A Micrometer That Cannot Tell Good From Bad
A shaft diameter is specified 25.000 ± 0.020 mm and is checked on the shop floor with a digital micrometer. A gauge R&R study (10 parts, 3 operators, 3 trials) gives repeatability (EV) of 0.003 mm and reproducibility (AV) of 0.005 mm; the process sigma of the shaft is 0.012 mm. The micrometer's annual calibration certificate, issued at 20 °C under laboratory conditions, reports an as-found error of +0.017 mm at 25 mm with an expanded uncertainty U = 0.004 mm (k = 2). The calibration interval has just expired and production ran for three weeks on the expired sticker. The quality manager must decide whether the gauge is fit for the inspection task and what to do about parts measured during those three weeks.
1. Compute the GRR as a percentage of tolerance and the number of distinct categories. Is the gauge acceptable for this characteristic?
Read the worked answer
Combined GRR
sigma_GRR = sqrt(EV^2 + AV^2) = sqrt(0.003^2 + 0.005^2) = sqrt(9e-6 + 25e-6) = 0.00583 mm
- %GRR of tolerance = 6 × 0.00583 / 0.040 = 0.0350 / 0.040 = 87.5%
- %GRR of process variation = 0.0350 / (6 × 0.012) = 0.0350 / 0.072 = 48.6%
- ndc = 1.41 × (sigma_process / sigma_GRR) = 1.41 × (0.012 / 0.00583) = 2.9 → 2 categories
Verdict: unacceptable. Against the usual 10% / 30% bands, 87.5% of tolerance is far beyond any conditional-use threshold, and 2 distinct categories (5 needed) means the gauge can barely separate two parts. For a ±0.020 mm characteristic the measurement system alone would consume most of the tolerance.
Where the problem is: AV (0.005) exceeds EV (0.003), so reproducibility dominates. The instrument's repeatability is not the main issue; the operators, the fixture, the measuring force or the part handling are. Before scrapping the gauge, re-run the study with a fixed fixture and a written measurement procedure, and check whether one operator is an outlier. Note also that 6·sigma_GRR (0.035) is nearly the full 0.040 tolerance; no product decision should be taken with this gauge until it is improved or replaced.
2. The certificate gives an as-found error of +0.017 mm with U = 0.004 mm (k = 2). Using ISO 14253-1 with a guard band equal to U, is the micrometer conforming to ±0.020 mm? How would the answer differ under simple acceptance?
Read the worked answer
Guard-banded (ISO 14253-1, prove-conformance decision rule)
- Tolerance zone: ±0.020 mm
- Guard band w = U = 0.004 mm
- Acceptance zone: ±(0.020 − 0.004) = ±0.016 mm
- Observed error 0.017 mm > 0.016 mm
Result: conformity cannot be declared. The error lies in the guard band, so the correct statement is that the gauge is either nonconforming or indeterminate - under the ISO 14253-1 default the burden of proof is on the party claiming conformity, so it is treated as not proven conforming and must be investigated, adjusted and re-verified.
Simple acceptance (shared risk)
- Acceptance limit remains ±0.020 mm, and 0.017 mm would pass.
That is only legitimate if the customer and supplier have agreed in writing to share the risk, and if the 0.017 mm error is small relative to the tolerance. Here it is not: 85% of the tolerance limit. Even after adjustment, a gauge that was 0.017 mm out contributes a systematic offset to every reading taken since the previous calibration, and a 0.004 mm uncertainty combined with a 0.00583 mm GRR shows the shop-floor measurement is the dominant error term anyway.
3. What is the disposition of the product measured during the three weeks on the expired calibration?
Read the worked answer
Do not adjust the gauge and move on. Treat this as a measurement-system nonconformity with product impact.
Direction of the error. Reading = true + 0.017, so true = reading − 0.017. The gauge read high, meaning the parts were smaller than recorded:
- A part read at 24.980 (the LSL) was truly 24.963 mm, which is out of tolerance on the low side.
- Parts read between 24.980 and about 24.997 may have a true diameter below the LSL.
- Conversely, parts rejected for reading above 25.020 were actually within tolerance - good product may have been scrapped.
Containment steps
- Quarantine everything produced and accepted during the three weeks; identify it by date code and gauge serial number.
- Bound the drift from the previous certificate's as-left value and this as-found value. If the gauge was near zero at the last calibration, the bias grew over the interval and the early part of the window is less affected; if the drift rate is unknown, assume the full 0.017 mm for the entire window.
- Re-measure 100% of the affected population with a verified gauge, or at minimum all parts whose recorded reading falls in the affected band, and apply a documented risk assessment to the remainder.
- If some product has shipped, issue a customer notification; a 0.017 mm low-side error on a mating shaft is a fit-and-function risk, not a paperwork risk.
- Check why an overdue gauge was in service at all - that is a calibration-system failure, and it belongs in the corrective action, not in this disposition.