Truncation approach with the decomposition method for system reliability analysis

The esary proschan (EP) method and other approximations, based on minimal cut sets (MCSs) calculation, are commonly used in reliability system analysis. However, it is time consuming and even impossible to calculate all MCSs of large systems. Cut off by order or by probability is applied to find the most important MCSs. In this paper we discuss the efficiency and accuracy of this approach by comparing results of calculations, obtained for large industrial benchmarks using both EP and pivotal decomposition method (DM). DM (and similar binary decision diagram method) allows obtaining exact solutions for large fault trees, but it is still time consuming. We have shown that for large fault trees it is efficient to apply approximate DM in combination with truncation approach. We suggest an algorithm, which is mathematically sound and accurate enough in the entire range of probability. It is also applied efficiently in the calculation of different system parameters, such as: total downtime, frequency, expected number of failures, and mean time to failure (MTTF). The efficiency and accuracy of the approach is demonstrated by numerous calculations of complex industrial benchmarks.