I'm looking for a sampling plan/table to determine sample size and inspection frequency based on a given rate of production. For example, a process produces 500 pieces. How many pieces should be checked and how frequently?

If you're looking for an AQL (Acceptable Quality Level), why not use the old Mil-Std-105? It's technically a canceled document (as is the way with many old military specs) but you can still use it. I know an organization 'took it over' but I can't remember who it was.

bimco,
I agree with Marc. Even tho MIL STD 105 is discontinued, the OC's and sampling plans are still statistically valid. Use these as a good guide. I recently received a post that gave guidance as to sample sizes:

n>=((Za/2*sigma)/E)^2 wher Za/2 is (1-confidence(i.e.0.95))/2. Sigma is standard deviation of the data and E is the expected Error. This is also considered the difference between the mean and your sample and the mean (estimated, maybe) of your population.

I have another equation somewhere (?) and will also try to forward this one as well.

Regards,
Don

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....

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.

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

Wanna talk sampling plans?

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

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

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,

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

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

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).

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

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

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.

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?

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.

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 ’98 (long story).

Does this help?

Regards,
Don

I realize that this is an old thread, but I was just browsing through and noticed the following which does not seem quite right:

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 :)

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.

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.

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

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

Don, This is where I get confused

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.

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.

As a reminder, anyone interested in sampling should look at:

www.samplingplans.com (http://www.samplingplans.com)

Regards,
Don

QS Auditor wants to see proof that 3 piece smaples for run charts is a statistically valid number. I have researched and pretty much proved he's right - its not. Employees feel five piece checks are too cumbersome. What to do? Thanks for any help-Dawn

Hi Dawn!
A subgroup of three may be right for you, five may be better, one may be correct also. Look at your process and determine the correct sample size and frequency. When we start a process, we take many samples in a short time, identify the assignable causes, remove or reduce them, start the process again, take less frequent samples, assess control, and so on, until the assignable causes are eliminated (or at least identified) and we know how long we can run until variation is expected to show up, thus samples are taken prior to this, for possible adjustment.

You can do this for present processes also, if needed.

I find that frequency has more to do with "control" than the sample size, except with multi-cavity tools.

Dawn,

Batman pretty much sums it up. Do not think of sample size in terms of the MIL-STD-105 mentality. Size and frequency are the keys. Show the assessor your justification in statistical terms where n=3 is valid.

Regards,
Don


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

From: ISO Standards Discussion
Date: Mon, 19 Jun 2000 11:26:19 -0500
Subject: Re: MIL-STD-105D /Khan/Westall

From: "Greg Westall"

FYI
MIL-STD-105D was revised to MIL-STD-105E May 1989 and was canceled Feb.
1995. Suggested replacement is ANSI/ASQC Z1.4

As far as a 1 page plan, I have never seen one that covers all AQL's and
Inspection Levels.

Greg Westall

<< From: "Jawad Khan"
I am looking for a one page matrix with sampling plan per Mil-STD-105D.
Can anyone send me this page? >>

From: ISO Standards Discussion
Date: Tue, 20 Jun 2000 09:31:33 -0500
Subject: Re: MIL-STD-105D /Khan/Westall/McElhiney
From: Larry McElhiney

>> From: "Jawad Khan"
>> I am looking for a one page matrix with sampling plan per Mil-STD-105D.
>> Can anyone send me this page?


I agree with what Greg says, however, many customers still have things written into their specifications like:

"All inspections will be accomplished using a Mil-STD-105D Level II 1.0 AQL (single normal)"

It is difficult to change their conceptions when we are really only talking about a statistically valid sample plan.

When we were using a C=0 plan, it was referenced to a similar plan as above, but our customers had no trouble accepting it even though it was to the "D" revision because it was, in fact, statistically valid.

Many companies still use a single page sample plan wherein they have a fixed lot size which draws them to a fixed sample size for a given AQL--this is extracted from the appropriate standards and issued by the Quality Engineer to the appropriate work areas. Since the QE can always show how the single page plan relates back to the standards, I have rarely seen it as a problem.

I think that this is the sort of support that Mr. Khan is requesting.

Just my opinion.

Larry

From: ISO Standards Discussion
Date: Thu, 22 Jun 2000 11:32:23 -0500
Subject: Re: MIL-STD-105D /Khan/Westall/Melvin

From: "Pat Melvin" colorgraphic.net

Even though MIL-STD-105E was canceled and replaced, it may be located at www.variation.com/techlib/standard.html (http://www.variation.com/techlib/standard.html)

This site also references the suggested replacement, associated ANSI standards, and ISO standards for Sampling Procedures

Pat Melvin

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.

Hi everyone,
I need some help clarifying a few things and unfortunately this is a long story but it's necessary to help with answering.

I'm currently looking into developing a variables sampling plan for a safety critical item were there is no room for accepting non-conforming items/lots of product. Failure to protect the consumer from poor quality items/lots could mean a death situation. The product in question has a lower specification limit, is destructively tested and the aim is to obviously exceed the LSL to a certain degree to provide a safety margin whilst giving a high process capability. I'm contemplating using a single sampling plan for the process average where the process standard deviation is unknown. Reason: Destructive testing is required and therefore an expensive exercise, also samples only provide estimates of the population mean and standard deviation. Another thing, keeping costs to a minimum is of importance whilst still providing protection to the consumer.

Questions:
1) Is this the right approach? If not could someone please advise of an altenative!
2) Would a chain sampling plan be better to this situation where acceptance c=0.
3) One thing I don't understand with these sampling plans is that they specify that if n samples are taken and no non-conforities are found, accept the "LOT". What is considered a lot? If I have a batch of 100 items and I test 1 in that batch, is the 100 a "LOT" size?

Thankyou for taking your valuable time to read and answer this INCREDIBLY long question.

Nick

This site http://www.variation.com/library.html has some good stuff on sampling.

This site http://www.variation.com/techlib/standard.html has some standards for download that may be of use.

Regards,

dWizard

------------------
I was better but I got over it.

Nick,

Interesting situation. Not having worked in a safety related industry I do not have a good answer for you. Never the less, I would think you should have more than just a sampling plan in place. Do you have any reliability testing or ongoing life testing in place? I would think you should be monitoring the product reliability to determine how much lies in that unacceptable tail of the population.

With regard to sampling, remember a sampling plan works on the premise of average outgoing quality levels and alpha and beta risk. AQL levels simply put you in the position of saying I am willing to accept an X probability of accepting product that has Y level of defectives.

Hi Rick,
thankyou for the prompt reply. Yes we do do additional reliability testing on the products and all is fine in that respect. I'm still not sure if I'm on the right track but I've been doing a few calc's and modelling at home and I have a reasonbly good understanding of the construction of OC Curves for sampling plans and the effects of the different parameters. One of a few reasons that made me ask the original set of questions is, "If we are testing a product that is yielding a process capability in excess of 2 and the estimated proportion non-conforming is in the order of 0.000196%, then why sample at the current level?" If all we are getting as a fraction non-conforming is 0.00196%, the probability of acceptance from the OC Curve is going to be exceptionally high. Is this a good case for reducing sample size/frequency? I'm in the opinion that it is and feel that a Chain Sampling plan (Chsp-1)would suit our situation. What is your thought on this, or anyone elses for that matter?

Thanks,
Nick

Nick,

While the chain sampling plan is certainly an option, the OC curve for a c = 0 plan is poor. The fraction defective could double or triple and your probability of acceptance will still be extremely high. If you could use a variables sampling plan you would have the advantage of better protection for the same sample size.

Rick

"Sampling Inspection Tables, Single and Double Sampling," Dodge and Romig, John Wiley and Sons (2nd Edition) 1959.

Related Threads:

QS-9000 3rd Edition Acceptance Sampling - Reduces RI (Return on Investment) (http://Elsmar.com/Forums/showthread.php?t=2020)

ISO/IEC 17025 Sampling Plans - Sampling clauses not applicable for test labs? (http://Elsmar.com/Forums/showthread.php?t=6334)

Sampling Plan (ANSI/ASQC Z1.4) - Can anyone tell me how it is made? (http://Elsmar.com/Forums/showthread.php?t=5781)

Multi Cavity Sampling Plan - MSPs (Multi-Stream Processes) (http://Elsmar.com/Forums/showthread.php?t=4352)

SMT (Surface Mount Technology) Sampling Plan in a SMT & COB Assembly Company (http://Elsmar.com/Forums/showthread.php?t=4880)

AQL and RQL Calculation for Variables Sampling Plan (http://Elsmar.com/Forums/showthread.php?t=2022)

Chain (Continuous) Sampling (http://Elsmar.com/Forums/showthread.php?t=1983)

Sampling Plans (ISO 2859-1)(BS6001-1) - Probability of defects within a lot (http://Elsmar.com/Forums/showthread.php?t=1949)

Fabric Dying - Sample Technique - Sample size to check evenness of dyeing shade? (http://Elsmar.com/Forums/showthread.php?t=1930)

Skip Lot Sampling - How to Perform Skip-Lot and Chain Sampling (http://Elsmar.com/Forums/showthread.php?t=1927)

Other links and/or comments welcome!!!

Where do i get a hold of MIL-STD-105 im new be patient :)

The updated version is Z1.4:2003. You can get it from ASQ at:
http://qualitypress.asq.org/perl/catalog.cgi?item=T004

Where do i get a hold of MIL-STD-105 im new be patient :)There are some US military standards in the Mil Stds directory (http://elsmar.com/pdf_files/Military%20Standards/) here, including mil-std-105

Thanks very much guys much appreciated:D

That is the key question....

How to statistically justify that n=3 is valid?

That is the key question....

How to statistically justify that n=3 is valid?

I think you have two different issues. I can show statistically what the risks are for a n=3 sampling plan. Only you, your customer or a regulatory body can assess if that risk is acceptable and valid.