AQL tables: how to read them


Starting to get Involved
I downloaded the MIL-STD-105E standard, which describes acceptance quality level (AQL) sampling plans. Reading throw other posts I realised that I probably misread the table, because if I calculate alpha risk (type I error) and beta risk (type II error) they are all over the place. Thus this question on how to read the tables:

Let's take the simplest case of single normal sampling, and suppose we have a lot size of N=200.
1. Using Table I we get the sampling size code letter "G"
Bildschirmfoto 2022-01-09 um 10.36.01.png

2. Let's further assume that the customer demands that the probability of a defective part is p=0.065=6.5%. This correspond to an AQL value of 6.5. Next we look in Table II-A in the sample size code letter "G" and find that we have to use a sample size of n=32. Hence, we have to inspect n=32 products. In the column 6.5 (for the AQL value) we find that we accept the lot if we find 5 or less defects and that we reject the lot, if we find 6 or more.
Bildschirmfoto 2022-01-09 um 10.47.20.png
First question: Have I picked the AQL value correctly? I'm a little concerned that the table shows defect probabilities of 1000%. I reckon these are for products were I allow multiple defects (up to 10 on average) per product.

3. If a rejection of a lot would result in a 100% inspection and all defective parts are replaced by non-defective parts, I would obtain the so called "Average Outgoing Quality (AOQ)". The AOQ value is listed in Table V-A. Hence, if the customer demands that only 6.5% of the parts are defective, he gets (on average) 9.9% defective parts.
Bildschirmfoto 2022-01-09 um 11.08.26.png
Second question: Who is performing the 100% inspection, the supplier or the customer? I reckon the customer returns the parts and the supplier is required to inspect each part -- not for punishment, but merely to learn what went wrong and how he could optimise the production processes ;)

4. Finally, if I'd like to get the alpha and beta risks of this sampling plan I have to use Table X-G and Table X-G-, which display the operating characteristic curve for the hypothesis test. I do not reproduce the plot here, because the quality of the plot is low.

Main question: Is this process flow correct?

Comment: My key problem with the described procedure is that step 2 and step 3 should be swapped -- in real life we probably iterate to keep it simple: After getting the AOQ in step 3 we have to stop and ask, if this risk is acceptable to our customer (= in compliance with our quality goal). If it is not, we have to scan though Table V-A (the AOQ values) and find an acceptable risk. This defines the AQL value we use in step 2.
However, this issue might be due to the fact that I am an engineer and not a quality person. Hence, I would have picked the AQL value due to the quality goal of my company, and not thought twice whether or not the average outgoing quality might be lower than the AQL value. Also, I watched three videos describing the procedure and found the "check the average outgoing quality" step in none of those videos. I'm well aware that the quality is usually better than the AQL value, nevertheless, I believe that this is an inconsistence in the upper procedure -- which is of course resolved, if the person who picks the AQL value has lots of experience.
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
Keep in mind that the MIL STD 105 tables are designed for ongoing production . . . so you will gain more information with time. Yes, the alpha and beta errors are "all over the place" as a result. Smaller lot sizes will have higher opportunity for false alarms and failure to detects.

"First Question". Short answer is yes. BUT Longer answer is - this is the AVERAGE - so you will end up with rejected lots as (approximately) half will be above average and half will be below. This average is the worst case ACCEPTABLE (which is what the "A" stood for) quality level. You may add in a buffer if you want and reduce the AQL on your own. OR increase the inspection level (better answer). You missed this table (see your Main Question) where you take into account the risk (Special Inspection Levels and General Inspection Levels. The graphic is from the video I reference at the end of this.


3. Rejection does not necessarily result in 100% inspection, it depends on what you write in your sampling plan. Also, there are the opportunities for "tightened" inspections as an answer to failures. But yes, you would have a 9.9% effective defect rate detected. Refer to my comments above about the AVERAGE. A better answer rather than 100% inspection is to go tightened. Now, presumably IF you inspection process does not miss any defects, this lot, with 100% inspection and the defects removed would be 100%.

Second Question - you perform the 100% inspection, and remove any defects. AND consider going to tightened inspection level. The customer may be performing their own inspections, perhaps to the MIL STD tables as incoming inspection.

4. True.

Main Question. Actually the question of risk is first in the process. You do that before choosing the table to use.

See Acceptance Sampling and ANSI Z1.4 Sampling Procedure Explained - YouTube . Go to minute 2:50 - note it talks about default plans. BUT in that left hand table could go to a different level. NOTE that AQL is "Acceptable Quality Level". Worst tolerable process average that is considered acceptable.


Starting to get Involved
Hi Steve,
thank you very much for your kind reply. It helped to clarify things and I am happy that I didn't misinterpret the MIL STD 105 document. Personally, I always find these kind of documents hard to understand, because they have plenty of text without formulas. A picture is worth one thousand words, and a formula is worth thousands of pictures ;)

As I said in my intro
Let's take the simplest case of single normal sampling
This is why I didn't consider tighter sampling or switching between normal and tight sampling. My goal was to make sure that I understand the concept. The simplest case is usually best to achieve this goal.

3. Rejection does not necessarily result in 100% inspection, it depends on what you write in your sampling plan
Of course I agree. A major part of quality is to ensure that "we do as we say". Hence, whatever we define in the sampling plan is what we are going to do. I also understand that it does make sense to change from normal to tighter sampling.

Second Question - you perform the 100% inspection
Unfortunately, this is not clear to me. Do you mean that
a) there is no default definition who (supplier or customer) performs the 100% inspection, or
b) it depends where the initial sampling took place: If the defective count is too large during outgoing goods inspection, then the supplier performs the 100% inspection. In contrast, if the defective count is too large during receiving goods inspection, then the costumer performs the 100% inspection.

As stated above, everything depends on the definition used in the sampling plan. So, my question is whether (a) or (b) is the standard procedure. I expect that your answer is
_________ (b) + "change to a tight sampling plan"
However, the question remains: What is the standard process, if the tight sampling plan leads to a reject of the lot. As stated in my question, if the customer performs receiving goods inspection and the lot is rejected, I expect that the lot is shipped back to the supplier for a 100% inspection -- or for scraping the lot, if this is cheaper. Is this true? Is this the default process?

Main Question. Actually the question of risk is first in the process. You do that before choosing the table to use.
Ok, as this is my main question, I am afraid that I misunderstood MIL STD 105. So here an example:
* Suppose my quality department demands that our product possesses a certain defect only with a probability of Pmax <= 8% on average.
* As written in my question, I would "naturally" pick the AQL 6.5, because 6.5% <= 8%.
* However, if we use the sampling plan described in the question, the average output quality limit (AOQL) would be 9.9%, which means that I could get 9.9% defects. Thus, I do not comply to the quality demand.
* Of course I could use a tight sampling plan, and this would solve the issue as for this particular case the AOQL becomes 6.3%. However, if one inspects table V-B (for single tight sampling) there exists AOQLs which exceed the chosen initial AQL (I marked only a few).
Bildschirmfoto 2022-01-09 um 21.14.26.png
* Hence, instead of choosing the AQL 6.5 I need to choose 4.0. If we again assume the simple normal sampling we get AOQL = 6.1%, which is below the demanded 8%.
Is this example correct or do I misinterpret MIL STD 105? If I wish to use single normal sampling and my quality goal is 8% defect rate, do I have to choose AQL4.0 instead of AQL6.5?

Steve Prevette

Deming Disciple
Staff member
Super Moderator
There is the caveat - you and your customer should agree to the sampling process - they need to know what your sampling plan (and corrective actions for any failures) is. Preferably. you should also know what their receipt inspection plan is.

On a 100% sampling response - why would you saddle the customer with doing the 100% sample? At least in the context of the military acquisistions (which is what I was trained in - a course in my Operations Research degree at Naval Postgraduate School included Acheson Duncan's Quality Control and Industrial Statistics, which included a copy of MIL STD 105D and its background). So I am answering from the point of view of a military customer of a contractor supplying parts. I will again state - if you complete a 100% sample and you find no defects AND you eliminated the defects you found in the original sampling, you are at zero defects (with the practical problem being something could have still slipped through.

And you must keep in mind - if you have a sampling plan set up for an Acceptable Quality Level of 6.5%, and you never have any failed acceptance tests, the likelihood is STILL that one half of the production runs could exceed 6.5% defects. (with the approximation that the median and the average are the same).

NIST has a good derivation of AOQ at Choosing a Sampling Plan with a given OC Curve (

They do state:

"From examining this curve we observe that when the incoming quality is very good (very small fraction of defectives coming in), then the outgoing quality is also very good (very small fraction of defectives going out). When the incoming lot quality is very bad, most of the lots are rejected and then inspected. The "duds" are eliminated or replaced by good ones, so that the quality of the outgoing lots, the AOQ, becomes very good. In between these extremes, the AOQ rises, reaches a maximum, and then drops."

So if you end up with a lot of rejected lots, AND do 100% sampling, you get credit for "removing the duds".

Critical Points -

AQL relates to the minimum acceptable AVERAGE quality level. Many lots could and will exceed this average individually but in the long run (which is what MIL STD 105 is concerned about) you will be at the AQL or bettern.

For AOQ you get credit for removal of defective items.

Steve Prevette

Deming Disciple
Staff member
Super Moderator
By the way, I am assuming you are the supplier in this relationship. If you are the customer, you would still end up doing the 100% receipt inspections, but usually if this keeps up, you first send back the lots as rejected, and then if it still keeps up, take that supplier off your approved supplier list.


Starting to get Involved
Thank you very much, Steve. From your answer I understood that your stand-point is: "who ever finds an unacceptable lot will perform the additional sampling". As I have no experience with this subject I accept that this is the standard.

On a 100% sampling response - why would you saddle the customer with doing the 100% sample?
My idea is to set a spec of say 0.1% defect rate, and to validate the supplier. Hence, the supplier will probably show that they are able to perform the process using a 0.025% defect rate. In addition, I would demand that the supplier installs a SPC control using the key input parameters. Next, I would ask the supplier to perform an AQL2.5 sampling plan for outgoing goods inspection. Incorporating your comments, I would ask that changes from normal to tight sampling is used, if a process is changed. Finally, my company would perform an AQL10 sampling plan for ingoing goods inspection. Thus, the general idea is that the supplier is able to control the quality and that in each inspection stage we reduce the workload. However, if we find an unacceptable lot in the incoming goods inspection, we don't have the capacity to perform a 100% inspection. However, in order to keep our machines running, we need that the supplier steps up and perform additional inspections. In addition, the supplier would be asked to perform a 8D report, and to bring the process back to its original quality. After the problem is solved we would re-validate the supplier and probably add the "problem causing input parameter" to the SPC control.
As it is probably clear, I have not implemented this "step-wise quality control", yet. However, in my opinion it makes sense to (1) reduce the cross-check effort, and (2) to "out-source" the heavier part to the supplier. Of cause, my company will loose "resolution" of the incoming quality. We will only be able to detect "extremely low quality lots". Hence, on a regular basis we will either have to increase the inspection effort ourself and perform a "re-validation", or we have to visit the customer to perform an audit.

Steve Prevette

Deming Disciple
Staff member
Super Moderator
It is common in some instances for the customer to regularly send QA audit teams to their supplier's facility for a check of conditions on site, and that is part of keeping them on the "Approved Supplier List" (see also Approved Supplier List - ASQ ( ). It is not unheard of to have the customer help solve problems that the supplier has. And if the supplier is smart, they go and visit their customer(s) on occasion to see how they are using their product.
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