The Capability Number Nobody Checked
A medical device assembler reports Cp = 1.45 on a critical 12.0 ± 0.1 mm dimension, based on 125 parts measured by one inspector with a digital caliper of 0.01 mm resolution. A customer auditor asks for the measurement system study. The gauge R&R (2 operators × 10 parts × 3 trials) returns %GRR = 31% of tolerance and number of distinct categories = 3. The operations manager argues the study is invalid on two grounds: only two operators were used, and "the parts chosen were all about the same size, so the study exaggerates the gauge error." Production is scheduled for 40,000 units next month against a 1.33 Ppk requirement, and the line will not stop.
1. Interpret the gauge study. Can the 1.45 be relied on to certify against a 1.33 requirement? Show the reasoning, including how the true capability might compare.
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Interpretation
- %GRR = 31% of tolerance is above the 30% ceiling that most automotive and medical conventions treat as unacceptable for a critical characteristic. A gauge consuming a third of the tolerance band cannot be used to certify conformance to a third-decimal capability target.
- ndc = 3 is the more damaging number. The gauge can distinguish roughly three levels across the part range; the conventional minimum is five. With three categories you cannot reliably rank parts, which is precisely what a capability study does.
- Resolution is fine, and it is worth saying so - 0.01 mm is one-twentieth of the 0.2 mm tolerance, comfortably inside the ten-to-one rule. The problem is not the caliper's readability, it is everything else: fixture, measurement point definition, operator technique.
Can 1.45 be relied on? No. The observed figure is a single measurement of a process through a blurry lens, and it cannot be presented as evidence of compliance with 1.33 Ppk. Two further caveats: Cp is a short-term, within-subgroup index; the requirement is stated as Ppk, which includes drift and between-lot variation and will be lower than Cp on the same data. Comparing a Cp of 1.45 against a Ppk target of 1.33 is not an apples-to-apples comparison at all.
Directional correction, for context only: removing gauge variance from the observed variance gives true sigma ≈ observed sigma × √(1 − 0.31²) ≈ 0.95 × observed, so true capability is on the order of 1.5 - which sounds reassuring and should not be relied on. The correction assumes the gauge error is random about zero and that the study is representative; both assumptions are what is in question. A biased or non-linear gauge can flatter or penalise the process in either direction.
2. Respond to the operations manager's two objections, then state what you would actually do given the 40,000-unit run next month.
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Objection 1 - "only two operators." Partly fair and not decisive. Two operators is the accepted minimum for a GRR and is enough to estimate reproducibility, but it gives no useful read on operator-by-part interaction and cannot characterise the full operator population. The correct response is "two operators is thin, it is not invalid, and it does not explain a 31% result" - adding a third operator would refine the number, not rescue it.
Objection 2 - "the parts were all about the same size." Misplaced as applied here. Homogeneous parts shrink the part-variation term, which inflates the %GRR of study variation - so the criticism would be valid if the metric were %SV. But the reported figure is %GRR of tolerance, which is computed against the 0.2 mm specification and is unaffected by how similar the sampled parts were. Part selection does matter for another reason: parts spanning the process range are what allow ndc and the interaction term to be estimated meaningfully, and 10 similar parts is why ndc came out at 3. The objection points at a real weakness in the study design that does not rescue the conclusion.
What I would do, given the schedule:
- Address the measurement system before the capability claim. Re-run the study properly: 3 operators, 10 parts spanning the production range including near-limit parts, a defined fixturing and measurement-point method, and a type-1 bias check against a calibrated standard for linearity.
- Reduce the error at source - fixture the part so the bore is measured in the same orientation every time, define the measurement location on the drawing, and retrain. This is usually days, not months, and can drop %GRR a long way without buying anything.
- Do not certify 1.33 Ppk on this evidence. If the 40,000 units must ship while the study is redone, ship them under a defensible interim control: 100% inspection of this characteristic with a gauge and method qualified for the purpose, plus a documented risk acceptance signed at the level that owns the risk. Containment is legitimate; a chart that says 1.45 is not.
- State the honest position to the auditor: the gauge is not adequate for capability certification and the capability figure is provisional. Auditors tend to accept a documented corrective action and much less often accept a number defended after the fact.