A measurement uncertainty budget is a structured list of every significant source of uncertainty in a measurement, with each source converted to a standard uncertainty and then combined, following the Guide to the Expression of Uncertainty in Measurement (the GUM, ISO/IEC Guide 98-3 / JCGM 100), into a combined standard uncertainty and finally an expanded uncertainty at a stated coverage. It is the evidence behind any uncertainty value printed on a calibration certificate and a core requirement for ISO/IEC 17025 accredited laboratories. A budget makes the result defensible: it shows exactly which effects were considered, how each was quantified, and how they add up.
Start by stating the measurand — the specific quantity being measured — and writing the measurement model that relates it to the input quantities, y = f(x1, x2, ... xn). The model matters because it determines the sensitivity coefficients later: how strongly each input influences the result. For a simple comparison calibration the model may be the indication plus corrections for the reference, resolution, and environment; for a derived quantity it may involve several inputs combined by a formula. Getting the model right is what separates a real budget from a guess.
List every input that contributes uncertainty, then classify each evaluation as Type A or Type B. Type A uncertainty is evaluated from repeated observations using statistics — typically the experimental standard deviation of the mean of repeated readings. Type B uncertainty is evaluated by other means: the reference standard's calibration certificate, the resolution of the device under test, manufacturer specifications, drift, and environmental effects such as temperature. The Type A/Type B distinction is about the method of evaluation, not about the nature of the source.
Each source is expressed as a standard uncertainty (one standard deviation). Type A components use s divided by the square root of n. Type B components are derived from the assumed distribution: a quantity stated with a coverage factor on a certificate is divided by that factor; a rectangular (uniform) distribution — common for resolution and many specification limits — has its half-width divided by the square root of 3; a triangular distribution divides the half-width by the square root of 6. Each standard uncertainty is then multiplied by its sensitivity coefficient, the partial derivative of the model with respect to that input.
For uncorrelated inputs, the combined standard uncertainty is the root-sum-square of the weighted standard uncertainties: the square root of the sum of (sensitivity coefficient times standard uncertainty) squared across all sources. Correlated inputs require covariance terms. To choose the right coverage factor, compute the effective degrees of freedom using the Welch-Satterthwaite formula, which blends the degrees of freedom of the Type A components (limited by how many repeats you took) with the effectively infinite degrees of freedom usually assigned to well-characterized Type B components.
Multiply the combined standard uncertainty by a coverage factor k to obtain the expanded uncertainty U. For an approximately normal result with large effective degrees of freedom, k = 2 gives roughly 95% coverage; for small effective degrees of freedom, take k from the Student t-distribution at the desired confidence. Report the result as the measured value plus or minus U, stating the coverage factor and the approximate level of confidence — for example, U with k = 2 for about 95%. That statement, backed by the budget, is what an accreditation assessor expects to see.
CalibrationOS includes a GUM-compliant uncertainty module that captures Type A and Type B components, applies the correct divisor for each distribution, holds sensitivity coefficients from the measurement model, computes the combined standard uncertainty and effective degrees of freedom by Welch-Satterthwaite, and prints the expanded uncertainty directly onto the calibration certificate. A free uncertainty calculator is available for one-off budgets without an account.
It is a structured list of every significant uncertainty source in a measurement, each converted to a standard uncertainty and combined per the GUM (ISO/IEC Guide 98-3) into a combined standard uncertainty and an expanded uncertainty at a stated coverage. It is the evidence behind any uncertainty stated on a calibration certificate.
Type A uncertainty is evaluated from repeated observations using statistics (the standard deviation of the mean). Type B uncertainty is evaluated by other means — calibration certificates, resolution, specifications, environmental data — using assumed distributions. The distinction is about the evaluation method, not the source.
For a rectangular (uniform) distribution, divide the half-width by the square root of 3 to obtain the standard uncertainty. A triangular distribution uses the square root of 6, and a value stated with a coverage factor is divided by that factor.
It estimates the effective degrees of freedom of the combined standard uncertainty by blending the degrees of freedom of the Type A and Type B components. The effective degrees of freedom then determine the coverage factor k used to compute the expanded uncertainty.
For an approximately normal result with large effective degrees of freedom, k = 2 gives roughly 95% coverage. For small effective degrees of freedom, take k from the Student t-distribution at the desired confidence level rather than defaulting to 2.
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