ZBDD algorithm features for an efficient Probabilistic Safety Assessment

Abstract

This paper explains a Zero-suppressed Binary Decision Diagram (ZBDD) algorithm and introduces advanced ZBDD algorithm-based features that are implemented into a fault tree solver Fault Tree Reliability Evaluation eXpert (FTREX). The ZBDD algorithm and its advanced features have been developed for solving a fault tree in Probabilistic Safety Assessment (PSA) of a nuclear power plant. The ZBDD can be interpreted as a factorized structure of minimal cut sets (MCSs). A ZBDD algorithm was developed in 2004 for performing a Boolean operation of ZBDDs. The ZBDD algorithm is based on a set of new ZBDD operation formulae. The ZBDD algorithm is known as an efficient replacement of a cutset-based algorithm that is based on traditional Boolean algebra. This paper explains how to perform a delete-term operation and a rule-based post-processing of MCSs by the ZBDD algorithm and demonstrates the efficiency of the ZBDD algorithm by performing benchmark tests. By using the ZBDD algorithm in this study, a long run time for (1) solving a fault tree, (2) performing a delete-term operation to handle negates, and (3) performing a rule-based post-processing of MCSs could be significantly reduced. Since the ZBDD algorithm is based on the factorized form of MCSs, it uses much less memory than the cutset-based algorithm. Due to the small memory requirement of the ZBDD algorithm from solving a fault tree to performing a rule-based post-processing, a much smaller truncation limit can be used than that in the cutset-based algorithm. By lowering the truncation limit, accurate PSA results such as a core damage frequency and importance measures could be calculated by the ZBDD algorithm.