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Author Topic:   Sampling Plans
Dawn
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posted 20 March 1999 10:17 PM     Click Here to See the Profile for Dawn   Click Here to Email Dawn     Edit/Delete Message   Reply w/Quote
Wanna talk sampling plans? I know. I read and read and I just don't get it. Wish I was born with a statistics mind. How do you determine the OC curve in the first place? I don't see the sample size anywhere on the OC curve samples I have looked at and I don't see any explanation on how they get it on there. Lost again....

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Batman
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posted 21 March 1999 09:05 PM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
Dawn, I cannot answer you specifically, since I am also continually puzzled by statistics beyond Xbar and sigma, and histograms. However, Stan Hilliard has a sampling plan website called www.samplingplans.com. He also sells software there. I have never seen the software and am not promoting it, but he does have some info there.

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Don Winton
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posted 22 March 1999 12:22 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
Wanna talk sampling plans?

I personally am not a big fan of sampling plans, but that is another story.

quote:
How do you determine the OC curve in the first place?

The OC curve is developed by determining the probability of acceptance for several values of incoming quality. Pa is the probability that the number of nonconforming in the sample is equal to or less than the acceptance number for the sampling plan.

There are three distributions that can be used to find the probability of acceptance: the hypergeometic, binomial and the Poisson distribution. The Poisson distribution is the preferred because of the ease of Poisson table use. Be sure you can satisfy the assumptions for Poisson use. The Poisson formula is:

P = [(e^-np)*((np)^r)]/r!

n = Sample Size
p = Proportion nonconforming
r = Number of nonconforming or less

Assume n = 150 and r = 3, (called c in sampling plans) then:

Lot Percent Nonconforming
1%, np = (150)(0.01) = 1.50, P(r <= 3) = 0.93
2%, np = (150)(0.02) = 3.00, P(r <= 3) = 0.65
3%, np = (150)(0.03) = 4.50, P(r <= 3) = 0.34
4%, np = (150)(0.04) = 6.00, P(r <= 3) = 0.15
5%, np = (150)(0.05) = 7.50, P(r <= 3) = 0.06
6%, np = (150)(0.06) = 9.00, P(r <= 3) = 0.02

You then construct the table from these values with Lot Percent Nonconforming as the X value and Pa as the Y value.

Hope this helps.

Regards,
Don

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Don Winton
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posted 22 March 1999 02:55 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
Dawn,

Oops. Forgot something. I detailed the distributions to use, but forgot to describe when to use them. Here we go:

Binomial Probability Distribution: Applies when the population is large (greater than 50) and the sample size is small compared to the population, generally less than 10%.

Poisson Probability Distribution: Is an approximation to the binomial when P is equal to or less than 0.1 and the sample size is large. (I prefer this one).

Hypergeometric Probability Distribution: Whenever the sample is drawn from a smaller, finite lot. This calculation is a bear, but spreadsheets and computers make it easier these days.

Then, there is always the normal distribution. It can be used as a probability distribution as well when the population size is large.

The above are general guidelines. There are no firm, fixed rules when to use one or the other. My suggestion would be to balance time versus benefit in the calculations.

Generally, the sample tables in MIL-STD-105 are statistically valid, even though the document itself is obsolete. Rather than design sampling plans from scratch, I suggest, if a sampling plan is used, design it from these tables.

Regards,
Don

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Woraphot
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From:Ayuttaya,Thailand
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posted 23 March 1999 02:18 AM     Click Here to See the Profile for Woraphot   Click Here to Email Woraphot     Edit/Delete Message   Reply w/Quote
According to QS-9000 3rd edition Element 4.10 Inspection and Testing "4.10.1.1 Acceptance criteria for attribute data sampling plans shall be zero defects........"
Does it mean that Mil-std-105 can not meet to QS-9000 requirements on this item? Because of it allows acceptance not zero defects depend on AQL level and Lot/Batch size.
Please advise your opinion.
Thanks,

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Don Winton
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posted 23 March 1999 11:37 AM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
Woraphot,

I do not do the QS thing, but I think what they are talking about might be this. The tables contained in MIL-STD-105 contain Ac and Re codes. If you use one of the tables from this standard, you must use an Ac of zero and an Re of one for the plan. Perhaps some QS folks could expound on this.

Regards,
Don

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Marc Smith
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posted 23 March 1999 12:28 PM     Click Here to See the Profile for Marc Smith   Click Here to Email Marc Smith     Edit/Delete Message   Reply w/Quote
I've never set up a Zero Defects plan for attribute sampling - sorry I can't help. Maybe Howard has addressed this issue.

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Batman
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posted 23 March 1999 07:42 PM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
I believe 4.10.1.1 is refering to the acceptance criteria, not the sampling itself. The attribute gage (in this case, a "hard" gage) must not allow any defects to pass. Your sampling plan - size, frequency - is up to you, as long as it is adequate. Any other attributes - color, flash, chips, for example, that are visually inspected must have "border" examples agreed to by your customer

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Dawn
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posted 25 March 1999 08:24 PM     Click Here to See the Profile for Dawn   Click Here to Email Dawn     Edit/Delete Message   Reply w/Quote
I agree with Batman,
Use your Mil-Std and do not accept. You can also use a C=0 table which is much easier. My concerns are we + you need to be able to justify what sample plan you use and I can't get through the OC curves. I have studied what everyone has told me and I still don't get it. Maybe its the blonde hair....(I left myself wide open on that one).

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Don Winton
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posted 25 March 1999 08:54 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
Dawn,

Can you give a specific example of exactly you are looking for? I could supply all I have on OC curves, but it is WAY too long.

Regards,
Don

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Woraphot
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posted 25 March 1999 10:25 PM     Click Here to See the Profile for Woraphot   Click Here to Email Woraphot     Edit/Delete Message   Reply w/Quote
May I give an example that we are currently using sampling plan method of Mil-std 105 on visual inspection for attribute data at sampling plan 0.4% AQL normal inspection single sampling level 2. Our lot size =6000 pieces. Based on the rule of Mil-std 105,the sample size for inspection shall be 200 pieces and accept=2 pieces,reject=3 pieces.
At this point, I am not sure whether it satisfies QS-9000 requirements,4.10.1.1

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Batman
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posted 26 March 1999 08:40 PM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
Hi Woraphot.
4.10.1.1 requires "Acceptance criteria for attribute data sampling plans shall be zero defects."
So, whatever attribute sampling 'plan' you set-up, it must be set-up with zero defects only.

Accepting 2 defects is is not acceptable in this regard.

This is not to say that someday a bad part may escape, but your sampling plan better be established to allow no rejects.

By the way, when I refer to attributes I mean go / no go type features. Color, texture, chips, flash, etc that are usually visually inspected must have "border" samples and your inspectors must reject anything that crosses the border.

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Dawn
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posted 27 March 1999 05:03 PM     Click Here to See the Profile for Dawn   Click Here to Email Dawn     Edit/Delete Message   Reply w/Quote
In regardsto Oc curves, do you randomely pick a sample size, and how do you determine what the percent defective is? I understand the bottom of the curve id LTPD and it goes up to 10% to allow 90% confidence level. The same with the left side for percent defective. So do I just pick a sample size I think is appropriate and where do I go from there?

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Don Winton
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posted 30 March 1999 11:24 AM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
I don't see the sample size anywhere on the OC curve samples I have looked at and I don't see any explanation on how they get it on there.

Sorry, I missed that one on my first post.

quote:
So do I just pick a sample size I think is appropriate and where do I go from there?

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).

Once you estimate the sample size required and the r value, draw your OC curve using the technique I described above.

Suggestion: Set up an Excel spreadsheet to draw your curves for you based on value of n and r. Play around with the n and r values and see what happens to the curves. I used to have one, but I lost it during the hard disk crash of â98 (long story).

Does this help?

Regards,
Don

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Don Winton
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posted 08 April 1999 11:49 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
A spreadsheet that demonstrates various OC curves can be found at:

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Regards,
Don

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Richard K
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posted 01 June 1999 04:26 PM     Click Here to See the Profile for Richard K     Edit/Delete Message   Reply w/Quote
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

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Don Winton
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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   Reply w/Quote
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
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posted 02 June 1999 04:34 PM     Click Here to See the Profile for Richard K     Edit/Delete Message   Reply w/Quote
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.

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Don Winton
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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   Reply w/Quote
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

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Don Winton
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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   Reply w/Quote
As a reminder, anyone interested in sampling should look at:

www.samplingplans.com

Regards,
Don

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Charles
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posted 29 March 2001 08:04 AM     Click Here to See the Profile for Charles     Edit/Delete Message   Reply w/Quote
Hi folks,

First time around so sorry if I make a mistake in posting the message. We are now re-visiting all our sampling procedures. I have some comments and queries:

1 - Number of samples - We currently use Mil-Std and we draw from it the number of samples in accordance with the batch size and special/general levels of inspection available. So the number of samples doesn't take into account the OC.

2 - Acceptance Criteria - We, as a supplier, are moving from the use of AQL's to LQ (Limiting Quality). This is because the latter considers the specific level of defects supplied within a specific batch, whereas the AQL considers the average level of defects accepted over a series of batches. The LQ's are obtained after the evaluation of our Finished Product Specification based on the criticality of each defect. From there we work backwards to find the appropriate AQL we should agree with our suppliers in order to have them aligned with our LQ's.

3 - SPC - So for defects generated by our suppliers we will have a sampling plan at the receiving of the goods. Now, for defects produced during our internal processing, we are not totally clear about the roles of acceptance sampling vesus SPC. We thought about implementing SPC, but worry about people requesting a final acceptance sampling of the finished product too. How can we ensure that the number of samples taken for SPC will satisfy an acceptance sampling plan?

Regards,

Charles.

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