Bayesian Nonparametric System Reliability using Sets of Priors

TL;DR

This paper introduces a flexible imprecise Bayesian nonparametric method for assessing system reliability with multiple component types, incorporating uncertain prior knowledge and test data to produce bounds on system performance.

Contribution

It develops a novel approach that models partial prior knowledge via bounds on component functioning probabilities and propagates these to system-level reliability bounds, including conflict detection.

Findings

Provides bounds on system reliability using imprecise priors

Enables detection of prior-data conflict at the system level

Offers computationally efficient methods with software tools

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.