htmlabstractAs intermittent renewable energy penetrates electrical power grids more and more, assessing grid reliability is of increasing concern for grid operators. Monte Carlo simulation is a robust and popular technique to estimate indices for grid reliability, but the involved computational intensity may be too high for typical reliability analyses. We show that various reliability indices can be expressed as expectations depending on the rare event probability of a so-called power curtailment, and explain how to extend a Crude Monte Carlo grid reliability analysis with an existing rare event splitting technique. The squared relative error of index estimators can be controlled, whereas orders of magnitude less workload is required than when using an equivalent Crude Monte Carlo method. We show further that a bad choice for the time step size or for the importance function may endanger this squared relative error.