This is not a stupid question at all. It is a common misunderstanding that the AQL is the same as the average quality of the lot. In fact, the AQL is the **worst quality level** that is still acceptable on average¹. It does not mean that every lot with quality equal to or better than the AQL will be accepted. There is always a risk of rejecting good lots and accepting bad lots, depending on the sampling plan and the actual quality of the lot.

The sampling plan you are using is based on the **ISO 2859-1 standard**¹, which specifies sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection. The standard provides tables of sample sizes and acceptance/rejection numbers for different inspection levels, AQLs, and lot sizes. The sampling plan you are using is for **normal inspection**, **inspection level II**, and **AQL = 10 %**. The sample size is **125** and the acceptance number is **21**.

The reason why the acceptance number is higher than 10 % of the sample size is because the sampling plan is designed to have a certain **producer's risk** and **consumer's risk**. The producer's risk is the probability of rejecting a lot with quality equal to or better than the AQL. The consumer's risk is the probability of accepting a lot with quality worse than a specified **limiting quality (LQ)**². The standard gives values for these risks for different sampling plans.

For your sampling plan, the producer's risk is **0.05**, which means there is a 5 % chance of rejecting a lot with 10 % or less nonconforming items. The consumer's risk is **0.10**, which means there is a 10 % chance of accepting a lot with 21.5 % or more nonconforming items. The LQ for your sampling plan is **21.5 %**, which means that any lot with more than 21.5 % nonconforming items has a high chance of being rejected.

The sampling plan does not guarantee that every lot with quality better than the AQL will be accepted, or that every lot with quality worse than the LQ will be rejected. It only guarantees that, on average, over many lots, the proportion of accepted lots will be close to the AQL, and the proportion of rejected lots will be close to the LQ.

The paradox you are facing is due to the fact that you are comparing a single sample result with an average quality level. A single sample result can vary widely depending on the actual quality of the lot and the randomness of sampling. An average quality level is a long-term statistical measure that reflects the performance of a sampling plan over many lots.

(1) ISO 28590:2017(en), Sampling procedures for inspection by attributes .... https://www.iso.org/obp/ui/.

(2) ISO 2859-4:2020 - Sampling procedures for inspection by attributes .... https://www.iso.org/standard/64506.html.

(3) ISO - ISO 2859-2:2020 - Sampling procedures for inspection by .... https://www.iso.org/standard/64505.html.

(4) Sampling procedures for inspection by attributes - iTeh Standards Store. https://cdn.standards.iteh.ai/samples/64505/a63e1478944e47cf9c1afdeeed54549c/ISO-2859-2-2020.pdf.

You're welcome. I'm glad you found my explanation helpful. To answer your follow-up question, yes, you are correct. If you check 5 items and find 10 defects and this is acceptable, then the worst quality level that will be accepted on average is 100 nonconformities per 100 items.

This is because the sampling plan for 5 items and AQL = 100 (nonconformities per 100 items) has an acceptance number of 10 and a rejection number of 11¹. This means that if you find 10 or less defects in the sample, you accept the lot, and if you find 11 or more defects, you reject the lot. The OC curve for this sampling plan shows that the probability of acceptance is 1 (100 %) when the lot percent nonconforming is 0, and it decreases as the lot percent nonconforming increases. When the lot percent nonconforming reaches 100, the probability of acceptance is 0.006 (0.6 %)².

Therefore, if you accept a lot with 10 defects in a sample of 5 items, you are accepting a lot with a percent nonconforming of 200 (200 %). This is the worst quality level that will be accepted on average by this sampling plan. However, this does not mean that every lot with a percent nonconforming of 200 will be accepted. The probability of accepting such a lot is very low (0.6 %), so it is unlikely that you will encounter such a lot in practice.

I hope this answers your question. If you want more details, you can refer to these sources:

¹: ISO 2859-2:2020(en), Sampling procedures for inspection by attributes — Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot inspection

²: Sampling procedures for inspection by attributes - iTeh Standards Store

(1) ISO 2859-2:2020(en), Sampling procedures for inspection by attributes .... https://www.iso.org/obp/ui/.

(2) Sampling procedures for inspection by attributes - iTeh Standards Store. https://cdn.standards.iteh.ai/samples/64505/a63e1478944e47cf9c1afdeeed54549c/ISO-2859-2-2020.pdf.

(3) ISO - ISO 2859-2:2020 - Sampling procedures for inspection by .... https://www.iso.org/standard/64505.html.

(4) Acceptable Quality Limit (AQL) for Product Inspections | QIMA. https://www.qima.com/aql-acceptable-quality-limit.