A Simple Component Connection Approach for Fault Tree Conversion to Binary

Fault Tree Analysis (FTA) is commonly used when conducting risk assessments of industrial systems. A number of computer packages based on conventional analysis methods are available to perform the analysis. However, dealing with large (possibly non-coherent) fault trees can expose the limitations of the technique in terms of accuracy of the solutions and the processing time required. Over recent years the Binary Decision Diagram (BDD) method has been developed for the solution of the fault tree and overcomes the disadvantages of the conventional FTA approaches. The usual way of taking advantage of the BDD structure is to construct a fault tree and then convert it to a BDD. This paper will focus on the fault tree to BDD conversion process. Converting the fault tree requires the basic events of the fault tree to be placed in an ordering. This is critical to the size of the final BDD and ultimately affects the qualitative and quantitative analysis of the system and benefits of this method. Once the ordering is established several approaches can be used for the BDD generation. One approach is to apply a set of rules developed by Rauzy which are repeatedly applied to each gate in the fault tree to generate the BDD. An alternative approach can be used when BDD constructs for each of the gate types are first built and then connected together. A subnode sharing feature in the second of these approaches and a third, hybrid, combined approach will be presented. Some remarks on the effectiveness of these techniques will be provided

Qualitative analysis of complex, modularised fault trees using binary decision diagrams.

Fault Tree Analysis is commonly used in the reliability assessment of industrial systems. However, 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 utilises simplification rules, which 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

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