[en] A method of assessing the uncertainty in the TOP event probability of a fault tree by a Monte Carlo simulation is presented. This approach is used to produce an empirical Bayes estimate of the probability intervals of TOP event unreliability. The Monte Carlo simulation used proceeds by propagating basic event probabilities, chosen randomly from input probability distributions through the tree, producing an empirical TOP event probability distribution (with associated confidence limits) after combining the results of many trials. The basic principles of this Monte Carlo approach are discussed. A new computer code, LIMITS, is presented and is used in several examples, and compared with the earlier SAMPLE code developed for the Reactor Safety Study. The results show that the LIMITS code is significantly faster due to an optimized sorting routing and that, in general, an even slightly faster code would be possible by the use of special random-number generators. Finally, sample input and output, and a listing of the program are provided for the reader who might wish to use the LIMITS code