Probabilistic dynamics: Estimation of generalized unreliability through efficient Monte Carlo simulation

Abstract

The dynamic behaviour of a system is generally omitted in its PRA study, though it can greatly influence the failure risks. Probabilistic dynamics is a Markovian framework for the dynamic treatment of reliability. In this model, the concept of unreliability does not only consist in a transition to a failure state, but also in the crossing of the border of a safety domain in the space of the physical variables. Monte Carlo simulation appears to be the only tool likely to cope with realistic problems. However, since it aims at estimating the risk of very rare events, an analogue game is too time-consuming or inaccurate. Therefore, simulation techniques have to be improved to be practically used. Different ways of achieving this task exist: the definition of unbiased efficient estimators, the acceleration of the integration of the equations of the dynamics and the development of biased schemes. We review these possibilities in this paper and apply them on a study case.