Bayesian analysis of series system with dependent causes of failure

ABSTRACTMost studies of series system assume the causes of failure are independent, which may not hold in practice. In this paper, dependent causes of failure are considered by using a Marshall–Olkin bivariate Weibull distribution. We derived four reference priors based on several grouping orders. Gibbs sampling combined with the rejection sampling algorithm and Metropolis–Hastings algorithm is developed to obtain the estimates of the unknown parameters. The proposed approach is compared with the maximum-likelihood method via simulation. We find that the root-mean-squared errors of the Bayesian estimates are much smaller for the case of small sample size, and that the coverage probabilities of the Bayesian estimates are much closer to the nominal levels. Finally, a real data-set is analysed for illustration.