Comparison of variable ordering heuristics / algorithms for binary decision diagrams

Fault tree analysis is a commonly used technique to assess the systems reliability performance in terms of its components reliability characteristics. More 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 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. Numerous studies have tackled this variable ordering problem and a number of heuristic approaches have been developed to produce an optimal ordering permutation for a specific tree. These heuristic approaches do not always yield a minimal BDD structure for all trees, some approaches generate orderings that are better for some trees but worse for others. The most recent research to find an approach to produce an optimal ordering for a range of trees has looked at pattern recognition approaches, such as genetic algorithm based classifier systems. This paper reviews the heuristic approaches that have been established and examines the pattern recognition techniques that have been applied more recently. Another potential new algorithm for ordering using the structural importance of the components is proposed.