Sampling Plan Versus Process Reality in a Stamping Line
A stamping line produces 8,000 parts/shift. The quality plan uses a p-chart with n=100 sampled hourly, and a 100% final inspection. Last month: 3 customer returns out of 8,000 shipped, all with a burr defect. The p-chart showed all points in control, average fraction defective 0.8%. Operators say the burr appears only after a die sharpening, roughly every 12 hours, and clears within 20 minutes. Final inspection uses a go/no-go gauge that does not check burr height. The plant wants to reduce returns to zero and is considering tightening the p-chart control limits.
1. Explain why the p-chart stayed in control despite the returns, and assess whether tightening limits helps.
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A p-chart with n=100 detects shifts in the average fraction defective; it cannot see a 20-minute burst every 12 hours unless a sample lands inside it. With hourly sampling, the chance of catching a 20-min window is about 1 in 3 per event - and even then, one sample of 100 with, say, 3 defectives sits within normal variation of a 0.8% baseline (3σ limits ≈ 0.8% ± 3×0.89% ≈ 0 to 3.5%). So the signal is diluted and often missed.
Tightening control limits does not help: it increases false alarms on a process that is otherwise stable, and the true issue is a stratified, time-localized defect tied to die sharpening. The correct tools are a run/stratified chart keyed to sharpening events, or monitoring the burr directly after each sharpening.
2. Recommend changes to detection and to the inspection gauge.
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Two failures: the sampling scheme is mismatched to the defect's time structure, and the gauge cannot detect the defect at all. Fixes:
- Event-based sampling: take a small sample (n=5-10) immediately after every die sharpening and every 30 min for the next hour; chart burr height on an X-bar/R chart.
- Gauge upgrade: replace go/no-go with a burr-height check (visual comparator or a simple height gauge) with a defined limit; validate gauge R&R.
- Containment: since final inspection cannot catch burr, add a post-sharpening first-piece approval and a burr check at the press, not downstream.
- Root cause: investigate die sharpening procedure and clearance; the 20-min clearing suggests a settling effect that could be designed out.
3. If the process is improved to 0.1% defective, what is the expected number of returns per 8,000 shipped, and what does that imply for the 'zero returns' goal?
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At 0.1%, expected defectives = 8,000 × 0.001 = 8 parts/shift. Even at 0.01%, that is 0.8 parts/shift. 'Zero returns' is not achievable by tightening inspection alone; it requires defect prevention at the source (die condition) plus 100% effective detection. Realistic target: drive the post-sharpening burr to zero via process control, and set a measurable goal (e.g., <1 return per quarter) rather than an absolute zero, then verify with ongoing event-based monitoring.