AQL Inspection at the Acceptance Number, and a Needle Fragment in a Collar
A final inspection is being made on a lot of 4,800 finished cotton shirts. The buyer's contract specifies ISO 2859-1, general inspection level II, normal single sampling, with AQL 2.5 for major defects, AQL 4.0 for minor defects and zero acceptance for critical defects. The inspector draws one sample and finds 6 major defects (broken stitching at the armhole and unmatched checks), 14 minor defects (loose thread ends and minor untrimmed threads) and 1 critical defect: a fragment of broken needle found inside a fused collar. The production manager wants the lot shipped on time and argues the majors are 'well within' the limit. The buyer's representative is on site and asks for your disposition.
1. Determine the sample size and acceptance/rejection numbers from the plan, and give the disposition of the lot with your reasoning for each defect class.
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Sampling plan: lot size 4,801–10,000 at general inspection level II gives code letter L, which means a sample of 200 pieces, with the same sample examined for all defect classes.
Acceptance numbers for n = 200:
- Major, AQL 2.5: Ac = 10, Re = 11.
- Minor, AQL 4.0: Ac = 14, Re = 15.
- Critical: Ac = 0 (any critical defect rejects the lot).
Disposition:
- Major: 6 found against Ac 10 → accept on majors. The production manager is right on this class, but only on this class.
- Minor: 14 found against Ac 14 → accept, exactly at the acceptance number. This is not comfortable: one more minor defect would have rejected the lot. Flag it and check whether the switching rules require tightened inspection for the next lot.
- Critical: 1 found against Ac 0 → the lot is rejected. A needle fragment in a collar is a potential consumer injury and a recall risk; no volume of acceptable majors or minors can offset it.
The decision rule is: each class is judged separately, and rejection on any class rejects the lot. Shipping this lot would breach the contract and expose the factory to a claim far larger than the order value.
2. The factory proposes to 'draw a fresh sample and re-inspect'. Explain why that is not acceptable and what the correct route back to shipment is.
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A sampling plan is a decision rule agreed in advance. Once the sample has been drawn from an identified lot and the decision is reject, drawing a second sample from the same lot until a pass is obtained is not re-inspection - it is sampling to a desired answer. It destroys the statistical basis of the plan and shifts risk onto the buyer (consumer's risk, β): the buyer's protection comes precisely from the fact that you cannot keep sampling the same lot.
Correct route:
- Contain: quarantine the entire lot, including pieces already packed and any in transit to the warehouse; identify lot number, production dates and the operators/machines involved.
- Screen: 100% inspection for the critical defect class - in this case metal detection of every piece, plus a visual check of collars - and remove or rework all defective pieces.
- Rework the majors/minors that are economically repairable, and downgrade or reject those that are not.
- Re-offer as a new lot: the rectified goods are presented as a clearly identified new lot with a fresh inspection; the buyer may also require tightened inspection (smaller acceptance number) because of the history.
- Report and correct the cause, not just the symptom - the buyer will ask.
Explain to the production manager that the cost of screening is bounded and predictable, while the cost of a shipped needle fragment is unbounded: recall, injury claim, loss of the buyer.
3. Explain what control failed to allow a needle fragment into a fused collar, and describe the needle-control procedure you would implement and verify.
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A needle fragment in a sealed collar means the fragment was never recovered when the needle broke, and it passed the collar fusing and the final inspection. Two controls failed: needle-break recording and metal detection.
Needle control procedure:
- One-for-one issue: the store issues a needle only against a returned broken needle or a signed break record. Operators do not keep loose needles at the machine.
- Break procedure: stop the machine, switch off, and account for all fragments. A lockstitch needle breaks into a predictable number of pieces; the rule is that every piece must be found and taped to the record card with the operator's name, machine number, needle size and time. A magnetic tray and a torch help in the race and under the table.
- If a fragment cannot be found: the machine is stopped, the area searched, and all work produced since the last needle check is quarantined and metal-detected.
- Routine checks: needle condition checked at start of shift and after any machine adjustment or jam; bent needles replaced, never straightened and reused.
- Metal detection: 100% pass of every garment through a metal detector at packing, with a documented daily calibration using ferrous and non-ferrous test pieces; a failed detector stops the line.
- Root-cause the break: wrong needle size or point for the fused collar and interlining, needle striking the plate or a hard interlining edge, or pulling the work. Correct the cause or the breaks continue.
- Verify: audit the needle records weekly, check that break records match issue records, and keep the detector calibration log available for the buyer - this is reviewable evidence, not paperwork.