# sampling plan for product inspection

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SAMPLING PLAN FOR PRODUCT INSPECTION

The different types of sampling plans for QC inspections

If an inspector controls the quality of your products in China, he probably checks only a portion of the whole batch

But how does he decide how many pieces to pick for his inspection? In other words, what sampling plan does he follow?

The most commonly used is the single-stage sampling plan by attributes.

What does it mean, and what are the other options?

A single-stage sampling plan dictates that a certain number of pieces (n) should be drawn and inspected. That number n depends mainly on the size of the batch (and also on the inspection level). If the number of defects is under the AQL limit, the result is passed.

In a double-stage sampling plan, the inspector would start by taking a smaller number of sample (n1). If the number of defects in n1 is above certain limits, more samples are picked.

An accept on zero plan is a weird animal that is usually not a good idea in China. Some importers, who are sensitive to legal litigation by their customers, accept batches only if no defective unit is found. The only advantage is the fewer samples need to be checked. More in-depth information here.

A sampling plan by attributes classifies the samples as either non defective or defective. There is nothing in between.

A sampling plan by variables allows for a finer evaluation. For example, the length of the product is measured, and the exact findings are taken into account when a decision is made.

A rectifying sampling plan is applicable if the defects that are found can be corrected immediately. It is not very different from a sampling plan by attributes, but it takes into account that the batch is of higher quality after the inspection and, in case of inspection failure, the whole batch should be inspected.

Continuous sampling is the best plan when products are made individually in a continuous flow. It makes no sense to pick samples inside each batch. It consists of several phases:

At the beginning, each piece is checked (thats the screening).

After a certain number of pieces were found satisfactory, only certain pieces are checked randomly (thats the sampling).

If a piece is defective: back to screening.

If you want to use one of these plans, you should visit the excellent SQC Online website and get the numbers you will need.

And if you want more in-depth information about these plans, you should read Practical Acceptance Sampling: A Hands-On Guide. It was pointed out to me a few months back by Etienne Charlier.

I pasted this books description (from the publisher) below. I should add that it is a college textbook first, before being a practitioners guide.

Acceptance sampling plans provide criteria and decision rules for determining whether to accept or reject a batch based on a sample. They are therefore widely used by manufacturers, suppliers, contractors and subcontractors, and service providers in a wide range of industries.

The book introduces readers to the most popular sampling plans, including Military Standards and civilian ISO and ANSI/ASQC/BS standards. It covers the design, choice and performance evaluation of different types of plans, including single- and double-stage plans, rectifying and non-rectifying plans, plans for pass/fail and continuous measurements, continuous sampling plans, and more.

What do you think?Back to basics: what is the AQL?

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)

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 inspectors 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 checklist (they might not be performed on all inspected samples if they are time-consuming or destructive).

To go further

Related articles: all the basics an importer should know about quality control are explained in the articles listed on this page.

Author: Renaud Anjoran is an expert in quality assurance and quality control. His agency helps buyers in China. More info here.

Q: What are the reduced and tightened inspection severities?

A: 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.

Q: So, basically I have to authorize the factory to produce some defects?

A: Yes, some defects, since a factory cannot reasonnably 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.

Q: Based on my AQL, I calculated the proportion of defects authorized. Why dont they correspond to the maximum number of defects authorized?

A: 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 r

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