An Excel budget for one measurement. List every source of uncertainty, choose its distribution, and the sheet converts each to a standard uncertainty, combines them by root sum of squares, expands with your coverage factor and compares the result with the tolerance.
New templates, charts and calculators for quality and manufacturing engineers, when they ship.
Quality engineers, metrologists and calibration technicians who must state how good a measurement is, for an accredited scope, a customer request, a conformity decision near a limit, or a gauge selection.
Tip: The % contribution column shows where to spend effort. Halving a source that contributes 3% changes almost nothing.
Header
Measurand, instrument, result units, coverage factor k and the ± tolerance
Sources
One row per source with its Type A or B evaluation, value, unit and distribution
Conversion
Divisor from the distribution, sensitivity coefficient and standard uncertainty
Contribution
Each source in result units, squared, and its share of the total
Result
Combined standard uncertainty, expanded uncertainty, largest contributor and TUR
Example Budget for Example Precision Co., a fictional machine shop, measuring a 25 mm steel shaft diameter (tolerance ±0.010 mm) with a 0.001 mm outside micrometer. All values are invented for illustration; the expansion coefficient is a typical value for steel.
| Source | Type | Value | Distribution | Divisor | cᵢ | cᵢ·u (mm) | Share |
|---|---|---|---|---|---|---|---|
| Repeatability (10 readings, 1 SD) | A | 0.0012 mm | Normal k=1 | 1 | 1 | 0.00120 | 48.5% |
| Calibration certificate | B | 0.002 mm | Normal k=2 | 2 | 1 | 0.00100 | 33.7% |
| Resolution (half of 0.001 mm) | B | 0.0005 mm | Rectangular | √3 | 1 | 0.00029 | 2.8% |
| Temperature deviation from 20 °C | B | 2 °C | Rectangular | √3 | 0.0002875 mm/°C | 0.00033 | 3.7% |
| Anvil flatness and parallelism | B | 0.001 mm | Rectangular | √3 | 1 | 0.00058 | 11.2% |
| Combined standard uncertainty uc | 0.00172 mm |
|---|---|
| Expanded uncertainty U (k = 2) | 0.0034 mm |
| Largest contributor | Repeatability |
| TUR | 2.9 : 1 |
| Field | What to enter | Example |
|---|---|---|
| Coverage factor k | Usually 2, for roughly 95% coverage when the result is close to normal. State it with every expanded uncertainty. | 2 |
| Tolerance (±) | Half the tolerance width, in result units. Used only for the TUR. | 0.010 |
| Type | A if you evaluated it statistically from your own readings; B if it comes from a certificate, a spec sheet or judgment. | B |
| Value | For Normal k=1, one standard deviation. For a certificate, the stated expanded uncertainty with its k. For rectangular, the half-width of the limits. | 0.0005 |
| Distribution | Normal k=2 or k=1, Rectangular, Triangular or U-shaped. The divisor follows from it. | Rectangular |
| Sensitivity coefficient cᵢ | How much the result changes per unit of this source. 1 when the value is already in result units. | 0.0002875 |
| Standard uncertainty (calculated) | Value ÷ divisor, in the source’s own units. | 0.000289 |
| % contribution (calculated) | This row’s squared contribution as a share of the total. Work on the biggest first. | 48.5% |
Standard uncertainty is one standard deviation. Expanded uncertainty multiplies the combined standard uncertainty by a coverage factor k, usually 2, to give an interval with a stated level of confidence.
A 4 : 1 ratio is a widely used target. Below that, measurement uncertainty takes up a large part of the tolerance and you need a decision rule, such as guard bands, for results near the limits.
If any value between the limits is equally likely, the standard deviation of that distribution is the half-width divided by √3.
No. A gauge R&R estimates repeatability and reproducibility from a study. An uncertainty budget combines every source, including calibration and environment. Gauge R&R results can feed the budget as Type A entries.
Yes, and then root sum of squares understates or overstates the result. This sheet assumes independent sources; correlated inputs need covariance terms from the GUM.
COPLAIN AI PLATFORM
Coplain writes the measurement procedure behind your budget as a clear work instruction, so the readings that feed it are taken the same way every time.
Generate yours automatically with Coplain →Related Tools & Templates