  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 exist) and
show the efficiency of our approach on several case studies.
