Uncertainty in measurements by counting

Counting is at the base of many high-level measurements, such as, for example, frequency measurements. In some instances the measurand itself is a number of events, such as spontaneous decays in activity measurements, or objects, such as colonies of bacteria in microbiology. Countings also play a fundamental role in everyday life. In any case, a counting is a measurement. A measurement result, according to its present definition, as given in the ‘International Vocabulary of Metrology—Basic and general concepts and associated terms (VIM)’, must include a specification concerning the estimated uncertainty. As concerns measurements by counting, this specification is not easy to encompass in the well-known framework of the ‘Guide to the Expression of Uncertainty in Measurement’, known as GUM, in which there is no guidance on the topic. Furthermore, the issue of uncertainty in countings has received little or no attention in the literature, so that it is commonly accepted that this category of measurements constitutes an exception in which the concept of uncertainty is not applicable, or, alternatively, that results of measurements by counting have essentially no uncertainty. In this paper we propose a general model for measurements by counting which allows an uncertainty evaluation compliant with the general framework of the GUM.