Fault tree conversion to binary decision diagrams

Fault Tree Analysis is a commonly used technique to predict the causes of a specific system failure mode and to then determine the likelihood of this event. Over recent years the Binary Decision Diagram (BDD) method has been developed for the solution of the fault tree. It can be shown that this approach has advantages in terms of both accuracy and efficiency over the conventional method of analysis formulated in the 1970’s. The BDD expresses the failure logic in a disjoint form which gives it an advantage from the computational viewpoint. Fault Trees, however, remain the better way to represent the system failure causality. Therefore the usual way of taking advantage of the BDD structure is to construct a fault tree and then convert this to a BDD. It is on the fault tree conversion process that this paper will focus. In order to construct a BDD the variables which represent the occurrence of the basic events in the fault tree have to be placed in an ordering. Depending on the ordering selected an efficient representation of the failure logic can be obtained or if a poor ordering is selected a less efficient analysis will result. Once the ordering is established one approach is to utilise a set of rules developed by Rauzy which are repeatedly applied to generate the BDD. An alternative approach can be used whereby BDD constructs for each of the gate types are first formed and then joined together as specified by the gates in the fault tree. Some comments on the effectiveness of these approaches will be provided.