Analysis of large fault trees based on functional decomposition

摘要

With the advent of the Binary Decision Diagrams (BDD) approach in fault tree analysis, a significant enhancement has been achieved with respect to previous approaches, both in terms of efficiency and accuracy of the overall outcome of the analysis. However, the exponential increase of the number of nodes with the complexity of the fault tree may prevent the construction of the BDD. In these cases, the only way to complete the analysis is to reduce the complexity of the BDD by applying the truncation technique, which nevertheless implies the problem of estimating the truncation error or upper and lower bounds of the top-event unavailability. This paper describes a new method to analyze large coherent fault trees which can be advantageously applied when the working memory is not sufficient to construct the BDD. It is based on the decomposition of the fault tree into simpler disjoint fault trees containing a lower number of variables. The analysis of each simple fault tree is performed by using all the computational resources. The results from the analysis of all simpler fault trees are re-combined to obtain the results for the original fault tree. Two decomposition methods are herewith described: the first aims at determining the minimal cutsets (MCS) and the upper and lower bounds of the top-event unavailability; the second can be applied to determine the exact value of the top-event unavailability. Potentialities, limitations and possible variations of these methods will be discussed with reference to the results of their application to some complex fault trees.