UncertaintyBudgets

An uncertainty budget is a structured accounting of all significant sources of uncertainty that affect a measurement result. Its purpose is to quantify the total measurement uncertainty in a transparent and traceable way, in line with established metrology guidance such as the Guide to the Expression of Uncertainty in Measurement (GUM).

A budget typically lists the contributors to uncertainty and assigns a standard uncertainty to each source. Sources can include instrument precision, environmental conditions, calibration drift, method or model limitations, sample characteristics, data processing, and numerical rounding. Uncertainties are often categorized as Type A (evaluated by statistical analysis of repeated observations) or Type B (evaluated by other information such as prior data, manufacturer specifications, or scientific judgment). When sources are independent, their contributions can be combined by the root-sum-of-squares method; correlations require covariances or a correlation matrix.

The calculation proceeds by estimating the standard uncertainty for each source, combining them to obtain the combined standard uncertainty uc, and then applying a coverage factor k to obtain the expanded uncertainty U = k·uc. A common choice is k = 2, which corresponds to approximately a 95% confidence level for a normal distribution. Monte Carlo methods are sometimes used for nonlinear relationships or nonnormal distributions. If correlations exist, those covariances must be included in the combination.

Reporting typically expresses the result as x ± U, where x is the best estimate and U is the expanded uncertainty, along with a description of the main contributing sources and, if applicable, the method used to derive the budget. Uncertainty budgets support traceability, comparability of measurements, and quality assurance in laboratories and research.