Gage R&R on a Safety Characteristic Before PPAP
A Tier-1 brake supplier must certify Cpk ≥ 1.33 on a critical bore diameter (10.00 ± 0.10 mm) before PPAP submission in three weeks. Because the measurement is effectively destructive, a nested Gage R&R was run: 30 parts, 3 operators, 2 trials per part, with part-to-part σ = 0.040 mm, repeatability σ = 0.008 mm and operator σ = 0.005 mm. The process, measured on 200 parts, shows mean 10.004 mm and observed σ = 0.032 mm, giving an observed Cpk of 1.00. The quality engineer argues the study proves the gage is fine because %GRR against tolerance is 'only 28%' and the process 'just needs centering'. The customer requires that no out-of-spec bore is shipped, this is the only gage available, and a fixtured air gage has a 12-week lead time. The sponsor wants you to sign the PPAP today and open a centering kaizen tomorrow.
1. Calculate %GRR against tolerance, %GRR against study variation and ndc. Is this measurement system acceptable for the two decisions it will be used for: estimating capability and making accept/reject calls on individual parts?
Read the worked answer
GRR standard deviation σ_GRR = √(0.008² + 0.005²) = √(64 + 25) × 10⁻⁶ = 0.00943 mm; 6σ_GRR = 0.0566 mm.
Against tolerance (0.20 mm): 0.0566 / 0.20 = 28.3% - in the 10–30% 'marginal' band, not 'fine'.
Against study variation: PV = 6 × 0.040 = 0.240; total study variation = √(0.240² + 0.0566²) = 0.2466; %GRR = 23.0%.
ndc = 1.41 × (0.240 / 0.0566) = 5.98 → 5 (acceptable on discrimination alone).
Two different questions, two different verdicts.
- For capability estimation the gage is tolerable: measurement error inflates observed σ only slightly. True process σ = √(0.032² − 0.00943²) = 0.0306 mm, so true Cpk = 0.096 / (3 × 0.0306) = 1.05, not 1.00. The gage is not the reason the process fails.
- For accept/reject on individual parts it is not tolerable on a safety characteristic. A bore at 10.095 mm is inside the limit by 0.005 mm, only 0.53 σ_GRR, so roughly 30% of readings would call it scrap; symmetrically, a 10.105 mm part is accepted about 30% of the time.
Conclusion: the numbers must be split by purpose in the report, not summarised as '28%, acceptable'.
2. The quality engineer proposes centering the process as the complete fix. Quantify the best Cpk that centering alone can deliver and state what additional variation reduction is required.
Read the worked answer
Centering alone: the widest half-tolerance available is 0.10 mm (mean moved to 10.00). With true σ = 0.0306 mm:
Cpk = 0.10 / (3 × 0.0306) = 0.10 / 0.0918 = 1.09
Centering buys 1.00 → 1.09. It does not reach 1.33 and cannot, no matter how precisely the mean is placed.
Variation reduction required: with a perfectly centred mean,
σ_required = 0.10 / (3 × 1.33) = 0.0251 mm
That is a reduction from 0.0306 to 0.0251, i.e. about 18% in standard deviation (roughly 33% in variance). Centering and variation reduction are both necessary; neither is sufficient, and the centering kaizen alone will land at Cpk ≈ 1.09 and fail the next PPAP review.
Practical read-across: if the team centres first and then reduces σ by 18%, the gain is additive in the numerator and denominator respectively - re-run the capability study only after both, with the same nested design so the comparison is like-for-like.
3. What do you do about the PPAP and the ship/no-ship decision, given the 12-week gage lead time? Recommend a position you can defend to the customer.
Read the worked answer
Do not sign the PPAP. Cpk is 1.00 observed / 1.05 true; the requirement is 1.33 and the process is roughly 18% short on σ plus off-centre. Signing converts a known capability gap into a customer-facing escape risk on a safety characteristic.
Separate the two gage decisions:
- Capability: current gage is adequate; proceed with centering and variation-reduction work now - the gage is not gating this.
- Ship decision: 28% GRR without guardbanding gives ~30% misclassification at the limit. Interim controls: 100% inspection using guardbanded limits (accept only 9.905–10.095 mm, accepting the known yield loss) or a verified second method, plus a documented two-of-three retest rule for parts near the limit. Both are containment, not capability.
Commercial route: order the fixtured air gage immediately so it lands with the capability work; request a time-limited deviation or interim PPAP approval supported by the guardbanded containment data, the containment sample size and the containment escape rate. Show the sponsor the arithmetic: a 12-week gage lead time does not justify a 3-week false release.
Escalate one sentence: the gage is not the cause of the Cpk failure, but it is the reason a 100%-inspection containment cannot be fully trusted on its own.