A
Atish
Can someone explain how the sample sizes in an AQL table are calculated? In other words what is the math behind the calculating sample sizes for a given lot size and AQL level?
AQL Sample Sizes - Explain how Sample Sizes in an AQL table are calculated
Tim Folkerts
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I wish I could answer, but as far as I can tell, there is no simple mathematical formula for determining the sample size. (That is one of the reasons I would scrap the whole system and start from scratch.)
From a purely mathematical perspective, the lot size has very little to do with the sample size. Whether your lot is 1000 or 1,000,000, a sample of 100 pieces will give the same confidence.
It seems that the tables are based partly on math, and partly on perceived risk. For instance, accepting a bad lot of 1,000,000 carries a greater financial risk that accepting a bad lot of 1,000. So the tables call for a bigger sample to decrease the risk of accepting a bad lot.
From a purely mathematical perspective, the lot size has very little to do with the sample size. Whether your lot is 1000 or 1,000,000, a sample of 100 pieces will give the same confidence.
It seems that the tables are based partly on math, and partly on perceived risk. For instance, accepting a bad lot of 1,000,000 carries a greater financial risk that accepting a bad lot of 1,000. So the tables call for a bigger sample to decrease the risk of accepting a bad lot.
A
ARTEMIS
The sampling plans are based on mathematical equations focused on the amount of risk you are prepared to take. Looser AQL are used if you have good quality history with the particular part in question. You can determine what your risk level is and then choose the AQL based on past performance. If your subject part has consistently been rejected during incoming inspection then you need to tighten your AQL.
The math is tedious and can only be solved by iteration/trial and error.
Basically you have to equate two equations of probability density functions and find the sample size that would satisfy both the consumer's risk and the producer's risk.
It's so tedious to do by hand so I decided early to forget about it.
A Larson Nomogram can give you approximate results with less effort.
PS:
Tim is right. You have to define first two risks: The Consumer's and the Producer's. Then equate the two equations.
Basically you have to equate two equations of probability density functions and find the sample size that would satisfy both the consumer's risk and the producer's risk.
It's so tedious to do by hand so I decided early to forget about it.
A Larson Nomogram can give you approximate results with less effort.
PS:
Tim is right. You have to define first two risks: The Consumer's and the Producer's. Then equate the two equations.
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It is also essential to understand that the original AQL tables (which haven't significantly chagned if at all) were a result of statistics AND negotiation when they were formed.
The mil-std based AQL tables are a sham and should either
The mil-std based AQL tables are a sham and should either
- be used by rote because they are easy and uninformed customers accept them without thought.
- be scrapped and develop your own plans. There are some good iterating spreadsheets out there to use for this purpose.
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