Constructing an AQL matrix for our QC operators in a flexographic printing outfit

C

capnkrk

#1
Hi, I was hoping for a little advice...

I'm trying to construct an AQL matrix for our QC operators in a flexographic printing outfit. We operate at roughly 3 sigma, which is ~93% yield and fairly standard for our industry.

Our sample size will be 10%, and I need a matrix showing pass/fail levels for different ranges of sample sizes, i.e.

100-500
500-1000
1000-5000
5k-10k, etc.

I'd like to do it in the context of Tim's spreadsheet found in another thread that I can't link to due to forum rules, using an AQL of 7 and UQL of 8. Alpha and beta should be around 5.

My question is, how wide should the sample size ranges be for this to be meaningful? The ISO 2859 standard has huge ranges (35k-150k, 150k-500k) that have the same sample sizes and pass/fail thresholds. It's pretty counter-intuitive to this SSGB that 7 failures in a 150k lot is the same acceptance level as 7 failures in a 500k lot.

I'm feeling very stupid, please help.

:thanks:
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
Remember sample size accuracy is not dependent on the lot size (unless the lot is very small)

Also remember that it isn't 7 failures in a 150k lot vs 7 failures in a 500k lot. it's 7 failures in the same size sample from either a 150k lot or a 500k lot. accept/fail is based on the number of defects in the sample...

you seem to be mixing two approaches: use a 10% sample size then try to use Tim's approach for accept numbers that is based on a different approach for determining sample size...the two can't be used together...

There is a way to relate the sample size you end up taking to an adequate acc/rej number and I can noodle on that over night if you still want to stick with a 10% sample size. (I don't recommend it by the way but)
 
C

capnkrk

#3
Thanks for the reply. The 10% sample size was imposed on me from above, and from what I had read, the spreadsheet was valid as long as the sample size was small, 10% or less than the lot size.

Maybe I framed my question incorrectly, I don't get why the same sample size is statistically valid for two numbers that are so far apart (150k vs 500k), and also why larger sample sizes seem to be discouraged. In our case, inspecting 1000 labels is just as easy as inspecting 100 since they are labels on a roll and need to be rewound anyway.

Thanks again for your insight!
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
OK - Tim's spreadsheet caution about a 10% or less sample size is this:
IF the lot is small or if we are taking a rather large sample, we need to utilize a lot size correction factor to determine the true probability of detecting any specific defect rate. It is not a reference to a % based sample size.

statistically (actually probability) based plans that determine the appropriate sample size for a given AQL or RQL only require the alpha and beta probabilities and the AQL & RQL defect rates. THEN the formulas calculate the appropriate sample sizes and Accept numbers.

The reason that lot size doesn't matter (unless the lot is ~< 50 or the sample size is fairly large for the lot size) is that the accuracy (more correctly the precision) of the sample size in estimating the defect rate is based only on the defect rate & the desired 'precision' or confidence level and nothing else.

+/- precision = z_alpa/2*sqrt[p*(1-p)/n]
where z_alpha/2 = the z score for your alpha risk. (there is also a formula that incorporates beta but this gives you the idea. Lot size simply doesn't matter.

There will be a range of sample sizes that have the same accept number as the accept number is based on the probability of getting x number of defects in a sample of size n when the true defect rate is p. There are discontinuties in the accept number because: the accept number is an integer and the probabilities increase incrementally in fractions of an integer...

You do have a real dilemma with the web based label rolls and inspection. I understand the thought about inspecting more than the predetermiend size because it's easy and right in front of your face, BUT it does make the accept number difficult to calculate.

I'm sorry that the sample size of 10% was dictated to you but it is not a statistically sound approach - you will get varying levels of protection for both your AQL and RQL levels...and if you allow the sample size to vary substantially - several hundred units at a time - you will also get varying levels of protection. You can use a version of Tim's spreadsheet that I added several tabs to. One tab is named OC curves. in this tab you can enter any sample size and accept number you want and it will generate the probability of rejection for that n/Accept number. You can plot up to 5 curves simultaneously for comparison.
OC Curve Spreadsheet

To determine your AQL go to 1-alpha on the y axis and draw a horizontal line to intercept the curve(s). At the intercept(s) draw a vertical line down to the x axis and that defect rate is the AQL. The same procedure can be done for the RQL using 1-beta on the Y axis.

I hope this provides a start for you...
 
C

capnkrk

#5
Thanks Bev, I'm sure it will take this weekend to digest this. I very much appreciate you taking the time to explain this to me!
 
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