FAMOCUTN and CUTQN: programs for fast analysis of large fault trees with replicated and negated gates

The paper describes the principal difficulties arising with cutset evaluation for large fault trees containing many replicated gates and events. The usual bottom-up algorithms based on the usual modularization technique with truncation of low-probability cutsets can lead to great computer-tine expenditures with a large upper bound for the probability of the system failure due to the truncated cutsets (truncation error). This paper presents a new method for multi-level representation of fault trees with replicated gates. This method finds and simplifies cutsets on the level of gates, and then descending from the higher to the lower level of fault-tree representation. This method essentially reduces both the computer time and memory needed for cutset evaluation and delivers a more exact upper bound for the truncation error. The computer codes FAMOCUTN using this method for fast evaluation of minimal cutsets (MCS) for large fault trees with negated and/or replicated gates and CUTQN for system reliability calculation on the basis of the determined MCS are described. These computer codes are illustrated by examples of real systems from the German Risk Study for Nuclear Power Stations, Phase B and tested with two fault trees from a fault-tree computer-code benchmark exercise. These codes are now used in Germany, by: (1) Gesellschaft fur Reaktorsicherheit (GRS) mbH, 85748 Garching, and (2) KFA-Forschungszentrum Julich GmbH, Institute for Safety Research and Reactor Technology (ISR-1), 52425 Julich