Analysis of non-Markovian repairable fault trees through rare event simulation

Carlos E. Budde*, Pedro R. D'Argenio, Raúl E. Monti, Mariëlle Stoelinga

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
29 Downloads (Pure)


Dynamic fault trees (DFTs) 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 seldom fail. Rare event simulation (RES) provides techniques to reduce the number of samples in the case of rare events. In this article, we present a RES technique based on importance splitting to study failures in highly reliable DFTs,
more precisely, on a variant of repairable fault trees (RFT). Whereas RES usually requires meta-information from an expert,
our method is fully automatic. For this, we propose two different methods to derive the so-called importance function. On the one hand, we propose to cleverly exploit the RFT structure to compositionally construct such function. On the other hand, we explore different importance functions derived in different ways from the minimal cut sets of the tree, i.e., the minimal units that determine its failure. We handle RFTs with Markovian and non-Markovian failure and repair distributions—for which no numerical methods exist—and implement the techniques on a toolchain that includes the RES engine FIG, for which we also present improvements. We finally show the efficiency of our approach in several case studies.
Original languageEnglish
Pages (from-to)821-841
Number of pages21
JournalInternational journal on software tools for technology transfer
Issue number5
Publication statusPublished - 4 Nov 2022


  • This work was partially supported by the EU Grant Agreement 101008233 (MISSION), ANPCyT PICT-2017-3894 (RAFTSys), and SeCyT project 33620180100354CB (ARES). Funded also by the EU Grant Agreement 101067199 (ProSVED).


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