Uncertainty propagation through non-linear measurement functions by means of joint Random-Fuzzy Variables

Abstract

A still open issue, in uncertainty evaluation, is that of asymmetrical distributions of the values that can be attributed to the measurand. This problem becomes generally not negligible when the measurement function is highly non-linear. In this case the law of uncertainty propagation suggested by the GUM is not correct any longer, and only Monte Carlo simulations can be used to obtain such distributions. This paper shows how this problem can be solved in a quite immediate way when measurement results are expressed in terms of Random-Fuzzy Variables. Under this approach, also non-random contributions to uncertainty can be considered. An example of application is reported and the results compared with those obtained by means of Monte Carlo simulations, showing the effectiveness of the proposed approach.