The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM) is the internationally accepted master document for the evaluation of uncertainty. It contains a procedure that is suitable for many, but not all, uncertainty evaluation problems met in practice. This procedure constitutes an approximation to the general solution of the Markov formula, which infers the probability density function (PDF) for the output quantities (measurands) from the model of the measurement and the PDFs for the input quantities. This paper shows that a Monte Carlo method is an effective and versatile tool for determining the PDF for the measurands. This method provides a consistent Bayesian approach to the evaluation of uncertainty. Although in principle straightforward, some care is required in representing and validating the results obtained using the method. The paper provides guidance on optimizing the approach, identifies some pitfalls and indicates means for validating the results.