A practically oriented, efficient alternative to the Monte Carlo method for measurement uncertainty estimation

Abstract This paper addresses the problem of uncertainty estimation for measurements made with computationally expensive numerical models, which are increasingly applied today. Typically, the Monte Carlo method (MCM) is used for uncertainty propagation in these cases. However, due to its stochastic nature, the MCM is inefficient, requiring a large number of model evaluations and thus resulting in long computation times. In this paper, an efficient alternative to the MCM is introduced. By using systematic samples of the influence quantities which are individually propagated through the measurement model, the overall number of required model evaluations can by drastically reduced. Additionally, the new method offers the possibility to simplify the measurement model for further reduced computational effort. The distributions of the propagated samples are reconstructed using a method specifically designed for systematic samples and combined to the uncertainty distribution of the measurand using convolution. The new method does not only offer increased computational efficiency but also a high information yield, as it estimates the uncertainty distribution of the measurand and the uncertainty contribution of individual influence quantities.