This article goes into the details of setting the sampling level when multiple AQLs are in use. For example if you wish to use 2.5 for Major defects and 4.0 for Minor defects which is very common.
The article assumes some familiarity with AQL, please refer to our Blog post for an introduction.
First, we will describe the way most companies use AQL: As an example we use AQL 2.5 / 4.0 Level II. This means General inspection level II and AQL 2.5 for Major and AQL 4.0 for Minor defects. For the example we use a lot size of 50.
In the code letter table this gives us D:
When looking up code D we hit an up arrow and a down arrow for the AQLs:
According to the ISO standard, you should then adjust the sample size by following the arrows. However, since we have two different AQLs we would like to cover in one inspection, the normal approach is to take the thresholds from where the arrows point. In this case we will accept 0 major and 1 minor defect and keep the sample size at 8.
This is the normal way of interpreting the AQL for consumer packaged goods inspections and the one used by default in Qarma.
However, the ISO 2859-1 standard actually addresses the situation when several classes of non-conformities with different AQLs are combined in section 10.3:
Qarma has implemented the option for our customers to select to follow a different approach for the sampling selection which better aligns with the text in the standard.
However, this can lead to significantly inflated sample size as illustrated with the next example. Taking AQL 1.0 / 2.5 Level II and a lot size of 50 again. The letter will be D:
When looking up D in the AQLs, we land again an up and down arrow:
Following the text in the standard, we should increase the sample size in this case, so we follow the arrow down to letter E:
However, this brings us to yet another arrow for AQL 2.5. Since there is no AQL limits for 2.5 for letter E, the standard does not really help us here, if we want to maintain AQL 1.0 / 2.5. The text in section 10.3 mentioned above does not address this situation, so we have to take a decision on how to proceed. Option A: We can then increase the sample size once again to follow AQL 2.5 arrow which points down to letter F:
For AQL 1.0 it will land another arrow, and we could continue shifting between F and E forever. The only way to end on a sample code which is not an arrow will be to go to letter H:
For letter H, there is a value for both AQL 1.0 and 2.5, so the statistics behind the AQL standard are correct. But the sample size is huge (50 pcs) compared to the starting point (8 pcs), which most will agree is too big a cost and unpractical for most inspections (remember the lot size of this example was 50 pcs).
In order to balance this approach, Qarma has decided on option B: Follow the arrows for the most stringent AQL and then inferring approximate limits for the rest of the AQLs. Using the same example as above, we would stop at letter E, since the arrow for 1.0 (the most stringent AQL) leads down to E:
For AQL 2.5 limits, we will follow the arrow and accept 1 minor defect. Although this is not fully consistent with the underlying probabilities that the standard is built upon, we believe this is the best way to follow the ISO 2859-1 standard, given the ambiguity it leaves for the mixed AQL cases which are very common for consumer packaged goods.