by Renaud Anjoran in 'Quality Inspection Blog'

The “AQL tables” are statistical tools at the disposal of buyers (for product inspections). They help determine two key elements:

• How many samples should be inspected?
• Where is the limit between acceptability and refusal, when it comes to defective products?

The need for an objective measurement of quality

In virtually every production batch, there will be defective products. It is true even after the manufacturer has checked each individual product and has repaired the defective ones.

Thus, in a supplier/buyer relationship, the supplier cannot be expected to deliver defect-free goods. However, the buyer wants to control the quality of purchased goods, since he does not want too many defects. But what does “too many” mean?

How to set the limit between acceptability and refusal in a way that can be agreed upon and measured?

Definition and application of ‘AQL’

The limit, as described above, is called the ‘AQL’. It stands for ‘Acceptance Quality Limit’, and is defined as the “quality level that is the worst tolerable” (ISO 2859 standard).

For example: “I want no more than 1.5% defective items in the whole order quantity” means the AQL is 1.5%.

In practice, three types of defects are distinguished. For most consumer goods, the limits are:

• 0% for critical defects (totally unacceptable: a user might get harmed, or regulations are not respected).
• 2.5% for major defects (these products would usually not be considered acceptable by the end user).
• 4.0% for minor defects (there is some departure from specifications, but most users would not mind it).

These proportions vary in function of the product and its market. Components used in building an airplane are subject to much lower AQL limits.

Getting familiar with the AQL tables

Before using the AQL tables, you should decide on three parameters:

• The ‘lot size’. If you ordered different products, the quantity of each product is a lot size, and separate inspections should be carried out for each lot. If you ordered only one product, the lot size is your total order quantity.
• The inspection level. Different inspection levels will command different number of samples to inspect. In this article, we will stick to the so-called “level II”, under “normal severity”.
• The AQL level appropriate for your market. If your customers accept very few defects, you might want to set a lower AQL for both major and minor defects.

There are basically two tables. The first one tells you which ‘code letter’ to use. Then, the code letter will give you the sample size and the maximum numbers of defects that can be accepted.

First table: sample size code letters

How to read this table? It is very easy.

If you follow my example, I assume your ‘lot size’ is comprised between 3,201pcs and 10,000pcs, and that your inspection level is ‘II’. Consequently, the code letter is “L”.

Second table: single sampling plans for level II inspection (normal severity)

How to read this table?

Your code letter is “L”, so you will have to draw 200pcs randomly from the total lot size.

Besides, I assume you have set your AQL at 2.5% for major defects and 4.0% for minor defects. Therefore, here are the limits: the products are accepted if NO MORE than 10 major defects AND NO MORE than 14 minor defects are found.

For example, if you find 15 major defects and 12 minor defects, the products are refused. If you find 3 major defects and 7 minor defects, they are accepted.

Note: in quality inspections, the number of defects is only one of the criteria. It is sometimes called “quality”, or “quality findings”. The other criteria are usually on the inspector’s checklist, which typically includes:

• Packaging conformity (barcodes, inner packing, cartons, shipping marks…).
• Product conformity (aspect, workmanship…). If all the products are in red color instead of orange, there is no need to count each sample as a defect. It makes more sense to refuse for product conformity.
• Specific tests defined in the inspection protocol (they might not be performed on all samples).

Frequently asked questions about AQL

“What are the reduced and tightened inspection severities?”

They are designed to be used in very specific situations, when a producer is particularly reliable, or on the contrary fails too often. In practice, these severities are used in less than 1% of QC inspections.

The normal severity already allows for a good variation of sample sizes. In the vast majority of cases, third-party inspectors follow only the normal severity.

“So, basically I have to authorize the factory to produce some defects?”

Yes, some defects, since a factory cannot reasonably be expected to turn out 100% good quality.

However, it does not mean the buyer tolerates everything as long as the number of defects are below the AQL limits. Please see below the note issued in the ISO2859 standard:

“Although individual lots with quality as bad as the acceptance quality limit may be accepted with fairly high probability, the designation of an acceptance quality limit does not suggest that this is a desirable quality level. Sampling schemes [...] are designed to encourage suppliers to have process averages consistently better than the AQL.”

“Based on my AQL, I calculated the proportion of defects authorized. Why don’t they correspond to the maximum number of defects authorized?”

It is true. In our example above, 2.5% of 200 samples is 5 samples, but we accept the goods even if 10 samples are found with a major defect.

Why this difference? There are heavy statistics behind this issue. To make it simple, the producer runs a risk of rejection (based on the random element when drawing the sample) even though his products (if they were all checked) would be accepted. And, in the same logic, the consumer runs a risk of accepting bad products. The statisticians had to account for these risks, that’s why the numbers were adjusted and seem not to make sense.

“Why not just say, ‘we’ll check 10% of the quantity’, or whatever percentage deemed appropriate?”

Here again, the statisticians tell us it is not that simple. As we go up in the total quantity, the proportion of products checked can decrease, for the same confidence in the inspection results.

As you can see in the chart below, the number of samples to check (vertical axis) increases at a slower pace than the total quantity (horizontal axis).

Renaud Anjoran is the founder of Sofeast Quality Control and helps importers to improve and secure their product quality in China. He writes advice for importers on the Quality Inspection blog. He lives full time in Shenzhen, China. You can contact him at info@sofeast.com.