Tensor-based reliability analysis of complex static fault trees: Regular paper

Fault Tree Analysis is widely used in the reliability evaluation of critical systems, such as railway and automotive systems, power grids, and nuclear power plants. While there are efficient algorithms for calculating the probability of failure in static fault trees, Mean Time to First Failure (MTFF) evaluation remains challenging due to state space explosion. Recently, structural and symmetry reduction methods were proposed to counteract this phenomenon. However, systems with a large number of different and highly interconnected components preclude the use of reduction techniques. Their MTFF analysis requires the solution of a system of linear equations whose size is exponential in the number of components in the system. In this paper, we propose a solution leveraging Tensor Trains as a compressed vector and matrix representation. We build upon Binary Decision Diagram-based techniques to avoid explicit state space enumeration and use linear equation solvers developed specifically for Tensor Trains to efficiently solve the arising linear systems. As a result, our novel approach complements the existing reduction-based techniques and makes some previously intractable models possible to analyze. We evaluate our approach on an industrial case study adapted from a railway system, and other openly available benchmark models.