Maximum likelihood and Bayesian inference for common-cause of failure model

Highlights: • Overviewing statistical methods to study common-cause of failure in systems. • Using an EM algorithm as an optimization method in the context of CCF. • Introducing the Modified-Beta distribution to deal with the Bayesian approach. • Addressing the issue of prior elicitation from information communicated by the user. -- Abstract: This paper considers the statistical analysis of the Binomial Failure Rate (BFR) common-cause model in detail. Computational aspects of maximum likelihood and Bayesian methods are investigated. An Expectation-maximization (EM) algorithm to obtain maximum likelihood estimates is suggested to deal with missing data inherent for common-cause failures. A Bayesian approach is developed and the modified-Beta distribution is defined to characterize the posterior distribution for one of the model parameters. The different methods are applied and compared on both simulated and real data.