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Author Topic:   Sampling Plans
Richard K
Lurker (<10 Posts)
posted 01 June 1999 04:26 PM     Click Here to See the Profile for Richard K     Edit/Delete Message
I realize that this is an old thread, but I was just browsing through and noticed the following which does not seem quite right:

quote:
My apologies for the delayed response, but work has been hectic. The sample size should be based on the percentage nonconforming, either historically or as a maximum tolerable proportion nonconforming. The formula I normally use is:

n = [p*(1-p)]*[(Z/E)^2] Where:

p = historical or maximum tolerable proportion nonconforming

Z = Z Value for your confidence factor for the estimate(typically 95% confident, so Z = 1.96)

E = Tolerable Error in your estimate of sample size (example, 2% or 0.02).


If you were to use p for your maximum tolerable proportion nonconforming the formula would give you smaller sample sizes as you tightened your tolerances. If my memory serves me correctly, p = the historical or estimated proportion nonconforming, and E = the tolerable proportion nonconforming. - Of course, my memory could be wrong

Don Winton
Forum Wizard
posted 02 June 1999 01:06 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message
There are various procedures for calculating sample size, depending upon your application and methods. The one I gave is for attribute data. The equation I cited above is from "Handbook of Statistical Methods in Manufacturing" by Clements (pp. 43), the "CQE Primer" by the Quality Council of Indiana (pp. XI-10) and "Statistical Techniques in Business and Economics" by Mason (pp. 379-385). The latter reference gives the derivation of the equation (although you have to search through the text for it), for those interested. While the variable definitions above are from Clements, the "CQE Primer" does give slightly different ones (below):

E = The desired proportion interval
p = Proportion rate

"Statistical Techniques in Business and Economics" gives the following definitions for p and E.

E = The maximum allowable error the researcher will tolerate.
p = The estimated proportion based on past experience, or a pilot survey.

From the references, Clements uses 'p' and the other two use 'p-bar' as the variables. While I prefer p-bar, my original post was from Clements, so it used his variables and definitions.

quote:
If you were to use p for your maximum tolerable proportion nonconforming the formula would give you smaller sample sizes as you tightened your tolerances.

The sample size goes down as the "tolerable or maximum" percentage nonconforming goes down. The equation does not consider tolerances in its calculation of sample size. The smaller the number of nonconforming items in the lot, the required sample size to accept or reject the lot goes down, as I understand its use. Of course, there are other things to consider when selecting sample size, but these are covered well in the references and would be redundant here.

quote:
p = the historical or estimated proportion nonconforming, and E = the tolerable proportion nonconforming.

As you can see from above, the published references gave different definitions. I am sure other definitions exist elsewhere as well.

Does this help, or did I just muddy the water?

Regards,
Don

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Richard K
Lurker (<10 Posts)
posted 02 June 1999 04:34 PM     Click Here to See the Profile for Richard K     Edit/Delete Message
Don, This is where I get confused

quote:
The sample size goes down as the "tolerable or maximum" percentage nonconforming goes down. The equation does not consider tolerances in its calculation of sample size. The smaller the number of nonconforming items in the lot, the required sample size to accept or reject the lot goes down, as I understand its use.

To me, 'tolerable percentage nonconforming' is a tolerance and is not the same as 'historical percent nonconforming'. I agree that if you use p as it is intended as the historical or maximum expected percentage nonconforming then as p decreases, the sample size required will decrease. However, if I read 'maximum tolerable' then I will say to myself, "OK, I can tolerate a maximum of x% nonconforming, so I will need a sample size of y" and this will give a wrong answer since as you lower x, y will also decrease. It seems to be just a difference in terminology, but I find the inclusion of 'tolerable' in the definition of p to be misleading. I think that instead of

p = historical or maximum tolerable proportion nonconforming

I would word it

p = maximum of historical or tolerable proportion nonconforming

and that way one would be sure to have a sample size appropriate to measure the proportion nonconforming with the desired level of confidence.

My memory was definitely wrong on E. It is indeed the max. allowable error, and not the max allowable nonconforming.

Thanks for your post. It has helped clarify my understanding.

Don Winton
Forum Wizard
posted 03 June 1999 12:40 AM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message
quote:
It seems to be just a difference in terminology, but I find the inclusion of 'tolerable' in the definition of p to be misleading.

Yea, I see your point. I like your wording better.

This leads to a point that has been a sore spot with me for some time. Various reference material (including the ones I cited above) cannot seem to agree on terminology. I agree with your statement and will re-word Clements material accordingly.

Regards,
Don

------------------
Just the ramblings of an Old Wizard Warrior.

Check Out dWizard's Lair:
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Don Winton
Forum Wizard
posted 03 June 1999 12:50 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message
As a reminder, anyone interested in sampling should look at:

www.samplingplans.com

Regards,
Don

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