Equivalence of Fault Trees and Stochastic Petri Nets in Reliability Modelling

Abstract

Modeling of reliability of the complex systems (machines, large networks, human body) is an important area of recent research. There are two main approaches applied: i) fault trees, ii) Petri nets. For the probabilistic study of a system is vital to know its minimal cut/minimal path sets. Both for fault trees and Petri Nets it is an NP-hard problem. Liu and Chiou (1997) described the equivalence of both representations for a given system. Furthermore, they found a top-down matrix algorithm to find critical cuts and minimal paths of the Petri net of the system. They claim without proof that their algorithm is more efficient than the ones for fault trees. We present both representations of a system. The algorithm is illustrated on a simple example of a three-masted vessel and a more complex “three-motor” system by Vesely et al. (1981).

Keywords

• reliability
• time to failure
• fault tree
• stochastic petri net
• exponential distribution