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.

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We propose an approach for assessing the impact of multi-phased repair procedures on gas distribution networks, capturing load profiles that can depend on time for different classes of users, suspension of activities during non-working hours, and random execution times depending on topological, physical, and geographical characteristics of the network. The problem is characterized through a semi-formal specification based on artifacts of the Systems Modeling Language (SysML), which is then translated into a formal model based on stochastic time Petri nets. The solution method interleaves fluid-dynamic analysis of the gas behavior and stochastic analysis of the time spent in the repair process, decoupling complexities and making stochastic analysis almost insensitive to the network size and topology. Hence, our approach turns out to be applicable to real scale cases, notably computing the optimal time of day to start the repair procedure. Moreover, by encompassing general (non-Markovian) distributions, the approach enables effective fitting of durations.

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