Binary decision diagram (BDD) methodology is the most recent approach to improve Boolean reliability models assessment. The final size of the BDD, and therefore the ultimate benefits of this technique, are very sensitive to the initial variable ordering that has to be fixed prior to conversion. Several variable ordering strategies have been proposed in the literature, all of them focused on the treatment of single fault tree models. This paper proposes some extensions of existing variable ordering schemes for the case of combinations of non-disjoint fault trees, as is the case in quantifying sequences of event trees. These extensions work by combining ordering schemes applied to each fault tree, and exploring the cases where variables within the domains intersection are kept together or not. They have been specifically designed to be applied together with an incremental procedure to compute the BDD of the sequence accumulatively and to be used to quantify sequences of dynamic event trees. Preliminary results show the potential of this approach.

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Binary decision diagrams (BDDs) are a well-known alternative to the minimal cutsets (MCS) approach to assess Boolean reliability models. While the application of fault tree analysis can be considered to be consolidated, its application to the event trees involved in the probabilistic safety assessment (PSA) studies of the nuclear industry require extended efforts. For many real PSA models the full conversion procedure remains out of reach in terms of computational resources owing to their size, non-coherency, redundancy, and complexity. A potential solution to improve the quality of assessment methods is to design hybrid algorithms that combine the information derived from the calculation of MCS with the BDD methodology.As a first step to develop this new approach, this paper explores various procedures and strategies based on this principle. First, a method is presented to reduce the fault tree model by considering only the domain of the most relevant MCS of the system prior to the BDD conversion and the impact on the final probability of the model is analysed. Second, several ordering heuristics derived from the MCS and the structural information of the model are proposed and compared, both in terms of their general performance and their sensitivity to the initial rewriting of the model. This preliminary study is applied on a set of fault tree models belonging to a real PSA study. The results obtained lead to some promising conclusions: it is shown that the topological information proves to be essential for the ordering and conversion procedures; it is also revealed that the rewriting strategies should be considered when designing variable ordering methods; and, finally, it is demonstrated that the reduction procedure provides a faster computation process without affecting the final probability. The long-term objective, which has motivated this work, is to apply this reduction procedure to quantify sequences of linked fault trees, both static and dynamic, a task for which further work is required. Downloaded from Proc. IMechE Vol. 223 Part O: J. Risk and Reliability JRR259 JRR259 Proc. IMechE Vol. 223 Part O: J. Risk and Reliability MCS-based reduction approach for the use of BDDs *OM denotes BDD computation out of memory. JRR259 Proc. IMechE Vol. 223 Part O: J. Risk and Reliability MCS-based reduction approach for the use of BDDs

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