Qualitative analysis of complex modularized fault trees using binary decision diagrams

Fault tree analysis is commonly used in the reliability assessment of industrial systems. When complex systems are studied conventional methods can become computationally intensive and require the use of approximations. This leads to inaccuracies in evaluating system reliability. To overcome such disadvantages, the binary decision diagram (BDD) method has been developed. This method improves accuracy and efficiency, because the exact solutions can be calculated without the requirement to calculate minimal cut sets as an intermediate phase. Minimal cut sets can be obtained if needed. BDDs are already proving to be of considerable use in system reliability analysis. However, the difficulty is with the conversion process of the fault tree to the BDD. The ordering of the basic events can have a crucial effect on the size of the final BDD, and previous research has failed to identify an optimum scheme for producing BDDs for all fault trees. This paper presents an extended strategy for the analysis of complex fault trees. The method utilizes simplification rules that are applied to the fault tree to reduce it to a series of smaller subtrees whose solution is equivalent to the original fault tree. The smaller subtree units are less sensitive to the basic event ordering during BDD conversion. BDDs are constructed for every subtree. Qualitative analysis is performed on the set of BDDs to obtain the minimal cut sets for the original top event. It is shown how to extract the minimal cut sets from complex and modular events in order to obtain the minimal cut sets of the original fault tree in terms of basic events.