The rule that the variance of the output equals the sum of each input's squared sensitivity coefficient times its squared standard uncertainty, plus, for every correlated pair, twice the product of their two sensitivity coefficients and their covariance. It rests on a first-order Taylor expansion of the measurement model, so it works well when the model is close to linear over the span of the input uncertainties. When the model is strongly nonlinear or one non-normal input dominates, labs switch to the Monte Carlo method.
The law of propagation falls apart here because the denominator sits near zero, run it through Monte Carlo instead.
Also heard as
- LPU
- uncertainty propagation
- GUM uncertainty framework
Related terms
Combined standard uncertainty
The total standard uncertainty of a result, found by combining all input uncertainties through the measurement model.
Sensitivity coefficient
The factor that converts an input's uncertainty into its effect on the output, the partial derivative of the model.
Correlation
A statistical link between two input quantities, so their errors move together and cannot be combined as independent.
Monte Carlo method
Propagating uncertainty by random sampling of input distributions through the measurement model, many thousands of times.
RSS
Root sum of squares, combining independent uncertainty contributions by squaring, adding and taking the square root.