measurementUncertainty

Measurement uncertainty is a parameter that characterizes the doubt about a measurement result. It defines a range within which the true value of the measurand is believed to lie with a stated level of confidence, considering all known sources of variation in the measurement process. It is not the error of a single measurement, but a quantitative statement about the possible deviations of the true value from the reported value.

Uncertainty components arise from random effects (repeatability) and systematic effects (bias). They are evaluated by Type A methods (statistical analysis of repeated measurements) and Type B methods (information from calibration data, manufacturer specifications, or expert judgment).

A measurement model relates the measurand to observable quantities through a function y = f(x1, x2, ... xn). The combined standard uncertainty u_c is obtained by propagating the component uncertainties through this model, using appropriate formulas and covariances when present. Expanded uncertainty U = k·u_c provides an interval with a stated confidence level, with k typically 2 for approximately 95% coverage.

Uncertainty values are reported with the measurement result, including the unit, the method, and the coverage factor. Results should be traceable to SI units via calibration with recognized reference standards. The distinction between measurement uncertainty and error is important; uncertainty describes doubt about the result rather than a fixed offset.

Examples include length measurements with rulers, mass with balances, or temperature using thermometers. Understanding uncertainty supports comparability, quality control, and decision-making in science and industry.