The two-stage Bayesian method used for the T-Book application

This paper presents a hierarchical or multistage empirical Bayesian approach that has been used for the estimation of uncertainty about component failure rates presented in the T-Book, a handbook concerning reliability data of components in Nordic nuclear power plants. The failure process is basically assumed to be a homogeneous Poisson process. A class of contaminated gamma distributions is considered to describe the uncertainty concerning the intensity of this process. These distributions in turn are defined through a set of hyperparameters, the knowledge of which is also described and updated via Bayes formula. inciple of Data Translated Likelihood is used for the derivation of non-informative prior distribution for the hyperparameters. The resulting Non-informative Contaminated Gamma-Poisson approach is illustrated by an example, the result of which is compared to alternative models. An application to a 2D problem is also presented.