Rare event simulation for non-Markovian repairable fault trees

Abstract

Dynamic fault trees (dft) are widely adopted in industry to assess the dependability of safety-critical equipment. Since many systems are too large to be studied numerically, dfts dependability is often analysed using Monte Carlo simulation. A bottleneck here is that many simulation samples are required in the case of rare events, e.g. in highly reliable systems where components fail seldomly. Rare event simulation (res) provides techniques to reduce the number of samples in the case of rare events. We present a res technique based on importance splitting, to study failures in highly reliable dfts. Whereas res usually requires meta-information from an expert, our method is fully automatic: By cleverly exploiting the fault tree structure we extract the so-called importance function. We handle dfts with Markovian and non-Markovian failure and repair distributions-for which no numerical methods existand show the efficiency of our approach on several case studies.

Automated Rare Event Simulation for Fault Tree Analysis via Minimal Cut Sets

“…In fact, we propose several variants of this idea, where we also normalize the cut sets by their maximum weights, or prune them based on their cardinality or failure probability. Our experimental evaluation shows that our functions, tested on the standard hecs benchmark for fta for a fixed simulation time budget, can produce estimates as accurate as more involved approaches that consider the whole structure of the tree [3]. Moreover, the res algorithms deployed by our functions show the highest stability in our tests.…”

“…weight) to more promising states in a trace. The main contribution of this paper is to assign to each fault tree an importance function that can be automatically derived from its structure, in a similar way to [3]. The goals is also to deploy functions with low computation overhead and low variability, so that the res algorithms implemented from them hare highly-performant.…”

“…However, both functions are hindered when the branches of the fault tree have different failure probabilities. In this work we propose to alleviate this issue via cut set pruning and importance normalisation [3]. Regarding automation, [4,5,12,13] are among the first to attempt a heuristic derivation of all parameters required to implement splitting.…”

“…Regarding automation, [4,5,12,13] are among the first to attempt a heuristic derivation of all parameters required to implement splitting. In essence, here we extended [2,4,5], using the cut sets of the fault tree in conjunction with the structural function derived in [3].…”

Masterminding change by combining secure system design with security risk assessment

“…In this talk, she summarized the lessons learned from previous work [6] on integrating fault tree analysis with attack trees for quantitative analysis. She sketched the research landscape and future challenges for formal methods in the presence of machine learning that are partly addressed in her current work on rare-event simulation [1].…”