Analytic probabilistic safety analysis under severe uncertainty

Exact analytic expressions are given to evaluate the reliability of systems consisting of components, connected in parallel or series, subject to imprecise failure distributions. We also proposed a simplified version of the first-order reliability method to deal with imprecision. This development allows engineers to evaluate the reliability of systems without having to resort to optimization techniques and/or Monte Carlo simulation. In addition, this framework does not need to assume a distribution for the epistemic uncertainty, which permits a robust analysis even with limited data. In this way, the approach removes a significant barrier to the modeling of epistemic uncertainties in industrial probabilistic safety analysis workflows.