Bayesian inference for Common cause failure rate based on causal inference with missing data

This paper proposes a methodology to handle the causality to make inference on common cause failure (CCF) in a missing data situation. The data are collected in the form of contingency tables but the only available tokens of information are the numbers of CCFs of different orders and the numbers of failures due to a given cause, i.e. the margins of the contingency table. The frequencies in each cell are unknown; we are in a situation of missing data. Assuming a Poisson model for the count, we suggest a Bayesian approach and we use the inverse Bayes formula (IBF) combined with a Metropolis-Hastings algorithm to make inference on the parameters. The performance of the resulting algorithm is evaluated through simulations. A comparison is made by analogy with results obtained from the recently proposed alpha-composition method.