required average posterior distribution of λ which reflects the corresponding uncertainty in x and/or t. The method improves upon existing methods and is also easy to implement using hierarchical Bayesian software that is freely available from the Web.