Comparison of two new approaches to variable ordering for binary decision diagrams

Fault tree analysis, FTA, is one of the most commonly used techniques for safety system analysis. There can be problems with the efficiency and accuracy of the approach when dealing with large tree structures. Recently the Binary Decision Diagram (BDD) methodology has been introduced which significantly aids the analysis of the fault tree diagram. The approach has been shown to improve both the efficiency of determining the minimal cut sets of the fault tree, and also the accuracy of the calculation procedure used to quantify the top event parameters. To utilise the BDD technique the fault tree structure needs to be converted into the BDD format. Converting the fault tree is relatively straightforward but requires the basic events of the tree to be placed in an ordering. The ordering of the basic events is critical to the resulting size of the BDD, and ultimately affects the performance and benefits of this technique. There are a number of variable ordering heuristics in the literature, however the performance of each depends on the tree structure being analysed. These heuristic approaches do not yield a minimal BDD structure for all trees, some approaches generate orderings that are better for some trees but worse for others. Within this paper two approaches to the variable ordering problem have been discussed. The first is the pattern recognition approach of neural networks, which is used to select the best ordering heuristic for a given fault tree from a set of alternatives. The second examines a completely new heuristic approach of using the structural importance of a component to produce a ranked ordering. The merits of each are discussed and the results compared.