Designing a Sampling Plan - AQL

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#11
Hello again,
Thanks you all for your support i have now lot of links and information to dig in. Bev D, i started to check your excel files you sent to me and i have 2 questions regarding one of them.
Regarding "Excel document: "Confidence Intervals Cpk Process Capability.xls",
- Can you please define "Error". Is it acceptable defect rate , 'accepted' 10 % of the time - or rejected 90% of the time.
-Can you also explain the difference between "CPK not less than" and "CPK min"?
- You wrote "for example if you want a Cpk of 1.67, and a 95% confidence (alpha) with an acceptable error rate of .1 then your sample size is 408." But if i choose a larger sample size than 408? For example 462, do i have 96% confidence (alpha)?
-
 
My colleague and i discussed if you also have an excel file for conversion of Cpk to PPM?
 
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Statistical Steven

Statistician
Staff member
Super Moderator
#12
Here is a PPM to Cpk/Ppk and Cpk/Ppk to PPM coversion


Hello again,
Thanks you all for your support i have now lot of links and information to dig in. Bev D, i started to check your excel files you sent to me and i have 2 questions regarding one of them.
Regarding "Excel document: "Confidence Intervals Cpk Process Capability.xls",
- Can you please define "Error". Is it acceptable defect rate , 'accepted' 10 % of the time - or rejected 90% of the time.
-Can you also explain the difference between "CPK not less than" and "CPK min"?
- You wrote "for example if you want a Cpk of 1.67, and a 95% confidence (alpha) with an acceptable error rate of .1 then your sample size is 408." But if i choose a larger sample size than 408? For example 462, do i have 96% confidence (alpha)?
-
 
My colleague and i discussed if you also have an excel file for conversion of Cpk to PPM?
 

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Bev D

Heretical Statistician
Staff member
Super Moderator
#13
Thanks Steven!
I've also attached a larger spreadsheet that has Cpk to ppm conversions as well as other indices. you might find this helpful.

as for the questions concerning the Cpk spreadsheets:
- the error is the amount of 'inaccuracy' you want in the Cpk estimate. the smaller this number is, the larger the required sample size.
- the confidence sets the 'precision' of the estimate and will control the confidence intervals. the more precise the estimate (the higher the confidence) the larger the required sample size.

The min Cpk is the lower confidence limit for the intended Cpk. This is an estimate of what might happen before you get any results. For example if you are trying to determine if you have a Cpk of 1.33 with an error of .15 and confidence of 95%, the spreadsheet will give you a sample size of 120. If you really have a process at 1.33 and you use the sample size indicated (120) you could conceivably get an actual result as low as 1.151 or as high as 1.509.

Once you get results, the 'not less than' column is used: If your actual result is 1.33 then in all likelihood the true value is not less than 1.18
 

Attachments

B

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#14
Thanks Statistical Steve and Bev D
I made som tests on my own just to increase my knowledge about how confidence interval is related to sample size. I randomly selected pieces from a existing batch and started with few sample size.
Before we measure the parts we decided that:
Desired Cpk=1.2 (159 PPM, One sided tolerance)
Confidence 95%
Error: 0,15
From the excel document: Sample Size 100
Cpk min:1,021 Cpk max: 1,379


Calculated Cpk in mintab 17
Sample Size: 5 =>Cpk: 0,71
Sample Size: 20 =>Cpk: 0,85,
Sample Size: 50 =>Cpk: 0,91,
Sample Size: 100 =>Cpk: 0,97, From excel doc. (Cpk min=0.82, Cpk max=1.12 , Cpk not less than: 0,844)
What conclusion can i take from this? My actual result is 0,97 and true value is not less than 0,844. Is that correct?

 
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B

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#15
I really appreciate if some one could reply on the above.
1) My actual Cpk result is 0.97 from my sample size of 100 but the true value is not less than 0,844?
2) And PPM is then 5671 based on 0,844 and one sided-tolerance?

If i study the Cpk from low selected pieces of just 5 to increased number of pieces, up to 100 pieces i can see that Cpk increased from 0,71 to 0,97. The tricky part is how represented the Cpk=0.97 is compared to the whole batch of 5000 pieces. If i calcultate with Cpk=0.844 and PPM=5671,can i say that 28 pieces from the batch of 5000 is out of tolerance?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#16
1) My actual Cpk result is 0.97 from my sample size of 100 but the true value is not less than 0,844?
yes, that is correct. there is always error in any sample - only 100% is 'accurate'. (although technically, the confidence intervals are only a measure of the precision of the estimate and not the accuracy. It is wrong to say that the true Cpk is not less than .844, but since this distinction is lost on so many people - such as auditors - it is not a bad thing to claim)

2) And PPM is then 5671 based on 0,844 and one sided-tolerance?
yes. OR you can use the actual estimate instead of the worst case estimate...
If i study the Cpk from low selected pieces of just 5 to increased number of pieces, up to 100 pieces i can see that Cpk increased from 0,71 to 0,97. The tricky part is how represented the Cpk=0.97 is compared to the whole batch of 5000 pieces. If i calcultate with Cpk=0.844 and PPM=5671,can i say that 28 pieces from the batch of 5000 is out of tolerance?
theoretically yes. BUT for this to be accurate, you must have a truly random sample from the lot of 5000 AND you must have a Normal distribution. even symmetrical bell shaped distributions often deviate substantially from the theoretical Normal in the tails - where few values truly reside. most distributions are truncated and the theoretical Normal model has infinite tails - so you are most likely overstating the defect percent.

sorry - I'm sure you want a definitive accurate and precise answer - but those simply don't exists in real life.
 
J

JohnStewart

#18
As soon as you know all parameters you want to set you can try AQL Calculator app on google play market from blueSkyCorner.

It's really useful

Cheers
 
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