A coefficient c_i describing how much the output changes per unit change in an input, equal to the partial derivative of the measurement model with respect to that input. It converts each input's standard uncertainty into output units, so a temperature uncertainty in °C becomes a length uncertainty in µm. For a 100 mm steel block with an expansion coefficient of 11.5 × 10^-6 per °C, the coefficient on temperature is about 1.15 µm per °C.
Sensitivity coefficient on temperature is 1.15 microns per degree, so a 0.2 degree uncertainty is worth 0.23 microns.
When a derivative is ugly, nudge the input by its uncertainty in the spreadsheet and watch the output; that numerical coefficient is good enough for most budgets.
Also heard as
- c_i
Do not mix it up with
- Coverage factor: The coverage factor expands the final combined uncertainty; sensitivity coefficients convert individual inputs into output units before combining.
Related terms
Measurement model
The equation linking the output quantity you report to all the input quantities that feed into it.
Law of propagation of uncertainty
The first-order formula that combines input standard uncertainties, weighted by sensitivity coefficients, into the output uncertainty.
Combined standard uncertainty
The total standard uncertainty of a result, found by combining all input uncertainties through the measurement model.
Uncertainty budget
A table listing every uncertainty source in a measurement with its size, distribution, divisor and contribution to the total.