A Gauge R&R That Invalidates a Submitted Cpk

What the numbers mean %GRR of 32% of tolerance says the combined repeatability and reproducibility spread consumes about one third of the 20 µm tolerance band. AIAG MSA treats below 10% as acceptable, 10–30% as conditionally acceptable with documented justification, and above 30% as unacceptable. ndc = 3 means the system can only split the process spread into about three categories, against a minimum of 5. In plain terms, the gauge cannot reliably tell a 12.005 mm part from a 12.008 mm part - and both are only halfway to the limit.

Does this invalidate the Cpk? Not in the direction people usually assume. Observed variation decomposes as σ²obs = σ²true + σ²MSA, so correcting for measurement error makes the true Cpk larger, not smaller:

• σobs = 0.020 / (6 × 1.67) = 2.0 µm
• 6σMSA = 0.32 × 0.020 = 6.4 µm → σMSA = 1.07 µm
• σtrue = √(2.0² − 1.07²) = 1.69 µm → Cpk_true ≈ 1.97

So the process is probably better than reported. Nevertheless the statement 'Cpk = 1.67, therefore the process is capable' cannot be supported, for three reasons:

1. The study was never valid. Parts drawn at random from a bin do not span the process range; MSA requires parts selected to represent the variation the gauge must resolve.
2. Bias is not captured by GRR at all. The 4 µm operator offset shifts the mean; at a ±10 µm tolerance that consumes 40% of the one-sided margin, and GRR statistics will not show it.
3. Decision risk dominates. Near the limits the system will misclassify parts in both directions, and it is misclassification - not distribution width - that puts nonconforming product in a box or scrapped good product in the bin.

Capability should be withdrawn or flagged as 'pending re-validation', and re-demonstrated only after the MSA passes.

Is it temperature? Not on its own. For 316L, α ≈ 16 × 10⁻⁶/°C. A 12 mm diameter measured 3 °C away from the 20 °C reference changes by 12 × 16 × 10⁻⁶ × 3 ≈ 0.6 µm; even an 8 °C error gives about 1.5 µm. The micrometer frame (steel, α ≈ 11.5 × 10⁻⁶/°C) expands in the same direction and partly cancels the effect. Temperature could account for 1–2 µm only if that operator measures parts straight off the machine before they cool - a plausible but testable hypothesis, and still not 4 µm.

More likely causes of the bias

• Ratchet or thimble force: a hand-held micrometer with no constant-force device compresses the part. A 4 µm systematic offset is typical of over-tightening.
• Measuring position: on a chamfer, at a different axial station, or with the anvils not square to the axis.
• Reading and zeroing habit, including parallax on the digital display.
• The instrument itself: check the calibration certificate and history before blaming the operator.

Corrective action

1. Fix the measurement: bench stand with constant force, master ring gauge for daily zero check, temperature-controlled room at 20 ± 1 °C with a two-hour soak, written work instruction, operators retrained and re-qualified.
2. Re-select GRR parts to span the full 20 µm band, 10 parts × 3 operators × 3 trials in randomised order, with the operators blind to part identity.
3. Investigate and eliminate the operator offset as a separate bias study against a master.
4. Then re-establish capability on at least 125 parts with an SPC chart, and report Cpk with a confidence interval and the MSA result attached to it.

Acceptance criteria for the re-run %GRR ≤ 10% is the target; 10–30% is acceptable only with documented justification and a control plan that compensates for the measurement uncertainty; ndc ≥ 5; and no statistically significant operator bias against the master.

Principle: a measurement-system failure is not evidence of product nonconformity - but it is not evidence of conformity either. Both lots are 'capability unknown', not 'bad'.

Warehouse stock (2,000) Quarantine immediately. Re-measure with a system fit for purpose: the corrected micrometer set-up, or a comparator or CMM with a known uncertainty well below 1 µm. At this lot size, 100% measurement is affordable and ends the argument. Separately plot the mean against 12.000 mm - if the process sits 3–4 µm off centre, the true nonconformance rate may be material even at Cpk ≈ 1.9, and that is the number that decides the disposition.

Shipped product (8,000) Do not recall on an MSA result alone. A recall with no evidence of nonconformity creates a supply crisis and a traceable record for no benefit. Instead:

1. Retrieve and re-measure the retained samples and the parts used for the PPAP study.
2. Run a documented risk assessment against the drawing and the shaft's function. If OD is a critical-to-function characteristic, escalate to a formal health-hazard evaluation under the customer's field-action procedure; if it is not, agree a customer-witnessed verification of a statistically valid sample.
3. Record the outcome either way.

Communication - before the audit, not at it Tell the customer's supplier quality engineer: what failed (the measurement system, not necessarily the product), what it means quantitatively, what is quarantined, when re-verification data will exist, and the CAPA number. Withdraw or mark the PPAP capability submission as pending re-validation.

Under ISO 13485 the invalid measurement system is a nonconformity in its own right and needs a CAPA record regardless of what happens to the parts; under the relevant medical-device quality requirements the instrument control failure must be investigated and its effect on product determined. Framing this as an MSA problem you found yourselves is a far stronger audit position than having the auditor find it.