Using Markov Chain Monte Carlo methods to solve full Bayesian modeling of PWR vessel flaw distributions

We present a hierarchical Bayesian method for estimating the density and size distribution of subclad-flaws in French Pressurized Water Reactor (PWR) vessels. This model takes into account in-service inspection (ISI) data, a flaw size-dependent probability of detection (different functions are considered) with a threshold of detection, and a flaw sizing error distribution (different distributions are considered). The resulting model is identified through a Markov Chain Monte Carlo (MCMC) algorithm. The article includes discussion for choosing the prior distribution parameters and an illustrative application is presented highlighting the modelʹs ability to provide good parameter estimates even when a small number of flaws are observed.