Measurement Uncertainty - Sensitivity Coefficients

Sensitivity Coefficients

Sensitivity coefficients ... describe how the estimate of would be influenced by small changes in the estimates ... of the input quantities ... . For the measurement model ..., the sensitivity coefficient equals the partial derivative of first order of with respect to evaluated at, etc. For a linear measurement model

with ... independent, a change in equal to would give a change in . This statement would generally be approximate for measurement models ... . The relative magnitudes of the terms are useful in assessing the respective contributions from the input quantities to the standard uncertainty associated with .

The standard uncertainty associated with the estimate of the output quantity is not given by the sum of the, but these terms combined in quadrature, namely by

which is known as the law of propagation of uncertainty.

When the input quantities contain dependencies, the above formula is augmented by terms containing covariances, which may increase or decrease .