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Tom Gaskell

Six Sigma

Quality Insights: How Do Sampling Plans and AQLs Work?

How you can use sampling plans and acceptable quality limits to manage quality.

Published: Tuesday, November 3, 2009 - 12:19

If you are buying two or three complex assemblies per month from a contract manufacturer, it would be reasonable to check every one carefully; there’s a lot that could go wrong. However, if you are buying 100,000 simple subassemblies per month it makes no sense for you to 100-percent check them and probably isn’t practical anyway; life is too short, costs are too high.

So how do you inspect or test products when 100-percent checking is impractical?

My first suggestion is to get someone else to do it. Ask your supplier to do the checking and provide evidence to you that they have done so. Beyond that, you or your suppliers could use a sampling plan. This works on the basis that you inspect or test a defined number of samples from each delivered batch, and if more than a fixed number of these units pass then you accept the whole batch. If fewer than that number pass you reject the whole batch or, at least, require that the batch is entirely checked.

It sounds obvious, and you may already be doing it, but how do you choose the batch size and the pass/fail numbers to be statistically valid?

Fortunately, a lot of work has been done to work out the numbers and incorporate them into industry-standard specifications; the U.S. Military’s MIL-STD-105E is the granddaddy of them all, although BS, ISO and ANSI standards have since emerged, all based on the same principles.

You have some decisions to make that will significantly affect the quantities of products to be inspected or tested and the results that you get. These are defined below:


 The acceptable quality limit (AQL) is set by you and represents the statistical limit for failures during inspection above which the batch is unacceptable and below which you will accept it. You can apply different AQLs to different types of defect. For example, for major defects such as clearly visible damage or nonfunctioning units, a typical AQL would be 1 percent, whereas for minor defects such as difficult-to-see cosmetic blemishes you might relax this to 2.5 percent.

Inspection level

Usually Level I, II, or III—Level II is normal; Level I requires about half the inspection; and Level III requires about twice the inspection.

Inspection type

Whether the inspection type is normal, tightened, or reduced depends on the quality history of these parts and the supplier. I’ll explain this in a moment.

Once you have chosen these parameters, you can then enter the batch size into the appropriate AQL/sampling tables. I don’t have room to reproduce these tables here, as there are many combinations of parameters, but they are available free from many sources on the internet.

To give you an example of the quantities involved for Type II inspection with an AQL of 1 percent, and a normal inspection type:

  1. Batch size = 100, sample size = 13: if zero fail, the batch is accepted, if one (or more) fails, the whole batch of 100 is rejected.
  2. Batch size = 1,000, sample size = 80: if two (or fewer) fail, the batch is accepted, if three (or more) fail, the whole batch of 1,000 is rejected.
  3. If we use the same example as in No. 2 but this time use the tightened inspection type: if one (or none) fails, the batch is accepted, but if two (or more) fail, the batch is rejected; so you can see that it’s a more stringent test.


A variant of the process is called “double sampling.” In this case, there are three outcomes of the sample inspection: accept—(e.g., if there are no fails out of 50 samples for a batch of 1,000), reject—(e.g., if there are three fails or more), or do  additional sampling—(e.g., if there are one or two fails, you take a further 50 units as samples and use different pass/fail criteria).

There are specific rules about what causes a “normal” inspection type to be changed to a tightened inspection type, and vice versa, and similarly for the change between “normal” and “reduced” (more relaxed) inspection. For instance, if a “normal” batch is rejected, you immediately change the inspection type to “tightened” until five consecutive batches have been accepted, at which point the inspection type can be changed back to “normal.”

So, in essence, that’s how sampling plans and AQLs work. Decide on the AQL you need, look up the numbers in the appropriate tables, inspect the specified quantity of the sample, and accept or reject the whole batch accordingly; then move the inspection between normal, tightened, and reduced depending on whether batches pass or fail.

Finally—here I go again—a note of caution: The use of AQLs and sampling doesn’t guarantee high quality; all it can do is give a statistical likelihood of quality being better than a set limit. Skeptics such as the quality guru, Phillip Crosby, criticized the technique as inevitably leading to a finite number of faults; instead he advocated the “Zero Defects” philosophy that I’ll talk about another time.

However, if you buy or make medium to high quantities of parts, I find it a useful approach that your supplier—or you—can adopt in preference to doing nothing or simply guessing at how many items to check.


About The Author

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Tom Gaskell

Tom Gaskell offers business quality, product quality and reliability, manufacturing management, and trouble-shooting services through the consultancy, Primilis Ltd. Contact him at www.primilis.com/contact_us.html.


AQL Sampling Plan

Would an AQL sampling plan that rejects a lot on one failure be appropriate for a process that is validated to say a 95% confidence level? It seems counter-intuitive to expect no defects when the process by design accepts a level of potential rejects.