Invited Article: Concepts and tools for the evaluation of measurement uncertainty

Measurements involve comparisons of measured values with reference values traceable to measurement standards and are made to support decision-making. While the conventional definition of measurement focuses on quantitative properties (including ordinal properties), we adopt a broader view and entertain the possibility of regarding qualitative properties also as legitimate targets for measurement. A measurement result comprises the following: (i) a value that has been assigned to a property based on information derived from an experiment or computation, possibly also including information derived from other sources, and (ii) a characterization of the margin of doubt that remains about the true value of the property after taking that information into account. Measurement uncertainty is this margin of doubt, and it can be characterized by a probability distribution on the set of possible values of the property of interest. Mathematical or statistical models enable the quantification of measurement uncertainty and underlie the varied collection of methods available for uncertainty evaluation. Some of these methods have been in use for over a century (for example, as introduced by Gauss for the combination of mutually inconsistent observations or for the propagation of "errors"), while others are of fairly recent vintage (for example, Monte Carlo methods including those that involve Markov Chain Monte Carlo sampling). This contribution reviews the concepts, models, methods, and computations that are commonly used for the evaluation of measurement uncertainty, and illustrates their application in realistic examples drawn from multiple areas of science and technology, aiming to serve as a general, widely accessible reference.