Probabilistic dynamics offers a general Markovian framework for a dynamic treatment of reliability. Monte Carlo simulation appears to be a powerful and flexible tool to deal with the high dimensionality of realistic applications. Yet an analog game turns out to be ineffective for two main reasons: Very rare events leading to failures are not sampled enough to obtain a good statistical accuracy, and the equations of the dynamics have to be integrated all along each history, which results in very large computation times. Recent improvements in Monte Carlo simulation applied to probabilistic dynamics allow a much faster and more precise estimation of the unreliability of large systems, and they are illustrated on a pressurized water reactor pressurizer.