On the convergence of the Monte Carlo block design

The Monte Carlo method is recommended to propagate distributions through the equation of the measurand in the first supplement to the GUM. The result of this method is an approximation of the probability density function (PDF) representing the output quantity of the measurement. This approximation can be used to calculate all necessary statistical parameters such as the expectation value or the standard uncertainty of the measurand. For computational reasons, it is advisable to use a block-by-block evaluation, the Monte Carlo block design, when implementing this method. The statistical parameters of the measurand are then calculated using the statistical parameters of equal sized blocks. This paper demonstrates that this procedure delivers reasonable estimators for the true statistical parameters of the PDF representing the measurand.