Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

TL;DR

This paper introduces a robust Bayesian method for reliability analysis of complex systems that effectively manages prior-data conflicts by using sets of priors, leading to more reliable bounds on system failure probabilities.

Contribution

It proposes a novel robust Bayesian approach employing sets of priors and survival signatures to handle prior-data conflicts in complex system reliability estimation.

Findings

Wider system reliability bounds reflect early or late component failures.

The method mitigates false certainty caused by prior-data conflicts.

Applicable to systems with arbitrary layouts using Weibull distributions.

Abstract

In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is straightforward in the Bayesian approach by using an informative prior distribution. A problem called prior-data conflict then can arise: observed data seem very surprising from the viewpoint of the prior, i.e., information from data is in conflict with prior assumptions. Models based on conjugate priors can be insensitive to prior-data conflict, in the sense that the spread of the posterior distribution does not increase in case of such a conflict, thus conveying a false sense of certainty. An approach to mitigate this issue is presented, by considering sets of prior distributions to model limited knowledge on Weibull distributed component lifetimes, treating systems with arbitrary layout using the survival signature. This approach can be seen as a robust Bayesian procedure or imprecise probability method that reflects surprisingly early or late component failures by wider system reliability bounds.