Some acceleration methods for Monte Carlo simulation of rare events

The reliability analysis of instrumented safety systems is an important industrial issue. The standard modeling languages (e.g., Fault trees and Markov chains) and methods employed for these studies become difficult to apply mainly because of the increasing complexity of the operating context (e.g., maintenance policies and aging process). Thus, a powerful alternative is Petri nets associated with Monte Carlo simulation (MC). However, obtaining accurate estimators on rare events (system failures) requires very long computing times. To address this issue, common methods are not well-suited to Petri nets whereas the ‘Methode de Conditionnement Temporel’ (MCT), a truncation method, seems to be. Indeed, MCT is independent of the duration distributions involved in a model. However, it is only defined when the rare event consists in reaching an absorbing state. To overcome this limitation, we first propose an extension of MCT (EMCT) to cases of repeated cycles where the failure event is either direct or in competition with other events. Numerical results show that EMCT gives better estimates than MC. Second, we introduce a new computational technique, called Dissociation Method, for systems with independent components. We combine it with both MC and EMCT. Through different numerical examples, we observe a significant improvement of the results.