Bootstrapping Procedure to Determine Convergence in Monte Carlo Simulations

Monte Carlo simulations are routinely performed in many branches of engineering to determine the distribution of possible system performance. In particular, Monte Carlo simulation, or a variant of it, is the most likely candidate for realistic simulation of reliability in mechanistic–empirical pavement design methods. However, it is common to find no justification for the number of simulations run or any analysis to determine whether, in fact, the distribution has converged. Although standard sampling rules can be applied to the estimate of the performance of the mean, especially in the presence of distributions that are approximately normal, they are difficult to apply to full distributions or percentiles. This paper presents a simple method for using statistical bootstrapping techniques to improve the quality of distributions estimated by Monte Carlo simulation, especially the quality of the estimates for percentiles in the tail of the distribution. This method is applied to the results of a mechanistic–empirical simulation of rutting on an asphalt pavement to demonstrate the issues and the procedure. However, the procedure is applicable to any type of performance model.