Sampling plans: AQL, zero acceptance and the risk in between

Why a sample, not the whole lot

Most lots are too large to inspect completely, and some checks damage the part. A sampling plan sets how many pieces to inspect and how many failures are allowed before the lot is rejected. The plan is a decision rule, and every decision rule carries risk.

The risk runs both ways. A good lot can be rejected because the sample happened to contain more defects than usual. A bad lot can be accepted because the sample missed them. The plan controls how often each mistake happens, not whether it can happen.

What an AQL means

AQL stands for acceptable quality level. In ISO 2859-1 it is the quality level that, for sampling purposes, is the limit of a satisfactory process average. It is tied to a high probability of acceptance, commonly around 95 per cent for the standard plans, not to a guarantee that every lot is below that level.

An AQL of 1.0 does not mean a supplier may ship one per cent defective. It means the plan is designed to accept lots at that quality level most of the time. A process that runs at the AQL will still generate rejected lots, and a process that runs worse than the AQL will generate many of them.

Reading the tables

The tables use the lot size and the inspection level to assign a code letter. The code letter gives the sample size. The AQL and the sample size give the acceptance number and the rejection number. Inspection level II is the usual default for general use.

The tables assume random sampling from the lot. If the sample is taken from one carton, one shift or the top layer, the plan no longer matches the standard.

Zero acceptance plans

A zero acceptance plan accepts a lot only when the sample contains no nonconforming pieces. It is simple to administer and it avoids the argument that a plan allows a certain number of defects. That simplicity is why it is popular with buyers and with auditors.

The catch is that the risk does not disappear. With the same sample size, a zero acceptance plan rejects more good lots than an AQL plan, which is a cost to the supplier. It also still accepts some bad lots, because a small sample can miss a low defect rate. To match the discrimination of an AQL plan, a zero acceptance plan usually needs a larger sample.

The risk in the curve

Take a lot that is one per cent defective and a sample of 125 pieces. An AQL 1.0 plan with an acceptance number of three accepts that lot about 96 times in 100. A zero acceptance plan with the same 125 pieces accepts it about 28 times in 100. The zero plan is stricter, but it is not a wall.

The difference grows with the defect rate. At three per cent defective, the AQL plan still accepts about half the lots, while the zero plan with 125 pieces accepts about two in 100. Neither plan inspects the whole lot. If the characteristic is safety related, use 100 per cent inspection or a control that prevents the defect, not a sample.

The sample size matters as much as the acceptance number. A zero acceptance plan with 50 pieces accepts a one per cent defective lot about 61 times in 100. With 200 pieces it accepts about 13 times in 100. A small zero plan can be weaker than a larger AQL plan, even though its rule sounds tougher.

Choosing a plan

Start with the consequence of a bad part. A cosmetic mark and a live electrical contact do not deserve the same plan. Critical characteristics usually need 100 per cent inspection, error proofing or a process control, because sampling cannot give the assurance the risk requires.

Then look at the process history. A stable process with a good record can use a smaller sample or reduced inspection. A new process, a new supplier or a recent rejection should use a larger sample or tightened inspection. The plan should change with the evidence, not stay fixed for years.

A plan also has an administrative cost. Every sample has to be drawn at random, identified, measured and recorded. A complex double or multiple sampling scheme can save inspection time on a stable lot, but it asks more from the inspector. Match the scheme to the skill on the line.

Common mistakes

The most common mistake is treating the AQL as a target. A supplier that aims for one per cent defective when the AQL is 1.0 will spend much of its time on rejected lots. The process average should be well below the AQL for the plan to run smoothly.

Other mistakes are switching from normal to reduced inspection without the switching rules, taking the sample from the top of the carton, using a visual check with no attribute agreement study, and applying an AQL plan to a critical feature because it is convenient.

What to write on the purchase order

Name the standard and the edition, the inspection level, the AQL, the sampling type and the inspection severity. Say which characteristics are critical and what happens to a rejected lot: screening, replacement, credit or a concession. A plan without a rejection route is only half a rule.

Ask for the inspection record with the lot. It should show the lot size, the sample size, the number of nonconforming pieces and the decision. That record is what lets a buyer audit the plan later without reconstructing it from memory.