Calculating top event probability of a fault tree with many repeated events

Abstract

Purpose

Calculating the exact top event probability of fault trees is an important analysis in quantitative risk assessments. However, it is a difficult problem for the trees with complex structure. Therefore, the paper aims to provide an efficient calculation method to obtain an exact top event probability of a fault tree with many repeated events when the minimal cut sets of the tree model are given.

Design/methodology/approach

The method is based on the inclusion‐exclusion method. Generally, the inclusion‐exclusion method tends to get into computational difficulties for a large‐scale fault tree. The computation time has been reduced by enumerating only non‐canceling terms.

Findings

The method enables the calculation of the probability more quickly than the conventional method. The effect increases as the number of repeated events increases, namely the tree structure becomes complex. This method also can be applied to obtain the lower and upper bounds of the top event probability easily.

Originality/value

The paper expresses the top event probability by using only non‐canceling terms. This is the first application in fault tree analysis.

Citation

Yuge, T., Tagami, K. and Yanagi, S. (2006), "Calculating top event probability of a fault tree with many repeated events", Journal of Quality in Maintenance Engineering, Vol. 12 No. 4, pp. 364-372. https://doi.org/10.1108/13552510610705937