A Gage R&R Run on One Hour of Production
Vega Machine measures a shaft diameter to a tolerance of 25.00 ± 0.10 mm using a digital micrometer with 0.001 mm resolution. A crossed Gage R&R is run with 2 operators, 10 parts, 3 trials. Results: %GRR (study variation) = 32%, number of distinct categories = 3. The ten parts were pulled from a single hour of production on one machine. In the same work cell, plating appearance is checked pass/fail by 3 inspectors on 50 parts; overall agreement between inspectors is 78% and kappa is 0.41. The team lead wants to accept the Gage R&R - "the gage reads to 0.001 mm and the operators were trained last year" - and move straight to capability.
1. Is the conclusion "this measurement system is unacceptable" reliable? What should the team do before running capability?
Read the worked answer
The number says unacceptable; the study design says don't trust the number yet.
- On its face: %GRR of 32% of study variation exceeds the 30% threshold, and ndc = 3 is below the recommended minimum of 5. A system with 3 categories cannot resolve the process variation well enough to track improvement.
- But the study violates a core assumption: parts must span the actual process variation. Ten parts from one hour on one machine represent a narrow slice, so part-to-part variation is understated. Because %GRR is GRR variation divided by total study variation, shrinking part variation inflates %GRR and depresses ndc. The lead's instinct is not entirely wrong - but neither is the 32% conclusion established.
- Resolution is not the problem: 0.001 mm is 1/200 of the 0.20 mm tolerance, far finer than the 1/10-of-tolerance rule. The lead's argument fails because resolution was never the issue; equipment, fixturing, method, or operator technique is.
Do next:
- Re-select 10 parts spanning the full expected process range (across machines, shifts, and lots), not one hour.
- Decide the yardstick first: for a tolerance-based accept/reject decision, report %GRR against tolerance (P/T ratio) as well as %study variation.
- Standardize the method - fixture, measurement location, clamping torque, part temperature, reading convention - then randomize part order and blind the operators to part identity.
- Re-run and examine the variation split: if repeatability (equipment) dominates, fix gage/fixture; if reproducibility (operator) dominates, fix training and method.
Do not compute capability on this data. A 32% measurement system consumes a third of the observed variation and will make Cpk look worse - or better - than reality.
2. Interpret the attribute agreement study and state what it means for the project.
Read the worked answer
78% agreement sounds acceptable but is not evidence of a usable inspection system; kappa 0.41 is the real signal.
- Kappa corrects for agreement expected by chance. 0.41 sits in the "moderate" band and well below the ~0.70–0.90 usually required before an attribute system is used for decisions. The 78% figure is inflated whenever defects are rare or common, because inspectors agree simply by saying "pass" most of the time.
- Break it down before acting. Within-inspector agreement (repeatability: does each inspector agree with themselves across trials?) versus between-inspector agreement (reproducibility: is one inspector systematically stricter?). Also compute, against a known standard: effectiveness (overall correct calls), miss rate (bad parts accepted), and false-alarm rate (good parts rejected). The two error types have asymmetric consequences - escaped defects reach the customer, false alarms generate scrap and rework.
Project implications:
- Plating appearance cannot serve as a reliable Y until the system is fixed. Any defect rate the team measures now is partly inspector drift.
- If a before/after comparison uses different inspectors, a change in the metric may reflect a change in inspectors, not the process.
- Fixes: written acceptance criteria with limit samples/visual standards, controlled lighting and viewing distance, inspector training and qualification, periodic re-audit; or eliminate the judgment with a gage or automated vision check. Then re-run the study and require kappa ≥ 0.70 before baseline collection.