System safety assessment under epistemic uncertainty: Using imprecise probabilities in Bayesian network

Abstract

System safety and reliability assessment relies on historical data and experts opinion for estimating the required failure probabilities. When data comes from different sources, be it different databases or subject domain experts, the estimation of accurate probabilities would be very challenging, if not impossible, and subject to high epistemic uncertainty. In such cases, the use of imprecise probabilities to reflect the incomplete knowledge of analysts and their epistemic uncertainty is inevitable.
Evidence theory is an effective tool for manipulating imprecise probabilities. However, challenges in the assignment of prior belief masses and the lack of effective inference algorithms for combining and updating the belief masses have impeded the widespread application of evidence theory.
To address the foregoing issues, in the present study, (i) an innovative heuristic approach is developed to determine the prior belief masses based on the prior imprecise probabilities, and (ii) it is demonstrated how Bayesian network can be used for both propagating and updating the belief masses. In a nutshell, the developed methodology converts the prior imprecise probabilities into prior belief masses, propagates and updates the belief masses using Bayesian network, and back-transforms the predicted/updated belief masses to posterior imprecise probabilities.