A fast BDD algorithm for large coherent fault trees analysis

Abstract

Abstract Although a binary decision diagram (BDD) algorithm has been tried to solve large fault trees until quite recently, they are not efficiently solved in a short time since the size of a BDD structure exponentially increases according to the number of variables. Furthermore, the truncation of If–Then–Else (ITE) connectives by the probability or size limit and the subsuming to delete subsets could not be directly applied to the intermediate BDD structure under construction. This is the motivation for this work. This paper presents an efficient BDD algorithm for large coherent systems (coherent BDD algorithm) by which the truncation and subsuming could be performed in the progress of the construction of the BDD structure. A set of new formulae developed in this study for AND or OR operation between two ITE connectives of a coherent system makes it possible to delete subsets and truncate ITE connectives with a probability or size limit in the intermediate BDD structure under construction. By means of the truncation and subsuming in every step of the calculation, large fault trees for coherent systems (coherent fault trees) are efficiently solved in a short time using less memory. Furthermore, the coherent BDD algorithm from the aspect of the size of a BDD structure is much less sensitive to variable ordering than the conventional BDD algorithm.