Efficient fault tree analysis using binary decision diagrams
The Binary Decision Diagram (BDD) method has emerged as an alternative to conventional techniques for performing both qualitative and quantitative analysis of fault trees. BDDs are already proving to be of considerable use in reliability analysis, providing a more efficient means of analysing a system, without the need for the approximations previously used in the traditional approach of Kinetic Tree Theory. In order to implement this technique, a BDD must be constructed from the fault tree, according to some ordering of the fault tree variables. The selected variable ordering has a crucial effect on the resulting BDD size and the number of calculations required for its construction; a bad choice of ordering can lead to excessive calculations and a BDD many orders of magnitude larger than one obtained using an ordering more suited to the tree. Within this thesis a comparison is made of the effectiveness of several ordering schemes, some of which have not previously been investigated. Techniques are then developed for the efficient construction of BDDs from fault trees. The method of Faunet reduction is applied to a set of fault trees and is shown to significantly reduce the size of the resulting BDDs. The technique is then extended to incorporate an additional stage that results in further improvements in BDD size. A fault tree analysis strategy is proposed that increases the likelihood of obtaining a BDD for any given fault tree. This method implements simplification techniques, which are applied to the fault tree to obtain a set of concise and independent subtrees, equivalent to the original fault tree structure. BDDs are constructed for each subtree and the quantitative analysis is developed for the set of BDDs to obtain the top event parameters and the event criticality functions.