Uncertainty Analysis for Uncorrelated Input Quantities and a Generalization of the Welch-Satterthwaite Formula which handles Correlated Input Quantities

摘要

The Guide to the Expression of Uncertainty in Measurement (GUM) has been widely adopted in the different fields of the industry and science. This guide established general rules for evaluating and expressing uncertainty in the measurements. In this paper we will give an overview on how to use it for uncorrelated input quantities. We will also introduce correlated magnitudes and correlation types due to the important issue in the evaluation of measurement uncertainty as a consequence of the correlation between quantities. We will identify situations not included into the GUM, when the measurand can be expressed as a function of quantities with common sources. So the issue appears when we use the typical Welch-Satterthwaite formula used to calculate the effective number of degrees of freedom when the measurement errors are not with finite degrees of freedom and uncorrelated. We will introduce a generalization of the Welch-Satterthwaite formula for correlated components with finite degrees of freedom. This paper will also include other methods for computing confidence limits and expanded uncertainties such as using Convolution based on mathematical methods or evaluating the measurement uncertainty based on the propagation of distributions using Monte Carlo simulation.