Reliability analysis of large fault trees using the Vesely failure rate

Fault trees provide a compact, graphical, intuitive method to analyze system reliability. However, combinatorial fault tree analysis methods, such as binary decision diagrams, cannot be used to find the reliability of systems with repairable components. In such cases, the analyst should use either Markov models explicitly or generate Markov models from fault trees using automatic conversion algorithms. This process is tedious and generates huge Markov models even for moderately sized fault trees. In this paper, the use of the Vesely failure rate as an approximation to the actual failure rate of the system to find the reliability-based measures of large fault trees is demonstrated. The main advantage of this method is that it calculates the reliability of a repairable system using combinatorial methods such as binary decision diagrams. The efficiency of this approximation is demonstrated by comparing it with several other approximations and provide various bounds for system reliability. The usefulness of this method in finding the other reliability measures such as MTBF, MTTR, MTTF, and MTTFF is shown. Finally, extending this method to analyze complex fault trees containing static and dynamic modules as well as events represented by other modeling tools.