Fast Monte Carlo Simulation Methods Adapted to Simple Petri Net Models

In oil and gas industry, the reliability analysis of High Integrity Protection Systems is an important issue. The standard modeling languages and the traditional methods employed for these studies are difficult to apply mainly because of the complexity of the operating context of these equipment. Thus, a powerful alternative is Petri nets associated with the Monte Carlo simulation (MC). However, obtaining accurate estimators on rare events (system failures) calls for very long computing times. To address this issue, the common methods are not well-suited to Petri Nets whereas the "Methode de Conditionnement Temporel" (MCT) seems to be. Indeed, this method does not require to know the model distributions, however, it is only defined when the rare event is an absorbing state. To overcome this limitation, we first propose an extension of MCT (EMCT) to simple cases which represent repeated cycles where the failure event is either direct or in competition with other events. The first results show that EMCT gives better estimates than MC for a similar computing time. Second, we introduce a new computational technique, called Dissociation method, which is valid only if the components of the system are independent. We combine it with both MC and EMCT. Through different numerical examples, we observe a significant improvement of the obtained results.