Sensitivity coefficients: how input uncertainties reach the result
A sensitivity coefficient converts an input's uncertainty into its effect on the output. For a direct temperature comparison it is 1; for derived quantities it comes from the model.
The GUM's law of propagation of uncertainty multiplies each input's standard uncertainty by a sensitivity coefficient — the partial derivative of the measurement model with respect to that input — before combining. The coefficient answers: if this input moves by one unit, how much does the result move?
Examples
- Correction = reference − indicated: both coefficients are ±1 in temperature units.
- A resistance thermometer: converting an uncertainty in ohms to kelvin needs the sensor's sensitivity, about 0.39 Ω/K for a Pt100 near 0 °C, so c ≈ 2.6 K/Ω.
- Relative humidity from a temperature error: the coefficient can be several %rh per kelvin near saturation.
Writing the measurement model down explicitly is the step most budgets skip — and the step that reveals the coefficients.
Frequently asked questions
- Can a sensitivity coefficient be estimated experimentally?
- Yes: change the input by a known amount and observe the change in the result. The GUM allows this when the model is not available analytically.
References
- [1]JCGM 100:2008 — Guide to the expression of uncertainty in measurement (GUM)
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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Combine Type A and Type B components per the GUM: divisors by distribution, sensitivity coefficients, u_c, effective degrees of freedom and U at k = 2.
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