Two-stage Bayesian models-application to ZEDB project

A well-known mathematical tool to analyze plant specific reliability data for nuclear power facilities is the two-stage Bayesian model. Such two-stage Bayesian models are standard practice nowadays, for example in the German ZEDB project or in the Swedish T-Book, although they may differ in their mathematical models and software implementation. In this paper, we review the mathematical model, its underlying assumptions and supporting arguments. Reasonable conditional assumptions are made to yield tractable and mathematically valid form for the failure rate at plant of interest, given failures and operational times at other plants in the population. The posterior probability of failure rate at plant of interest is sensitive to the choice of hyperprior parameters since the effect of hyperprior distribution will never be dominated by the effect of observation. The methods of Pörn and Jeffrey for choosing distributions over hyperparameters are discussed. Furthermore, we will perform verification tasks associated with the theoretical model presented in this paper. The present software implementation produces good agreement with ZEDB results for various prior distributions. The difference between our results and those of ZEDB reflect differences that may arise from numerical implementation, as that would use different step size and truncation bounds.