From Univariate to Multivariate Uncertainty Calculation

TL;DR

This paper introduces a multivariate extension to the GUM framework for calculating measurement uncertainties involving multiple related output quantities, addressing a gap in the existing univariate approach.

Contribution

It proposes a novel multivariate uncertainty calculation method extending the GUM to handle multiple correlated output quantities.

Findings

Extends GUM to multivariate cases

Provides a framework for correlated output uncertainties

Enhances measurement uncertainty evaluation accuracy

Abstract

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.