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

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|November 17, 2025
PubMed
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This study presents a new method for calculating fault tree (FT) unreliability in complex systems. The approach offers a more efficient way to assess system safety and resilience, overcoming limitations of current algorithms.

Keywords:
Fault treesPolynomial algebraReliability analysis

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Area of Science:

  • System safety engineering
  • Reliability engineering
  • Computational mathematics

Background:

  • Quantitative analysis of risk models is crucial for complex system resilience.
  • Fault trees (FTs) are standard risk models, with unreliability as a key safety metric.
  • Current algorithms for FT unreliability lack guaranteed time complexity, especially for large systems.

Purpose of the Study:

  • Introduce a novel method to compute FT unreliability for general fault trees.
  • Address the computational complexity challenges posed by large-scale risk models.
  • Provide a theoretically sound and practically efficient algorithm for FT unreliability analysis.

Main Methods:

  • Extend the fast bottom-up algorithm for tree-shaped FTs to general FTs.
  • Utilize algebras of squarefree polynomials for arithmetic operations.
  • Develop and validate a new algorithm for computing FT unreliability.

Main Results:

  • The proposed algorithm is proven valid for general FTs.
  • Achieves linear time complexity under limited multiparent nodes.
  • Demonstrates competitiveness against state-of-the-art methods through experiments.

Conclusions:

  • The new method offers a significant improvement in computing FT unreliability.
  • Provides better time complexity guarantees than existing binary decision diagram-based algorithms.
  • Enhances the ability to ensure the resilience of complex systems through efficient risk analysis.