Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence

Monte Carlo analysis has become nearly ubiquitous since its introduction, now over 65 years ago. It is an important tool in many assessments of the reliability and robustness of systems, structures or solutions. As the deterministic core simulation can be lengthy, the computational costs of Monte Carlo can be a limiting factor. To reduce that computational expense as much as possible, sampling efficiency and convergence for Monte Carlo are investigated in this paper. The first section shows that non-collapsing space-filling sampling strategies, illustrated here with the maximin and uniform Latin hypercube designs, highly enhance the sampling efficiency, and render a desired level of accuracy of the outcomes attainable with far lesser runs. In the second section it is demonstrated that standard sampling statistics are inapplicable for Latin hypercube strategies. A sample-splitting approach is put forward, which in combination with a replicated Latin hypercube sampling allows assessing the accuracy of Monte Carlo outcomes. The assessment in turn permits halting the Monte Carlo simulation when the desired levels of accuracy are reached. Both measures form fairly noncomplex upgrades of the current state-of-the-art in Monte-Carlo based uncertainty analysis but give a substantial further progress with respect to its applicability.