An ordering heuristic for building binary decision diagrams from fault-trees

Binary decision diagrams (BDD) have made a noticeable entry in the RAMS field. This kind of representation for Boolean functions makes possible the assessment of complex fault-trees, both qualitatively (minimal cutsets search) and quantitatively (exact calculation top event probability). Any Boolean function, and in particular any fault-tree, whether coherent or not, can be represented by a BDD. The BDD is a canonical representation of the function, as soon as one has chosen a variable (i.e., in the fault-tree case, basic event) ordering. Tools based on the use of BDDs, like METAPRIME, or ARALIA, can in some cases give more accurate results than conventional tools, while running 1000 times faster. EDF has investigated this kind of technology, and tested METAPRIME, ARALIA, and other tools based on BDDs, in the framework of cooperations with the BULL company and with the Bordeaux University. These tests have demonstrated that the size of the BDD, that has to be built thoroughly before any kind of assessment can begin, is dramatically sensitive to the ordering chosen for the variables. For a given fault-tree, this size may vary by several orders of magnitude. This can lead to excessive needs, both in terms of memory and CPU time. The problem of finding an optimal ordering being untractable for real applications, many heuristics have been proposed, in order to find acceptable orderings, at low cost (in terms of computing requirements).