Sampling Spreadsheet to help determine the Sample Size for Sampling Plans

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capnkrk

#41
Every time you change the AQL or lot size, you have a different chance of accepting lots of a specific quality.
Tim F
I'm waaaay confused here. I thought the whole premise of this was that the lot size did not matter as long as your sample was <10% of the lot size.




.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#42
you are correct (some references say <5% of the population...)

However, if you are using the Mil-Std or derivative ANSI tables everytime you 'change' the lot size (enough) those tables will take you to a different sample size which will change the actual odds.

My recommendation is always to stay away from these tables and use the direct calculations...
 
C

capnkrk

#43
Does the spreadsheet 'max out' above a certain sample size? With AQL=2, UQL=5, alpha=1, beta=5, a sample size of 500 is unacceptable (AC and RE =17). The plan becomes acceptable with a sample size of 1000 where AC=30, RE=31. As I increase sample size to 2K, 3K, 4K, etc, the AC/RE numbers remain the same. This is a little counter-intuituve since I would expect the allowable reject tally to climb with the sample size.

I work for a printing company, and I'm trying to set up a meaningful AQL and sampling regimen for some larger orders (>50K). It seems to me if I inspect 10% of a large order, I should be allowed a larger reject tally than 30 labels. We print these labels on rolls, so the web-based nature of the product is giving me some headaches as well.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#44
the spreadsheet does truncate at a c=30 level
you can fix this by copying the data cells (A13:G13 down), ensure the # defects cells increments by one and adjusting the range for the calcualtions in F11 and G11.

However, the effectiveness of sampling plans are not based on lot size.
a common misconception is that you get consistent coverage if you use a consistent percentage of the lot as your sample size...you actually do not.

For lot acceptance (after the lot is complete) you get effectiveness (consistency of detection) by using a constant sample size, a realistic alpha/beta and AQL/RQL and by samplign the lot randomly.

If you are trying to monitor the lot during production to detect defects and correct them before the entire lot is jeopardized you need a different sampling approach.

can you elaborate on what you are trying to accomplish with your sampling plan?
 
C

capnkrk

#45
Thanks for the help!
There are certain defects in the rolls of labels that do not manifest until 24 hrs after production. So if we have a run of 150K labels, we want to sample a percentage to determine the lot acceptability. The problem is that the rolls do not match the exact sample size recommendation, and it's difficult to inspect exactly '315' labels in a roll of 500.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#46
Thanks for the help!
There are certain defects in the rolls of labels that do not manifest until 24 hrs after production. So if we have a run of 150K labels, we want to sample a percentage to determine the lot acceptability. The problem is that the rolls do not match the exact sample size recommendation, and it's difficult to inspect exactly '315' labels in a roll of 500.
Just a few ideas to consider

It is not the NUMBER of samples but how those samples are collected. If you know that certain defects do not manifest till later in the run, sample 100 at beginning, middle and end for a total of 300. Another idea is to sample every 500th lable in the 150K for a sample size of 300.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#47
Thanks for the help!
There are certain defects in the rolls of labels that do not manifest until 24 hrs after production. So if we have a run of 150K labels, we want to sample a percentage to determine the lot acceptability. The problem is that the rolls do not match the exact sample size recommendation, and it's difficult to inspect exactly '315' labels in a roll of 500.
Hmmm. How are you defining a lot? Is it a roll? Or is is the batch of 150k?
 
C

capnkrk

#48
A lot is the entire run of 150k. A roll could be anywhere from 500 to 1000 depending on the label itself. If we're mounting a whole roll of 1000 for AQL inspection, it's just as efficient to inspect the entire roll rather than the 315 sample size recommendation for that lot size: it still has to be rewound so you may as well inspect it.
 
S

Stanley110

#49
The calculation are based on a binomial distribution, which assumes that the sample is small compared to the lot size (say the sample is 10% or less of the total lot). If this is not the case, then the sampling plans listed will be tighter than the alpha & beta that were inputted.

For example, if the spreadsheet says to use Ac=2 for a sample size of 130, but the lot is only 200 total, then you will be much better at accepting good lots and much better at rejecting bad lots than you predicted. If the lot size is 2000, then the predictions should be quite good.

In fact, given the numbers in the example, it would be impossible to reject a good lot for a lot size of 200, since Re=3 and the worst possible good lot would have 1% of 200 = 2 bad pieces. As the lot size increased, the odds of rejecting it would increase toward a maximum of 5%.

The next stage would be to make a new version based on the hypergeometric distribution. This would work better for small lots, where the sample size would likely be a large % of the total lot.

Tim F

P.S. It looks like Statistical Steven was half a step ahead of me in responding about lot size. :)
Yes, the hypergeometric that involves the lot or population size is important for sample sizes for inspecting isolated (single) lots. The binomial is suited for sample sizes for inspecting a continuing series of lots, for example, an incoming raw material. It is important that we sample with replacement which is approximated by keeping the sample below 10% of the population because every unit in the population must have an equal chance of being selected. The hypergeometric with population size addresses these requirements. Have you prepared an Excel sheet based on the hypergeometric? The hypergeometric allows one to determine the upper confidence bound of the number of defective units in the lot or population. Some people are conservative and use a sample size to assure a maximum number of defective units in the isolated lot or population at high confidence.
Regards,
Stan Alekman
 
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