Variable ordering schemes to apply to the binary Decision diagram methodology for event tree sequences assessment

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, is very sensible to the initial variable ordering that has to be fixed prior to conversion. Several variable ordering strategies have been proposed within 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-disjoints Fault Trees, as is the case in quantifying sequences of Event Trees. These extensions work combining ordering schemes applied to each Fault Tree, but considering whether variables within the domains intersection should be kept together or not. They have been designed specifically 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. ever, in many practical cases, BDD encoding Boolean functions of a particular nature, as it happens with Fault Trees, remain in a tractable size if the initial ordering selected is reasonably good. Hence, research has been focused on designing heuristics and strategies to find good variable orderings. Most of the work up to now has been devoted to the design of variable ordering heuristics for Fault Trees. Several heuristics have been proposed in the literature, mainly by research groups of France and England. On the other hand, much work has still to be done when dealing with sequences of Event Trees defined by products of non-disjoints Fault Trees. For those cases, not only it is important to design good strategies for each Fault Tree, but also to design strategies to handle the Fault Tree domains intersection. The aim of this article is to propose several extensions of existing ordering strategies for sequences of Event Trees amenable to the incremental computation of the BDD encoding the Boolean formula of a sequence. The remainder of the article is organized as follows. Section 2 introduces a brief description of Boolean models used in reliability. Section 3 is devoted to the concept of Binary Decision Diagram and its application into reliability analysis. In this section, the accumulative procedure to compute the BDD of the sequences is outlined. Section 4 presents a review of variable ordering schemes for Fault Trees existing in the literature, and presents the proposed extensions for sequences of Event Trees. Finally, the case study is presented in section 5, and the conclusion and future work, in section 6. 2 BOOLEAN RELIABILITY MODELS Boolean models are commonly used in risk analysis of industrial facilities, such as aviation, nuclear or chemical to develop a representation of the overall system in terms of logic diagrams. The essential and most common techniques used for schematic representation of a system, especially in the nuclear industry, are Fault Trees and Event Trees. Furthermore, its combination is the basis of the PSA studies in the nuclear industry (Steward & Melchers 1997). This section is devoted to present the basis of those models, and more specifically, the application to Dynamic Event Trees.