Meaningful expression of uncertainty in measurement

The Guide to the expression of uncertainty in measurement (GUM) has been the enduring guide on measurement uncertainty for metrologists since its first publication in 1993. According to the GUM, a measurement should always be accompanied by a reasoned and defensible expression of uncertainty, and the primary such expression is the standard uncertainty. In this article, we distinguish between the use of an expression of uncertainty as information for the recipient of a measurement result and its use when propagating uncertainty about inputs to a measurement model in order to derive the uncertainty in a measurand. We propose a new measure of uncertainty, the characteristic uncertainty, and argue that it is more fit for these purposes than standard uncertainty. For the purpose of reporting a measurement result, we demonstrate that standard uncertainty does not have a meaningful interpretation for the recipient of a measurement result and can be infinite. These deficiencies are resolved by the characteristic uncertainty, which we therefore recommend for use in reporting. For similar reasons, we advocate the use of the median estimate as the measured value. For the purpose of propagating uncertainty in a measurement model, we propose simple propagation of the median and characteristic uncertainty and show through some examples that this characteristic uncertainty framework is simpler and at least as reliable and accurate as the propagation of estimate, standard uncertainty and effective degrees of freedom according to the GUM uncertainty framework.

Automated summary

The Guide to the expression of uncertainty in measurement (GUM) has been the definitive guide for metrologists on measurement uncertainty since 1993. In this article, a new measure of uncertainty called characteristic uncertainty is proposed as a more suitable alternative to standard uncertainty. The characteristic uncertainty is recommended for reporting measurement results and the median estimate is advocated as the measured value. Simple propagation of the median and characteristic uncertainty is proposed for propagating uncertainty in a measurement model, which is shown to be simpler and at least as reliable and accurate as the GUM uncertainty framework.