How to check a calibration point by point
For each point on the certificate:
Error: E = instrument reading − nominal value
Conservative rule: pass if |E| + U ≤ MPE
Simple rule: pass if |E| ≤ MPE
MPE/U ratio (test uncertainty ratio, TUR): how many times the uncertainty fits in the MPE. Ask for 3 or more
The instrument passes only when every point passes. The MPE can be a fixed value, a percentage of reading (MPE × |nominal| ÷ 100) or a percentage of span (MPE × (end − start) ÷ 100).
The conservative rule uses the uncertainty as a guard band: the real acceptance limit becomes MPE − U. This is the idea behind ILAC-G8, the guideline on decision rules: when the result plus its uncertainty still fits the limit, you can state conformity. When the error fits the MPE but the error plus the uncertainty does not, the point is in the zone of doubt: you can say neither that it is in nor that it is out. ISO/IEC 17025 clause 7.8.6 requires the decision rule to be agreed beforehand whenever the lab states conformity.
Worked example
The values preloaded in the calculator are a 0 to 150 mm caliper, 0.01 mm resolution, with an MPE of ±0.03 mm and a calibration uncertainty of 0.01 mm at every point:
| Nominal (mm) | Reading | Error E | |E| + U | Margin | Status |
|---|---|---|---|---|---|
| 0 | 0.00 | 0.00 | 0.01 | +0.02 | Pass |
| 25 | 25.01 | +0.01 | 0.02 | +0.01 | Pass |
| 50 | 50.01 | +0.01 | 0.02 | +0.01 | Pass |
| 100 | 100.02 | +0.02 | 0.03 | 0.00 | Pass |
| 150 | 150.03 | +0.03 | 0.04 | −0.01 | Doubt |
- At 100 mm, 0.02 + 0.01 = 0.03, exactly the MPE. It passes with no margin at all
- At 150 mm, the 0.03 mm error fits the MPE, but 0.03 + 0.01 = 0.04 does not
- The MPE/U ratio is 0.03 ÷ 0.01 = 3 at every point, right at the usual minimum
- Result: 4 of 5 points pass, the instrument fails under the conservative rule
Under the simple rule (|E| ≤ MPE) the same caliper would pass. This is exactly the case the conservative rule is for: given the lab’s uncertainty, nobody can guarantee the error at 150 mm is within ±0.03 mm.
How to read the result
- Pass at every point: the instrument can go back into use until its next calibration.
- Fail or doubt: the instrument should not measure parts until it is adjusted, repaired or downgraded to a use with a wider tolerance. And what it measured since its last good calibration needs a review: are the parts accepted near the limit still good?
- Margin is what is left of the MPE at that point. Small margins at several points mean the instrument is close to the limit and may fail next time. Consider a shorter calibration interval.
- An MPE/U ratio below 3 means the lab’s uncertainty is too large for the MPE you chose. Ask for a calibration with a smaller uncertainty or review the MPE. To see where an uncertainty comes from and how it is built, use the measurement uncertainty calculator.
Who sets the MPE
The MPE is the company’s decision, not the lab’s. It comes from the tolerance of what the instrument measures: a common rule is an MPE between 1/3 and 1/10 of the tolerance of the tightest characteristic. An MPE that is too loose lets through an instrument that will accept bad parts. One that is too tight fails instruments that would do the job. To see whether the process fits the tolerance, the Cp and Cpk calculator and the control chart complete the picture.
Common mistakes
- Comparing only the error with the MPE and ignoring the uncertainty. A point can be out without you seeing it.
- Taking the manufacturer’s specification as the MPE without thinking about the use. It is a starting point. What matters is the tolerance of the parts the instrument checks.
- Ignoring the sign of the error. The rule uses |E|, but the sign tells you whether the instrument reads high or low, which helps with adjustment.
- Passing on the average of the points. One failed point is enough to fail the instrument over the range it is used in.
- Not reviewing what was measured with an instrument that came back failed. A failed calibration is where the analysis starts, not where it ends.