Gage R&R on a Critical Shaft Diameter
A supplier quality engineer is qualifying a digital caliper for a shaft outside diameter with specification 25.00 ± 0.05 mm. A Gage R&R study uses 10 production parts, 3 operators, and 2 trials per operator. Results: repeatability (EV) 0.018 mm, reproducibility (AV) 0.009 mm, part variation (PV) 0.032 mm, study %GRR = 20.1% of the 0.10 mm tolerance, number of distinct categories (ndc) = 2. Operator B reads consistently about 0.008 mm lower than operators A and C. Two parts have readings that straddle the specification limit depending on the operator. The caliper's calibration sticker is current and it reads zero on the reference block. The characteristic is flagged as critical on the drawing; the customer's supplier manual requires %GRR ≤ 10% for critical characteristics, with 10–30% allowed only by written deviation. Production has 4,000 shafts ready to ship and wants a decision today.
1. Interpret the study. Is this measurement system acceptable for the characteristic?
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It is not acceptable for a critical characteristic as it stands.
- %GRR = 20.1% of tolerance exceeds the customer's 10% limit. Measurement variation consumes about a fifth of the tolerance band, so decisions near the limits are unreliable.
- ndc = 2 means the gauge can barely separate parts into low and high groups; accepted practice wants at least 5, and 2 signals a system unable to discriminate within the tolerance.
- Repeatability (0.018) exceeds reproducibility (0.009), so the dominant problem is the gauge setup or part positioning - not simply operator-to-operator difference.
- Operator B's 0.008 mm bias is 8% of the tolerance, large enough to flip accept/reject calls. A current calibration sticker proves only that the caliper reads a reference block correctly; it says nothing about fixturing, technique, or discrimination on real parts.
2. How should the two borderline parts be dispositioned, and why not simply average the operators' readings?
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Re-measure them with a more capable system; do not average.
Averaging hides operator bias and artificially shrinks variation: the average of three biased readings is not a more accurate estimate of the true diameter, and the resulting uncertainty is unknown. If a part is genuinely near the limit, the honest question is whether it conforms, and that requires a gauge with demonstrated capability for the feature (for example, a micrometer or a gauge in a fixture with %GRR ≤ 10%, resolution appropriate to 0.001 mm).
Until then:
- Quarantine the two parts.
- Consider measurement uncertainty via a guard band: treat readings within the uncertainty band of the limit as indeterminate and decide by an independent method.
- Record the disposition and the gauge used for traceability.
Averaging nonconforming and conforming readings into a single number is a data-integrity problem, not a measurement solution.
3. What corrective actions and re-study criteria should be required before the 4,000 shafts are released?
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Improve the system, then demonstrate it.
Actions: add a fixture or part-holding device to control orientation; standardize measurement location and technique in a work instruction; investigate Operator B's bias (technique or gauge handling); verify resolution and grading of the caliper against the 0.10 mm tolerance; consider a different gauge type for the critical feature. Diagnose which of the five M's (method, man, machine, material, measurement) drives the 0.018 mm repeatability.
Re-study acceptance: %GRR ≤ 10% of tolerance, ndc ≥ 5, and no meaningful operator bias. If results land in 10–30%, obtain a written customer deviation and apply a documented guard band; do not self-approve.
Interim release of the 4,000 shafts: use the improved gauge for 100% verification, or obtain customer concession with the uncertainty disclosed. The $cost of a re-study is trivial against a shipped critical dimension that no gauge could reliably judge.