The contents of the current edition, JCGM 100:2008, of the Guide to the Expression of Uncertainty in Measurement (GUM) and its Supplements are reviewed and remarks made concerning a proposed revision of the GUM. A committee draft of the revision was circulated to member organizations of the Joint Committee for Guides in Metrology (JCGM) and all national metrology institutes in December 2014. The motivation for the proposed changes is given and reactions to the committee draft are summarized. Some of the contents of this paper are solely an expression by the authors and do not constitute an official statement by the JCGM.

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.

The evaluation of measurement uncertainty is often perceived by laboratory staff as complex and quite distant from daily practice. Nevertheless, standards such as ISO/IEC 17025, ISO 15189 and ISO 17034 that specify requirements for laboratories to enable them to demonstrate they operate competently, and are able to generate valid results, require that measurement uncertainty is evaluated and reported. In response to this need, a European project entitled “Advancing measurement uncertainty—comprehensive examples for key international standards” started in July 2018 that aims at developing examples that contribute to a better understanding of what is required and aid in implementing such evaluations in calibration, testing and research. The principle applied in the project is “learning by example”. Past experience with guidance documents such as EA 4/02 and the Eurachem/CITAC guide on measurement uncertainty has shown that for practitioners it is often easier to rework and adapt an existing example than to try to develop something from scratch. This introductory paper describes how the Monte Carlo method of GUM (Guide to the expression of Uncertainty in Measurement) Supplement 1 can be implemented in R, an environment for mathematical and statistical computing. An implementation of the law of propagation of uncertainty is also presented in the same environment, taking advantage of the possibility of evaluating the partial derivatives numerically, so that these do not need to be derived by analytic differentiation. The implementations are shown for the computation of the molar mass of phenol from standard atomic masses and the well-known mass calibration example from EA 4/02.

The main motivation for this research is the growing awareness of the impact of climate change and the increasing relevance of the United Nations Sustainable Development Goals, aiming to contribute to the measurement of quantities like precipitation and rate of rainfall. This knowledge is widely used in hydrology, climatology and meteorology, providing data and information applied in modelling, pattern definition and recognition, and forecasting. This work is concerned with estimating the average areal rainfall in a stipulated region from rainfall intensity observations made at measurement stations within that region. It focuses on three straightforward estimation approaches: the arithmetic mean method, the Thiessen polygon method and the isohyetal method. The evaluation of the associated measurement uncertainty, for which the law of propagation of uncertainty and a Monte Carlo method as described in guidance documents from the Joint Committee for Guides in Metrology are applied, is the main consideration. The approaches described may be readily applied by practitioners. A comparison of results from applying these methods to a simple example is made. Such results are required for conformity assessment and support in urban management and water resources management worldwide.