Bayesian Nonparametric System Reliability using Sets of Priors

Abstract: An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test data these bounds are propagated to bounds on the posterior predictive distribution for the functioning probability of a new system containing components exchangeable with those used in testing. The method further enables identification of prior-data conflict at the system level based on component level test data. New results on first-order stochastic dominance for the Beta-Binomial distribution make the technique computationally tractable. Our methodological contributions can be immediately used in applications by reliability practitioners as we provide easy to use software tools.