Weight updating in forced Monte Carlo approach to dynamic PSA

In dynamic PSA (Probabilistic Safety Analysis), in addition to the stochastic failures, normally accounted for in the classic, event tree/fault tree-based approach, one has to consider the physical evolution of the process variables. Correspondingly, the control/protection device needs to be simulated, its intervention being demanded when one of the process variables crosses pre-established thresholds. The Monte Carlo methodology lends itself to an efficient estimate of the reliability of systems with dynamic features. In this respect, the high reliability of current components and control/protection devices renders prohibitive the use of analog Monte Carlo, thus making the use of variance reduction techniques almost mandatory. In the present paper we tackle a new problem arising in this context. More specifically, once the next failure time is forced and the weight of the representative point is correspondingly updated, we have to follow the system dynamics up to that time, e.g. by numerical integration of the equations pertaining to that hardware configuration. During this time, some process variables may reach preestablished thresholds, thus requiring the intervention of the control/protection device. Each intervention modifies the system hardware configuration, thus invalidating the choice of the forced failure time and the accompanying Monte Carlo weight of the representative point. This issue is here analyzed in details and suitable expressions for a proper weight updating are provided.