Distribution-free fault-tree analysis for probabilistic risk assessment under uncertainty

This paper proposes a Bayesian framework for a distribution-free fault-tree analysis using a probability-boxes and confidence-boxes to estimate the reliability of a complex coherent system. The approach addresses key challenges arising from limited component reliability data, available as Boolean observations, “ k -out-of- n ” data, or reported probability values, alongside the uncertainty about the underlying distribution class and the statistical dependence between component and system failures. To overcome these issues, a calculus of distribution-free probability-boxes and confidence-boxes is implemented to characterise the aleatory and the epistemic uncertainties while also accounting for the uncertain event-level statistical dependence within the fault-tree structure. The framework enables the propagation of these uncertainties to obtain bounds on the Top-event probability. A novel interpretation of the resulting distribution-free output based on statistical performance is provided, addressing a gap in the existing literature. The proposed methodology is demonstrated through a real-world case study of a reactor coolant subsystem, with results validated against a reference top event probability, illustrating the feasibility and effectiveness of the approach.