Analysis of large fault trees based on functional decomposition

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 analyse large coherent fault trees which can be advantageously applied when the working memory is not sufficient to perform the analysis with current methods. It is based on the decomposition of the fault tree into simpler disjoint functions containing a lower number of variables. The number and complexity of these functions depend on the dimensions of the available working memory, i.e. the smaller is the working memory the greater is the number of functions and vice versa. The analysis of each simple function is performed by using all the computational resources. The results from the analysis of all simpler functions 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 cut sets (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.JRC.DG.G.7-Traceability and vulnerability assessmen