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From Univariate to Multivariate Uncertainty Calculation

The Guide to the Expression of Uncertainty in Measurement (GUM) mainly deals with measurement models having only a single output quantity. However, in many cases more than one output quantity is required, where all of them are related to a common set of input quantities. In order to evaluate the measurement uncertainties associated with estimated expectations of these output quantities, the uncertainty propagation as treated in the GUM requires an appropriate extension. This article will introduce the concept of the multivariate uncertainty calculation as an extension of the univariate uncertainty calculation.