The Guide to the Expression of Uncertainty in Measurement — universally shortened to GUM — is the JCGM 100:2008 framework that underlies essentially every defensible uncertainty claim in industrial measurement. Its core idea is simple even though the notation can look intimidating: identify every input quantity that feeds into a measurement result, assign each one a standard uncertainty, and combine them according to how the measurement equation actually depends on each input.
In practice, that means starting with the measurement equation itself — for a flow meter, something relating the raw signal to a volumetric or mass flow rate through calibration coefficients, fluid properties, and geometric factors. Each term in that equation is a candidate uncertainty contributor. Some are evaluated statistically from repeated observations (Type A); others come from calibration certificates, manufacturer specifications, or engineering judgment (Type B). GUM treats both the same way once they're expressed as standard uncertainties.
The combination step uses the law of propagation of uncertainty: each input's standard uncertainty is scaled by its sensitivity coefficient — how much the output changes per unit change in that input — and the scaled values are combined in quadrature (assuming independence) to produce the combined standard uncertainty, uc(y). Multiply by a coverage factor k, typically 2, to get the expanded uncertainty U — the number that actually gets reported and defended.
The practical payoff of doing this properly, rather than applying a flat percentage as a stand-in, is that the budget tells you exactly where the uncertainty is coming from. On a multiphase meter, that's often not the flow computer's arithmetic — it's phase-fraction sensitivity interacting with fluid behavior that shifts with pressure and temperature. Understanding that sensitivity requires pairing the GUM propagation with a real thermodynamic model of the fluid, not just a generic error bar.
That combination — rigorous GUM propagation informed by thermodynamic modeling of how the fluid actually behaves — is what lets an uncertainty budget hold up under audit instead of just looking authoritative on paper.