Dear Okido,
Actually, I should probably slightly apologise for querying yr “straightforward” since I mentally translated straightforward as simple and then confused “simple” with “single” (as compared to 2-stage sampling etc) in my original comment.
This is a topic where there are an almost infinite number of fascinating cookbook procedures, some of which actually have a vaguely statistical basis like the square root thing even if unknown (and uncaring) to the user. Similar to yourself, I most frequently use a 5, 2, 1, or even 0.5 percent basis for sampling cartons of product depending on experienced variability, quantity, value and sometimes my intuitive (lack of) trust in the producer. Absolutely no statistical basis I’m sure. In the theory for the AQL tables, I seem to remember there is a delightful comment from the originators like “the relationship between the various sample sizes does not quite follow the theoretical line since we ‘empirically’ adjusted up the values for larger quantities to minimise the chance of an expensive error !” Hmmm.
I am just looking at a text on sampling petrochemicals which has this nice one – in order to ascertain with at least 95% certainty that the consignment does not contain more than x% defectives, take samples from 300/x packages selected at random, or from the whole consignment, whichever is less (the practical requirement being zero defectives found in the sample). I guess this might work for the labels also. What is an acceptable max. defect rate for not printing allergens I wonder, 0.001% ?? the result is of course that sampling cannot routinely do it, a situation similar to sampling for zero tolerance for Salmonella at equivalent levels (In fact, the typical high end sample size of 60 units / negative result gives a 95% certainty of max. 5% defective units from above formula = "free of Salmonella")
Rgds / Charles.C