Propagation of distributions - Determination of uncertainties by Monte Carlo simulation

Supplement 1 (JCGM 101:2008) of the 2008 Guide to the expression of uncertainty in measurement complements the GUM (Guide to the expression of uncertainty in measurement) (JCGM 100:2008) by proposing a new approach to the estimation of measurement uncertainties. It concerns the propagation of input variable (parameter) distributions through a mathematical model of the measurement process. It is a practical alternative to GUM when the latter is not easily applicable, for example, if propagation on the basis of first-order Taylor expansion is unsatisfactory (inadequate model linearization) or if the probability density function for the output variable deviates significantly from a Gaussian distribution (leading to unrealistic confidence intervals). It therefore provides a general numerical approach that is compatible with all the general principles of GUM. The approach applies to models with a single output variable. The 2011 Supplement 2 (JCGM 102:2011), not covered here, is an extension to any number of output quantities.

After recalling the principle of estimating uncertainties by the analytical method and its drawbacks, the article explains the principle of the Monte Carlo method in comparison with the analytical method. The constraints and drawbacks of this numerical method are also explained. The paper is based on as many examples as possible, to give as many people as possible access to this technique.