The AQL value (e.g., 2.5) does not represent the required defect rate for the "sample," but is a statistical definition of the "acceptable upper limit" for the quality level of the "entlot."
Let's explain with an analogy:
a) Core Logic is "Inferring the Whole, Not Judging the Sample"
The purpose of sampling inspection is not to conclude on these 200 samples, but to use the condition of these 200 samples to scientifically infer the quality level of the entire batch (e.g., 10,000 pieces). AQL=2.5 means: We set a standard, hoping that for batches judged as acceptable, the actual defect rate of the entire lot has a probability greater than 95% of being no higher than 2.5%.
b) Why is a 5% defect rate allowed in the sample?
This reflects the "sampling risk" and "confidence level" in statistics. To work efficiently with a reasonable sample size, sampling plans allow for certain risks. Even if the true defect rate of the entire lot is exactly 2.5%, the number of defects in our sample of 200 has a probability of fluctuating higher (e.g., 5%). This sampling plan (200 pieces, Ac=10, Re=11) is designed to balance the risks for the producer (good lot wrongly rejected) and the consumer (bad lot wrongly accepted), achieving an internationally recognized balance.
c) The True Meaning of "Acceptance Number Ac=10"
When you find 10 or fewer defects in a sample of 200, this result does not say "the defect rate of the entire lot is 5%." It says, "Under the preset statistical risk, there is insufficient evidence to prove that the defect rate of the entire lot exceeds the 2.5% upper limit," therefore it is judged as "Accept."
Conversely, if 11 (Re=11) or more defects are found, then statistically there is sufficient confidence to say that the quality of the entire lot is likely worse than the AQL 2.5 standard, therefore it is judged as "Reject."
In summary:
i. You are correct: Under AQL 2.5, inspecting 200 pieces allows for up to 10 defects (5%) in the sample.
ii. This is not contradictory: AQL 2.5 is not the standard for the sample defect rate, but a statistical threshold for the quality level of the entire lot. The 5% defect rate in the sample is the decision-critical point set under this statistical rule to judge whether the entire lot is likely better than the 2.5% threshold.