Two inputs that share a reference or correction can be related. An uncertainty budget must account for that relationship.
Independence is an assumption
First-order propagation includes sensitivity coefficients and, where relevant, covariance between inputs. The familiar root-sum-squares simplification requires the appropriate independence or zero-covariance basis. A shared calibration effect should trigger a review of dependence rather than automatic duplication as unrelated entries.
An invented subtraction model
Let a hypothetical result be X−Y and let both readings contain exactly the same additive offset b. Algebra gives (X+b)−(Y+b)=X−Y: that particular shared effect cancels. Treating it as two independent offsets would miss the model’s structure.
This does not mean every uncertainty in a gross-minus-tare measurement cancels. Repeatability, sensitivity, loading conditions and time-dependent effects can differ. The example isolates a fully shared additive contribution; it is not a complete uncertainty calculation or an HM weighing claim.
Review common origins
Mark which inputs use the same reference, calibration model or environmental observation. Ask the analyst to determine the relevant covariance and sign through the measurement function. Retain the assumptions and avoid claiming cancellation for contributions that merely have similar numerical sizes.
Primary references: NIST measurement handbook, NIST measurement handbook.
Measurement review worksheet
This blank worksheet is for your own project. It contains no H M machine trial result.
| Question | Evidence to retain |
|---|---|
| Which inputs share information? | Reference and correction identities |
| How do they enter the model? | Signs and sensitivity coefficients |
| Is the dependence quantified? | Covariance or justified assumption |
Customer Questions
Can equal uncertainty numbers prove correlation?
No. The physical and information relationship matters.
Do all subtraction uncertainties cancel?
No. Only the applicable shared effects can cancel in the model.
Is ordinary root-sum-squares always sufficient?
No. Dependence must be evaluated when relevant.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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