Prior Robustness for Bayesian Implementation of the Fault Tree Analysis

Abstract

We propose a prior robustness approach for the Bayesian implementation of the fault tree analysis (FTA). FTA is often used to evaluate risk in large, safety critical systems but has limitations due to its static structure. Bayesian approaches have been proposed as a superior alternative to it, however, this involves prior elicitation, which is not straightforward. We show that minor misspecification of priors for elementary events can result in a significant prior misspecification for the top event. A large amount of data is required to correctly update a misspecified prior and such data may not be available for many complex, safety critical systems. In such cases, prior misspecification equals posterior misspecification. Therefore, there is a need to develop a robustness approach for FTA, which can quantify the effects of prior misspecification on the posterior analysis. Here, we propose the first prior robustness approach specifically developed for FTA. We not only prove a few important mathematical properties of this approach, but also develop easy to use Monte Carlo sampling algorithms to implement this approach on any given fault tree with and and/or or gates. We then implement this Bayesian robustness approach on two real-life examples: a spacecraft re-entry example and a feeding control system example. We also provide a step-by-step illustration of how this approach can be applied to a real-life problem.