C=0 Zero Acceptance Number Sampling Plan - Question

V

vphan27

#1
My question is in regards to the statistical derivation of the sample size numbers in the Zero Acceptance Number Sampling Plan table by Nicholas Squeglia. I am unable to link to the sampling table my manufacturing company is using, but it can be seen if you copy and paste the following in your internet search bar: guidebook.dcma.mil/226/tools links file/stat-sample

Can someone please elaborate on how all the sample size numbers in the table are calculated? What statistics formula is used to calculate the sample sizes for a given lot size and AQL value?

For example for a lot size between 16 to 25 and AQL of 1%, the table says a sample size of 13 should be used. My question is what statistics equation/formula is used to calculate that 13 is the appropriate sample size for this given lot size and AQL? How is this calculation performed?

I understand how to use the table, however I want to understand where the numbers come from. If someone can please provide a detailed explanation I would truly appreciate it. Thank you.
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
There is a similar discussion happening on the ASQ "Ask a QA Professional" board there.

I did look up a table reference there, and it appears that the very large lot size calculations correspond to a binomial distribution at a 64% level of significance.

I've found sniffs on the internet that the finite lot size calculations are based upon hypergeometric distribution. But you run into a problem that the hypergeometric can only be calculated for integers (expected number of defects). There is a claim that some form of regression was used to generate the OC curves, and determine the non-integer calculations.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#3
So are you the "Van Phan" on the ASQ board?

The key does seem that the table is based upon a relatively low level of significance, around 70%. I assume the sample plan assumes repeated sampling over time that will increase the level of significance with time.
 
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