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The analysis of large and complex fault trees is a very difficult task. The main limiting factor is an insufficient working memory. Several methods are available in literature to reduce the working memory requirement including modularization, the so-called 're-writing rules', and truncation, i.e. the use of logic and/or probabilistic cut-offs to determine only the most important system failure modes. The truncation method is very effective, as it allows significant reductions in the computational effort; however, it implies the estimation of the truncation error, a problem not yet solved satisfactorily.Recently, a new method based on the decomposition of a complex fault tree into a set of mutually exclusive simpler fault trees was proposed. The decomposition is repeatedly applied until the generated trees are sufficiently simple to be exactly analysed with the available working memory. Theoretically, this approach would allow the exact analysis of fault trees of any complexity, but the related computation times are generally too high.The scope of this paper is to show how the combined application of decomposition and truncation constitutes a valuable method to analyse complex fault trees. The upper and lower bounds of the top-event probability, obtained by applying this method, are very close to the exact value and their difference depends on the dimension of the available working memory. Furthermore, the probabilistic quantification, including the importance measures of basic events, can easily be performed by properly combining the results from the independent analysis of all simpler fault trees.The developed methodology has been implemented in a software tool and successfully applied to the analysis of several complex fault trees, some of which are considered in this paper.

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Binary Decision Diagram (BDD) based fault tree analysis algorithms are among the most efficient ones. They allow performing exact probabilistic analyses, as well as to derive a Zero-suppressed BDD (ZBDD) to efficiently encode Significant Prime Implicants (PI) or Minimal Cut Sets (MCS).The present paper describes a dynamic labelling method for BDD/ZBDD to analyse non-coherent fault trees. An L-BDD is a BDD in which the information about the variable type is associated to each node. This information is useful to select, for each node, the corresponding algorithms for performing the probabilistic analysis and for determining PI or MCS.When the computational resources are not sufficient to complete the BDD construction, it is convenient to construct the ZBDD directly from the fault tree. The second part of this paper describes rules for constructing a Truncated Labelled ZBDD (TL-ZBDD) of non-coherent fault trees.Results of the analysis of some non-coherent fault trees by means of L-BDD and TL-ZBDD are provided.

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