Coating line: a marginal gauge asked to prove a demanding Cpk
A coating line applies a nominal 100 micrometre film with specification limits of 85 to 115 micrometres. Before running a capability study, a Green Belt runs a crossed Gage R&R: 10 parts, 3 operators, 3 trials per part, non-destructive gauge. Results: %GRR of study variation = 28%, %GRR of tolerance = 31%, number of distinct categories = 3, and operator C's trials average about 4 micrometres above A and B. Gauge resolution is 0.5 micrometres. The parts chosen cover only 96 to 104 micrometres and were pulled from a single shift. The Belt's manager says 28% is under 30%, so it passes, and asks for the Ppk this week. The customer requires Cpk of at least 1.33 on this characteristic, and the gauge is also used by operators to decide whether to adjust the coating head.
1. Interpret the study. Is this measurement system acceptable for the intended use? Justify with the numbers.
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Verdict: not acceptable for capability or for adjustment decisions.
- %GRR of tolerance = 31% is the number that matters here, because the decision is against the specification. It is above the 30% threshold, and unlike the study-variation figure it is not distorted by the part selection.
- The narrow part range is a flaw, not a rescue. Parts spanned 96 to 104 micrometres inside an 85 to 115 micrometre tolerance. A narrow part range depresses part variation and inflates %GRR of study variation, so the 28% cannot be read as a pass. Both statistics point the same way: the system is marginal at best.
- ndc = 3 is below the useful minimum of 5. The gauge can separate parts into roughly three categories across the range studied; a Cpk comparison across 1.33 thresholds needs finer discrimination.
- Operator C offset of 4 micrometres is 13% of the 30 micrometre tolerance. That alone can move a reported Cpk by roughly 0.3, which is enough to flip a 1.33 decision.
- Resolution is fine at 0.5 micrometres, roughly 1/60 of tolerance; that is not the problem.
- Variance budget check. A %GRR of tolerance of 31% corresponds to a measurement standard deviation of about 1.55 micrometres. Demonstrating Cpk 1.33 on a 30 micrometre tolerance requires total process standard deviation of about 3.76 micrometres. Measurement error therefore consumes roughly 17% of the variance budget before the process contributes anything, and the gauge is currently used to trigger coating-head adjustments, which means it is also driving over-adjustment.
Conclusion: fix the measurement system first; any Ppk issued now is a property of gauge and operator as much as of the process.
2. What must be fixed before the capability study, and what do you tell the manager about the 30% rule?
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About the 30% rule
The 10% / 30% bands are heuristics for judging measurement systems, not a pass gate. The real question is whether measurement variation is small enough for the decision the gauge supports. Three decisions are in play here and they have different requirements:
- Customer Cpk at 1.33 against a 30 micrometre tolerance: a 31%-of-tolerance gauge leaves insufficient discrimination. This is the decision that rejects the pass.
- Operator adjustment decisions at the head: a gauge that is 31% of tolerance, operated with a 4 micrometre operator offset and no fixture, will trigger adjustments that are mostly noise.
- Detection of a trend on a control chart: the same gauge may be adequate, because averages over subgroups reduce measurement error by the square root of the subgroup size.
So the honest answer is: this system is marginally acceptable for coarse trending and unacceptable for the capability claim and for head adjustments.
Fix list before re-running
- Standard work for probe placement, distance and dwell, with a fixture if placement is currently free-hand.
- Training and re-qualification for operator C; investigate whether C's offset is technique or instrument channel.
- Linearity and bias check across 85 to 115 micrometres, since the study only covered 96 to 104, which is exactly the region where no decisions are being made.
- Stability check over several shifts; if the gauge drifts, repeatability is overstated.
- Re-run the crossed study with parts spanning the full tolerance, 10 parts, 3 operators, 3 trials, and confirm ndc of 5 or better before issuing capability.
Interim decision rule while the line runs
Do not report a Ppk. Apply a guard band: treat 87 to 113 micrometres as the action window for the coating head, and confine adjustment decisions to subgroup averages rather than individual readings, so decision risk is reduced without stopping shipment.