Fuzzy Fault Trees Formalized
This work addresses reliability analysis for safety-critical systems by formalizing fuzzy fault trees, though it appears incremental relative to existing fuzzy approaches.
The paper tackles the problem of imprecise data in fault tree analysis by defining a rigorous framework for fuzzy unreliability values and providing an efficient bottom-up algorithm to compute them, as demonstrated through two case studies.
Fault tree analysis is a vital method of assessing safety risks. It helps to identify potential causes of accidents, assess their likelihood and severity, and suggest preventive measures. Quantitative analysis of fault trees is often done via the dependability metrics that compute the system's failure behaviour over time. However, the lack of precise data is a major obstacle to quantitative analysis, and so to reliability analysis. Fuzzy logic is a popular framework for dealing with ambiguous values and has applications in many domains. A number of fuzzy approaches have been proposed to fault tree analysis, but -- to the best of our knowledge -- none of them provide rigorous definitions or algorithms for computing fuzzy unreliability values. In this paper, we define a rigorous framework for fuzzy unreliability values. In addition, we provide a bottom-up algorithm to efficiently calculate fuzzy reliability for a system. The algorithm incorporates the concept of $α$-cuts method. That is, performing binary algebraic operations on intervals on horizontally discretised $α$-cut representations of fuzzy numbers. The method preserves the nonlinearity of fuzzy unreliability. Finally, we illustrate the results obtained from two case studies.