Dynamic Fault Trees with Correlated Failure Times - Modeling and Efficient Analysis -

Abstract

Dynamic Fault Trees (DFTs) are a powerful and widely used class of models for reliability analysis of technical systems. They describe the relation between failure times of elementary components and failures of the system modeled by the DFT. Failure times of elementary components are assumed to be independent and often exponentially distributed. Then the underlying stochastic process is a Continuous Time Markov Chain (CTMC) which is often analyzed numerically. In this paper, we use phase type distributions to model failure times of elementary components and extend DFTs by introducing two new types of nodes to express different variants of correlation between failure times which often can be observed in real systems. Since the use of phase type distributions enlarges the state space of the CTMC, compositional techniques allowing a compact representation of the generator matrix and analysis techniques exploiting this compact representation are also introduced. In particular, analysis techniques are presented that exploit the specific structure of the DFT.