Rare-Event Estimation for Dynamic Fault Trees

TL;DR

This paper introduces specialized Monte-Carlo simulation algorithms with importance sampling for estimating rare events in dynamic fault trees, addressing the complexity of models with dynamic gates and non-repairable failures.

Contribution

It proposes a novel approach for rare-event estimation in dynamic fault trees using importance sampling tailored to their specific features.

Findings

Effective importance sampling expressions for dynamic fault trees

Numerical results demonstrating the approach's accuracy

Applicability to various failure time distributions

Abstract

Article describes the results of the development and using of Rare-Event Monte-Carlo Simulation Algorithms for Dynamic Fault Trees Estimation. For Fault Trees estimation usually analytical methods are used (Minimal Cut sets, Markov Chains, etc.), but for complex models with Dynamic Gates it is necessary to use Monte-Carlo simulation with combination of Importance Sampling method. Proposed article describes approach for this problem solution according for specific features of Dynamic Fault Trees. There are assumed, that failures are non-repairable with general distribution functions of times to failures (there may be Exponential distribution, Weibull, Normal and Log-Normal, etc.). Expessions for Importance Sampling Re-Calculations are proposed and some numerical results are considered