Abstract
This article derives an estimation procedure to evaluate how many Monte Carlo realizations need to be done in order to achieve prescribed accuracies in the estimated mean value and also in the cumulative probabilities of achieving values greater than, or less than, a particular value as the chosen particular value is allowed to vary. In addition, by inverting the argument and asking what the accuracies are that result for a prescribed number of Monte Carlo realizations, one can assess the computer time that would be involved should one choose to carry out the Monte Carlo realizations. These two complementary procedures are of great benefit in attempting to control the worth of undertaking an unknown number of Monte Carlo realizations, and of continuing to carry out the unknown number until the results have reached a level of accuracy that one deems acceptable. Such a procedure is not only computer intensive; however, is also very open-ended, a less than desirable trait when running a complex computer program that might take many hours or days to run through even once. The procedure presented here allows one to assess, ahead of performing a large number of Monte Carlo realizations, roughly how many are actually needed. Several illustrative numerical examples provide indications how one uses this novel procedure in practical situations.