Brief overview of methods for measurement uncertainty analysis: GUM uncertainty framework, Monte Carlo method, characteristic function approach

The basic working tool in measurement uncertainty analysis, as advocated in recent discussions related to the possible revision of the Guide to the expression of uncertainty in measurement (GUM), and in particular by its Supplements, is the state-of-knowledge distribution about the quantity derived based on the currently available information. The GUM uncertainty framework (GUF) provides a method for assessing uncertainty based on the law of propagation of uncertainty and the characterization of the output quantity by a Gaussian distribution or a scaled and shifted t-distribution. Supplement 1 is concerned with the propagation of probability distributions through a measurement model as a basis for the evaluation of measurement uncertainty, and its implementation by a Monte Carlo method (MCM). Supplement 2 describes a generalization of MCM to obtain a discrete representation of the joint probability distribution for the output quantities of a multivariate model. An alternative tool to form the state-of-knowledge probability distribution of the (scalar) output quantity in linear measurement model, based on the numerical inversion of its characteristic function, which is defined as a Fourier transform of its PDF. Here we present brief overview and some remarks on applicability of these approaches for uncertainty analysis, with emphasized focus on the Characteristic function approach (CFA).