KEVOS® MAKEOS · Quality
Independent Dimensional Uncertainty Budget
How do these independent measurement contributions combine?
Combine repeatability, calibration, resolution and one bounded dimensional contribution into standard and expanded uncertainty.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Reported result | choice | Choose a sample mean or one individual observation. |
| Sample standard deviation | mm | Sample standard deviation from independent repeated measurements under the relevant conditions. |
| Independent observations in the sample | observations | Observations used to estimate the standard deviation; also the averaging count in mean mode. |
| Calibration expanded uncertainty | mm | Expanded uncertainty from the calibration certificate in millimetres at the relevant point. |
| Calibration coverage factor | × | Coverage factor stated on that certificate; do not assume every certificate uses 2. |
| Digital resolution increment | mm | Smallest digital increment, modelled as independent rounding over ±half an increment. |
| Other rectangular half-width | mm | Half-width of one independent rectangular contribution, already converted to equivalent dimensional error in millimetres. |
| Output coverage factor | × | Coverage factor justified by the uncertainty procedure and effective degrees of freedom. |
Method and formulas
- Repeatability u = s/√n for a mean or s for one observation. Calibration u = certificate expanded uncertainty divided by its coverage factor.
- Resolution u = increment/√12. Other rectangular u = half-width/√3. Combined u is the square root of the sum of the four squared contributions. Expanded U = k × combined u.
- Example: s = 0.01 mm, n = 10, calibration U = 0.004 mm at k = 2, resolution 0.01 mm and half-width 0.003 mm gives combined u ≈ 0.005033223 mm and U ≈ 0.010066446 mm at output k = 2.
Limitations
- All contributions must be in millimetres with unit sensitivity coefficients. Covariances and general propagation coefficients are not modelled.
- Do not count resolution twice if another contribution already includes it. Resolution is not reduced by averaging here.
- k = 2 does not automatically establish 95% coverage. Small samples, distributions, bias corrections and degrees of freedom need review.
- An all-zero budget is rejected. No conformity decision or accredited certificate is issued.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- measurement budget
- repeatability
- coverage factor
Who it is for
- Metrology teams
- Quality engineers
- Inspectors
What you get
- Combined standard uncertainty
- Expanded uncertainty
- Component standard uncertainties and variance shares
Interpreting the result
- Document the measurement model and independence evidence before using the combined result.
- Variance shares help prioritise improvement. Record the quantity, unit, coverage factor and uncertainty together.
References
- NIST TN 1297: Law of propagation of uncertainty — https://www.nist.gov/pml/nist-technical-note-1297/nist-tn-1297-appendix-law-propagation-uncertainty
- NIST TN 1297: Reporting uncertainty — https://www.nist.gov/pml/nist-technical-note-1297/nist-tn-1297-7-reporting-uncertainty
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 709–738. Topic reference; implementation and examples are original, and no source tables are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
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