Christian Ranson:

In the evaluation of uncertainties, the use of the law of propagation of uncertainties and the application of the central limit theorem may not always allow to obtain a valid solution (highly non-linear model, asymmetric relevant distributions...).

In such circumstances, it is better to use the propagation of distributions. This approach is based on the direct use of the probability distributions assigned to the input quantities rather than just their means and standard deviations. An analytical treatment is not generally possible. However the problem can be solved numerically. The most efficient implementation of the propagation of distributions is through the use of Monte Carlo Simulation.

Supplemental Guide 1 provides detailed information on the propagation of distributions.