Analytic Methods to Calculate Fault Trees with Loops - Restrictions of Application and Solution Uniqueness

TL;DR

This paper discusses the challenges of analyzing fault trees with loops, focusing on the restrictions of classical methods and exploring the conditions for solution uniqueness in such complex structures.

Contribution

It investigates the limitations of traditional fault tree analysis methods with loops and provides insights into solution uniqueness for fault trees with arbitrary loops.

Findings

Classical methods are limited to loop-free fault trees.

Loops in fault trees complicate analysis and solution uniqueness.

Conditions for unique solutions in fault trees with loops are identified.

Abstract

One of the important tasks of the Reliability Estimation is Analysis of the Fault Tree. A problem of Fault Trees analysis is considered one of the most complex ones, since structure of such trees is characterized by a considerable number of interconnections. Usually analytical methods are used and most applicable method is Minimal Cut Sets building and calculation. Classical Fault Tree Analysis methods are applicable only for Fault Trees without loops. Loops can appear in Fault Tree, when a TOP or some intermediate gates appear as input to another gate at a lower level of the model. An occurrence of a Loop has been a problematic issue in a Fault Tree calculation. The article relates to the uniqueness of the solution for the Fault Trees with arbitrary Loops. There are assumed, that failures of the Basic Events are non-repairable and Fault Tree gates may be expressed by two main logic gates.