Acceptance Sampling: Two Rejections, a Certificate of Conformance, and a Misread AQL
Receiving inspection at a harness plant uses ANSI/ASQ Z1.4, general inspection level II, single sampling, normal inspection, AQL 1.0. Connector lots of 2,400 pieces map to code letter K, which gives n = 125, Ac = 3, Re = 4. Ten lots have arrived. Lot 6 had 6 nonconforming units and lot 9 had 4; the other eight were accepted, three of them with exactly 3 nonconforming units. The supplier now sends a certificate of conformance with every shipment and asks that receiving inspection be skipped. A production supervisor wants to know why lots containing nonconforming parts were ever accepted. The buyer says, "Our AQL is 1%, so up to 1% bad parts is acceptable - that is what we bought." The connectors go into an airbag harness, and the customer's line scrap rate has risen to 900 ppm.
1. Apply the plan's decision rules to lots 6 and 9 and state the inspection status of lot 10 and beyond. What must happen to a rejected lot?
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Decision rule: accept if the number of nonconforming units found is less than or equal to Ac; reject if it is greater than or equal to Re.
- Lot 6: 6 nonconforming, and 6 is greater than or equal to Re = 4, so reject.
- Lot 9: 4 nonconforming, and 4 equals Re = 4, so reject. This is where people slip - 4 is not "accept with 4"; Ac of 3 means the acceptance number is 3, and anything at or above 4 rejects.
- The three lots with exactly 3 nonconforming were correctly accepted (3 is less than or equal to Ac = 3).
Switching: under Z1.4, two rejections among five consecutive lots on original (normal) inspection require a switch to tightened inspection. Lots 5 through 9 span the two rejections, so tightened applies starting with the first lot after the second rejection - lot 10.
- Lot 10 and subsequent lots, tightened, code K, AQL 1.0: n = 125, Ac = 2, Re = 3.
- Return to normal only after five consecutive lots on tightened inspection are accepted (with the total nonconforming not exceeding the applicable limit number).
Rejected lots: they are not "returned and forgotten." Either 100% screen the lot and remove all nonconforming units (then the screened lot may be resubmitted, and resubmitted lots are normally inspected under tightened), or return the lot to the supplier with a request for corrective action. Record the disposition and the quantity found. Pushing the same lot back unchanged gets it counted twice and corrupts the switching history.
2. Can receiving inspection be replaced by the supplier's certificate of conformance? State the conditions you would require and the reason a certificate alone is insufficient here.
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A certificate alone is not verification. A CoC is a supplier's declaration; it provides no independent evidence that the 125-piece sample would have passed. Under ISO 9001 the organization remains responsible for verifying that externally provided product meets requirements, and the contract here is for a safety-critical characteristic (airbag harness), which is exactly the category where sampling reduction should be most conservative.
Legitimate paths, with conditions:
- Reduced inspection under Z1.4 requires qualification: a defined number of consecutive lots on normal inspection with the total nonconforming at or below the table's limit number, steady production, and agreement by the responsible authority. Reduced keeps a sample (typically about 40% of normal, so roughly n = 50 for code K) - it does not skip.
- Skip-lot / dock-to-stock requires a formal, documented supplier agreement, not a certificate. Evidence normally includes: demonstrated process capability on the characteristic (e.g., Cpk at or above 1.33 on the supplier's own data with a credible measurement system), a periodic audit of the supplier's process and calibration, an agreed defect-rate target with defined consequences, and a periodic verification sample at your dock to confirm the assumption still holds.
Why the timing is wrong right now: the supplier has just produced two rejecting lots in five, and the customer's line is at 900 ppm. Tightened inspection is the correct status. Moving to skip-lot in the same month as a tightened switch is a documented contradiction, and if an escape reaches the airbag assembly it will be visible in the records.
3. Write the correction for the supervisor and the buyer. Use the plan's actual statistical behaviour, not slogans.
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Why lots with nonconforming parts were accepted: sampling plans are lot-disposition rules, not defect filters. With n = 125, Ac = 3, using the Poisson approximation (np = 1.25 at p = 1%):
- At p = 1% incoming quality, P(accept) = P(X less than or equal to 3) with lambda = 1.25, which is about 0.96. Nine lots in ten at 1% defective will be accepted - by design.
- At p = 5%, lambda = 6.25, P(accept) is about 0.13. Even a 5% defective lot gets through roughly one time in eight.
- The lot tolerance percent defective (about 10% probability of acceptance) for this plan is roughly 5% to 6%. So a lot that is 5% bad still has a meaningful chance of acceptance.
That is consumer's risk, and it is why AQL sampling does not protect a safety-critical characteristic.
Correcting the buyer: AQL is not an allowance, a target, or a contractual defect entitlement. AQL 1.0 is the quality level at which this plan accepts about 95% of lots; it is an index used to pick a plan, and the corresponding process average is a ceiling for sampling purposes, not a specification. The purchased requirement is conformance - zero nonconforming units in the population. Saying "we bought 1% bad" would also be a poor contract position if an escape causes an injury.
Correcting the supervisor: the accepted 3-nonconforming lots are exactly what the plan predicts. The fix is not to argue with the arithmetic but to change the plan for this part: 100% inspection or automated test for the safety characteristic, a tighter AQL, or a capability-based supplier requirement with ongoing verification.
Reconcile with the 900 ppm figure: 900 ppm (0.09%) is ten times better than the 1% AQL, so the customer's scrap is not statistical evidence that the plan is failing - but it does show that nonconforming product is reaching the line, which at this criticality is unacceptable regardless of the sampling math.