AQL sampling: sample size and accept/reject

How the mechanics work: from lot size to accept/reject numbers

For an inspection using ISO 2859-1, ANSI/ASQ Z1.4 or GB/T 2828.1, use the chosen standard’s own edition. Name the standard, the edition and the sampling plan agreed in the purchase order; do not treat these separate standards as interchangeable. Use the complete instructions for the chosen plan to select the sample and acceptance/rejection numbers.

Select the standard plan first. The five steps below describe that selection; the separate hypothetical example then shows how to count results against expressly assumed decision rules.

1. Define the lot. The lot is the population the result applies to — normally units of the same model, rating and drawing revision under one purchase order line, produced under uniform conditions and presented for inspection at one time and place. Do not let unlike items be combined into one inspection population to make the numbers easier.

2. Choose the inspection level and regime. Agree the inspection level and whether normal, tightened or reduced inspection applies. For repeated lots, apply the chosen standard’s switching rules and inspection history; a level alone does not define the plan.

3. Read the code-letter table. Use the lot size and agreed inspection level in the selected edition’s table. Record the resulting code letter and the table reference.

4. Read the sample size and table instructions. Use the agreed AQL for each class and the chosen plan. Follow its notes and arrows, including any instruction to use another sample size. Draw the sample at random across the presented lot; factory-preselected units are not that random sample.

5. Apply the agreed counting and decision rules. Record whether the plan counts nonconforming units or individual nonconformities, how it handles multiple defect classes on one unit, and each acceptance/rejection number. Assess every class required by the plan and report the observations as well as the decision.

Record the counting basis and defect definitions before inspection. Sampling carries acceptance and rejection risks; it does not guarantee the condition of every unsampled unit. For a continuing series, apply the selected standard’s full switching rules and inspection history. For an isolated lot, choose an appropriate plan and state its quality and risk basis.

Hypothetical acceptance-count example

Assume a lot of 400 DN50 stainless steel ball valves and a random sample of 50. For this hypothetical exercise, assume major Ac3/Re4 and minor Ac5/Re6, plus a separately agreed contractual critical rule of Ac0/Re1. These are assumed counting rules, not values selected from an AQL table; an actual inspection uses the standard plan selected above.

For these assumed rules, count a unit once in each class in which it is nonconforming, even if it has several nonconformities in that class. A unit with both a major and a minor nonconformity contributes one to each count. Re = Ac + 1 applies to these illustrated pairs. Rejection in any class rejects the lot under this example. Counting individual nonconformities, or assigning a unit only to its worst class, is a different counting rule to define explicitly in the agreed plan.

Plain-English read: of the 50 sampled units, zero may have a critical nonconformity, at most 3 may have a major nonconformity, and at most 5 may have a minor nonconformity. Four major nonconforming units, six minor nonconforming units or one critical nonconformity rejects the lot under this plan. Three major nonconforming units out of 50 is 6 per cent (3 ÷ 50 × 100); it is the observed sample fraction, not a claim that 6 per cent of the 400-unit lot is defective or that AQL 2.5 permits that percentage in each shipment.

Critical, major and minor defects — who sets the three numbers

Sampling runs per defect class, and the classes mean roughly this:

• Critical — creates a safety hazard, breaches a statutory or certification requirement, or renders the product unusable. On industrial goods: missing earth bonding, wrong voltage configuration, a pressure part without its required certificate, an unapproved material substitution.
• Major — impairs function, durability or acceptability; likely to cause failure in service or rejection by the customer. On industrial goods: wrong gasket material, an IP rating below specification, coating below minimum dry-film thickness, incorrect tagging against approved drawings.
• Minor — a workmanship or appearance deviation that does not affect use. A small paint blemish in a non-critical area is minor. A document error that blocks site acceptance is not minor just because it is “paperwork”.

Agree the defect classes, counting basis and acceptance/rejection rules in the purchase order. The assumed counts above are not recommendations for every product; the buyer must select a plan suited to the consequences of an undetected defect.

“Critical: zero” is the separately specified contractual rule in this example, not an ISO AQL 0 table column. Any critical nonconformity found in the sample rejects the lot. Define the follow-up in the contract, including containment, sorting, correction and any 100 per cent screening of the affected feature. Finding none in 50 sampled units does not establish that all 400 units are free of critical nonconformities.

Where AQL breaks down for industrial equipment

The tables assume a large population of interchangeable units flowing from a homogeneous process. Industrial procurement violates each assumption in turn.

Small lots. For a small order of serialised machines, agree which checks are required on each unit and identify any sampled or destructive test. A small sample gives limited information about the remaining machines; define the coverage and detection limits of the method used.

Serialised units. Each machine carries its own nameplate data, mill certificates and factory test record. Conformity is established per serial number; sampling a population of four individuals is a category error.

Value asymmetry. Sampling is an economic trade-off between inspection cost and the cost of escaped defects. When one unit is a six-figure machine whose failure stalls a commissioning schedule, the trade inverts and 100 per cent inspection is cheap.

No series. AQL describes a tolerable process average across continuing lots. A one-off purchase order has no series, no switching rules, no average.

Function, not attributes. AQL counts defects an inspector can see, measure or quickly check on a sampled unit. Flow, pressure, torque, accuracy and control sequences have to be demonstrated under a defined test protocol — that is a type-test or witnessed factory acceptance test problem, not an AQL problem.

What replaces sampling where it does not apply:

The common real-world case is hybrid. One shipment might combine three machines with forty cartons of fittings, gaskets, fasteners and commissioning spares. The machines get per-serial verification linked to the FAT record; the cartons get ISO 2859-1 sampling. A competent inspection scope — and your pre-shipment inspection checklist — should state which regime applies to which purchase order line. The right question is never “can we use AQL?” but “which characteristics can safely be sampled, and which must be witnessed, tested or checked 100 per cent?”

Writing sampling into the purchase order so the inspection is enforceable

An inspection clause that just says “AQL 2.5” is not enforceable. When a lot fails, you do not want to be arguing the definition of “major” with the supplier’s quality manager while the vessel is booked. Seven elements make the difference:

1. Standard and plan, by name and edition. “Acceptance sampling per ISO 2859-1 (GB/T 2828.1), single sampling plan, normal inspection, General Inspection Level II.” Name the edition you mean; do not leave the inspector and supplier to guess which table applies.

2. Lot definition. Units of the same model, rating, drawing revision and purchase order line, completed and offered for the same shipment release — production 100 per cent complete and, by common practice, at least 80 per cent packed before the inspection is booked.

3. AQLs per defect class, as numbers. Critical — none permitted; major — AQL 2.5 (or 1.5/1.0 on critical-path equipment); minor — AQL 4.0. “Standard AQL applies” is not a specification.

4. A defect classification annex. A product-specific table mapping concrete defects to the three classes. Without it, the inspector’s generic checklist decides for you.

5. Counting rule. State whether you count defective units or individual defects. Commonly, one unit with several major defects is one major defective unit for the arithmetic — but the report should list every defect found.

6. Sampling authority. The inspector selects units at random across cartons and serial numbers — the square-root-of-cartons-plus-one drawing rule is common practice — with unrestricted access to the full lot. Factory-preselected or sealed samples void the result.

7. The override clause. This is the one that prevents the classic supplier argument:

And state the failure terms: a failed lot is held; sorting and rework are at the supplier’s cost, as is re-inspection (optionally under tightened acceptance numbers); and release — balance payment or shipping authorisation — is conditioned on a passed inspection with written buyer authorisation.

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