We are having an interpretation issue regarding the ANSI/ASQ Z1.4:2008 standard with some of our component vendors. We have a number of different defects that fall into an AQL of 1.0.
Please note that the same question applies to all AQL levels, as our critical and minor defects can also have multiple defects.
Our interpretation of the standard is that if the sampling plan table (based on sample size and inspection level) shows Accept 7 / Reject 8 then all defects in this major category would be cumulative for the accept / reject criteria. (i.e. 3 that fail outer diameter, 3 that fail height of the bottle finish and 3 that fail weight – total of 9 – would constitute a rejection of the lot). The vendor’s interpretation is that each of the items within the major category should have an accept / reject allowance of 7 / 8 (so potentially, in this case, 56 defects would still be accepted).
In this case, it depends on the question the lot sampling is trying to answer. If they want to know if individual units within the lot are acceptable – based on all criteria that is considered acceptable, then the tally of all defects found is correct. This is further supported by any item with one of the many specifications out of range would be deemed a failure.
On the other hand, if the lot sampling is to detect lots with specific faults, isolated to a specific specification then the defect types would be considered separately. If the AQL 1.0 is suitable for the specific defects, then considering them separate for the 8 criteria would no longer be an overall ASQ 1.0 protection; it would be much less.
Your example of 56 defects being accepted underscores the point that the AQL protection is no longer 1.0.
I’m assuming the specifications and causes of the defects are independent, yet that may not be the case. When not independent I’m not sure how to adjust the sample size to a present the same AQL protection. When independent you would need separate draws of samples for each defect of interest, then apply the Accept 7/Reject 8 criteria judging only the one specification.
In practice, if you want to inspect for isolated specifications, one should allocate the acceptable AQL and LPTD points and develop your sampling plan from there. Instead of a 1.0% defect rate for AQL it would need to less for one of the Reject 8 specifications; try 0.125 so that the tally of failure rates across the various specification of interest (assuming the possibility of failing any specifications is equal). This will lead to much larger sample sizes that may be useful when troubleshooting specific faults.
For more on this topic, please visit ASQ’s website.