# Fault Tree Reliability Analysis via Squarefree Polynomials: Mathematical and Experimental Analysis

## TL;DR

This paper introduces a new method for calculating system reliability using squarefree polynomials, improving efficiency for complex systems.

## Contribution

A novel algorithm for computing fault tree unreliability using squarefree polynomials with proven linear time complexity under certain conditions.

## Key findings

- The proposed algorithm is valid and mathematically proven.
- The algorithm's time complexity is linear when multiparent nodes are limited.
- Experimental results show the competitiveness of the new method.

## Abstract

Quantitative analysis of risk models is essential to ensure the resilience of complex systems. Fault trees (FTs) form a ubiquitous prominent risk model, and unreliability is its key safety metric. As complex systems have larger and larger models, the complexity of algorithms computing unreliability is a pressing concern. Unfortunately, state-of-the-art algorithms, based on binary decision diagrams, do not give time complexity guarantees beyond a worst-case exponential bound. To address this issue, this paper introduces a new method to compute FT unreliability, extending the fast bottom-up algorithm for tree-shaped FTs to general FTs by framing its arithmetic in algebras of squarefree polynomials. We prove the validity of this algorithm, and that its time complexity is linear when the number of multiparent nodes is limited. Experiments establish the competitiveness of our new method.