  Fault tree (FT) analysis is a prominent risk assessment method in industrial
systems. Unreliability is one of the key safety metrics in quantitative FT
analysis. Existing algorithms for unreliability analysis are based on binary
decision diagrams, for which it is hard to give time complexity guarantees
beyond a worst-case exponential bound. In this paper, we present a novel method
to calculate FT unreliability based on algebras of squarefree polynomials and
prove its validity. We furthermore prove that time complexity is low when the
number of multiparent nodes is limited. Experiments show that our method is
competitive with the state-of-the-art and outperforms it for FTs with few
multiparent nodes.
