Coefficient of contribution to the combined standard uncertainty

The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) describes a generic procedure for determining an estimate for the value of the measurand and its associated combined standard uncertainty from the estimates and their associated standard uncertainties for various input quantities. A user of the ISO-GUM who is interested in understanding, managing or improving the measurement procedure needs the details, usually expressed as an uncertainty budget, on how the estimate for the value of the measurand and its associated combined standard uncertainty were calculated. In particular, a user may be interested in quantifying the degrees of contribution to the combined standard uncertainty from its components. When the measurement equation is a linear function of uncorrelated input variables, the contribution from a component is usually quantified by the product of the component of uncertainty and its sensitivity coefficient. This paper introduces a coefficient of contribution that is suitable for both uncorrelated and correlated input variables. The proposed coefficient of contribution is useful for a variety of measurement equations. Correlations between input variables can significantly alter the relative importance of the contributions to the combined standard uncertainty from its components.