KEVOS® MAKEOS · Quality
Measurement Uncertainty Budget (Combined, Expanded, Test Ratio)
What is the total uncertainty of this length measurement, is it small enough against the tolerance, and what guard-banded limits should I accept to?
Uncertainty budget for a dimensional measurement: standard uncertainties from the gauge calibration certificate, the display resolution, repeatability, the Abbe error from an offset and tilt (as the Abbe error tool, taken as a rectangular limit), and the temperature uncertainty of the part, combined by root-sum-square, expanded with a coverage factor, the test uncertainty ratio against the tolerance band, and guard-banded acceptance limits inside the tolerance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tolerance band (total) | mm | Width of the tolerance band (upper minus lower limit). |
| Calibration uncertainty of the gauge (expanded, k = 2) | µm | Expanded uncertainty on the gauge’s calibration certificate (usually at k = 2). |
| Resolution of the gauge | µm | Smallest step of the gauge display. |
| Repeatability (standard deviation of repeat readings) | µm | Standard deviation of repeated readings on the same part (from a repeatability study). |
| Abbe offset | mm | Distance between the measuring line and the scale (Abbe offset). |
| Tilt of the moving element | arcsec | Tilt of the moving jaw or slide in arc-seconds. |
| Length measured | mm | Length being measured. |
| Part expansion coefficient | µm/m·K | Expansion coefficient of the part (the gauge is assumed corrected). |
| Uncertainty of the part temperature (±) | K | Plus-or-minus uncertainty of the part temperature from 20 °C after correction. |
| Coverage factor | Coverage factor for the expanded uncertainty (2 for about 95%). | |
| Least test uncertainty ratio | Least ratio of tolerance band to twice the expanded uncertainty you accept (often 4). |
Method and formulas
- Calibration u = U ÷ 2; resolution u = res ÷ √12; repeatability u = s.
- Abbe limit a = offset × tan(tilt) (as the Abbe error tool), u = a ÷ √3; temperature limit a = L α ΔT, u = a ÷ √3.
- Combined u_c = √Σu²; expanded U = k u_c; TUR = tolerance ÷ 2U; guard-banded acceptance = tolerance limits brought in by U.
- Example: U = 5.9696 µm (k = 2); the test uncertainty ratio is 4.1879; accept within ±19.03 µm of nominal.
Limitations
- Uncorrelated contributors; correlated ones (same gauge, same temperature) add linearly.
- Gauge temperature effects assumed corrected; add them if not.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a gauge is good enough for a tolerance
- Set guard-banded acceptance limits
- Find the biggest contributor to measurement error
Who it is for
- Quality engineers
- Metrologists
- Inspectors
What you get
- Standard uncertainty of each contributor
- Combined and expanded uncertainty
- Test uncertainty ratio and guard-banded limits
Interpreting the result
- The largest contributor dominates the root-sum-square: reduce it first.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 709–735. Topic reference; no source tables or recommended settings are reproduced.
- ISO/IEC Guide 98-3 Uncertainty of measurement (GUM)
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.
Open the Measurement Uncertainty Budget (Combined, Expanded, Test Ratio) calculator
