Design of Lot Acceptance Sampling Plan - Zero Acceptance Number Sampling Plans

[Karen Whitehead]

My brain is almost numb from reading material on acceptance sampling plans. It seems that one almost needs to be a statistician (and I know just enough to be dangerous). I am needing a plan for inspecting received parts. Most of our incoming parts are machined. Many of the characteristics to be inspected have a variable measurement (i.e., .353 - .356). None of the characteristics to be measured are "critical."

I have purchased the book, "Zero Acceptance Number Sampling Plans, Fifth Edition." My question: Can I use the c=0 plan for both types of measurements (attribute & variable). I am thinking the variable is "go" when inside the limits and "no-go" when outside the limits. It seems to make sense to me to use the table presented in the book to determine the number to sample using an index of 1.0 on our "major" characteristics. This is less time-consuming & costly that recording and analyzing variable data.

Is this a wrong approach?

I would like any advice that I can get.

 

[Tim Folkerts]

Hi Karen, and welcome.

A couple comments ...

• AQL=1 is pretty poor. you are saying you are willing to usually accept lots with up to 1% defective (And often to accept lots with many times this defect rate!)
  
  From the ASQ Z1.4 (former Mil-std-105) with AQL =1 and c=0, you would inspect 13 parts. Looking at the OC curve, there is a 5% chance of rejecting a lot with 0.38% defective, but a 5% chance of accepting a lot with a whopping 20.6% defective! (The tables from your book may be a little different, but presumably not much.)
• It is certainly possible to take a variable measurement and convert it the way you suggest. The problem is that you are throwing out a lot of information when you change this way. A sample of 13 (as above) but with variable measurements would give you a MUCH better understanding of the incoming lot. You might check out ASQ Z1.9 (the former MIL-STD-414 which is available free here .. http://www.variation.com/anonftp/pub/milstd414.pdf)
• I had put together a spreadsheet that helps in creating your own sampling plan. You can input the defect level you are willing to accept and the defect level you want to reject; then you adjust the sample size to find something that will work. There are no specific instructions, but I think it is mostly intuitive. See this thread... http://elsmar.com/Forums/showthread.php?t=12836
  
  
• Consider SPC. If you can work with and trust the supplier, a X-Bar/R chart (or a few similar charts) would pretty much eliminate the need for incoming inspection. If nothing else, you could create control charts of the incoming lots and look for changes in average & spread. Then capability calculations would tell you how well your supplier is doing and detect changes.

Tim F

 

[Randy Stewart]

Hi Karen,
I agree with Tim (good job by the way) but I have 1 more question. If you are taking varible data, why not use it? If the measurment can be a Go/No-Go make it one.
Tim makes a good point maybe without knowing it. The MIL-STDs are great guidelines but you have to know what % or # is acceptable. Zero defects is nice but you're not going to achieve that with inspection, inspection will only protect your customers from (hopefully) a majority of the problems.
And that's not to say a particular characteristic isn't going to have a separate sampling plan (inverted deltas, etc.) all it's own.
Also, the plans are not written in stone. Prove stability and back off some. I've always liked to be front heavy and tweek the process than to fall down at the start and play catch up.

 

[Karen Whitehead]

Well, the concept of c=0 is becoming more confusing. My interpretation of Mr. Squeglia's book: (1) the c=0 plans are not AQL plans (just has a table for comparison purposes & uses an "index" #), (2) one goes to an operating curve based on the lot size, (3) if ONE defective is found in the sample, the "lot is withheld" for review and disposition.

If I have a lot size of, say, 1200 and I sample 47 pieces, I read from the chart that I have a 99% probability of accepting a lot with .02% defectives and a 10% probability of accepting a lot with 4.69% defectives.

If I samples 125 pieces, I would have 99% probability of accepting a lot with .01% defectives and a 10% probability of accepting a lot with 2.93% defectives.

Have I read this chart for lot size 501-1200 correctly? Also, I should be able to put some faith into my supplier's capability based upon my study when I approved them as a supplier.

We are a small company and do not have a full-time inspector. To take variable data on all of the dimensions that we check and enter this data into a program would be very time-consuming, and I am not sure how much added value this would provide. It seems that with the c=0 plan, rather than accepting a certain number of defects based on AQL (as the ANSI standard allows), I will be forced to make a decision on the quality of the lot if I find ONE bad part.

We will be starting to machine some parts in-house and we will indeed do SPC on these parts.

Please comment on the interpretation of the Squeglia c=0 plan operating curves.

Thanks very much.

 

[howste]

It seems that with the c=0 plan, rather than accepting a certain number of defects based on AQL (as the ANSI standard allows), I will be forced to make a decision on the quality of the lot if I find ONE bad part.

That's exactly the intent of the c=0 plan. I don't think you mentioned why you are looking at the c=0 plan to begin with, but if you are dealing with AS9100 (aerospace) or TS 16949 (automotive) then if you use sampling you cannot accept a lot with known nonconformities.

Well, the concept of c=0 is becoming more confusing. My interpretation of Mr. Squeglia's book: (1) the c=0 plans are not AQL plans (just has a table for comparison purposes & uses an "index" #), (2) one goes to an operating curve based on the lot size, (3) if ONE defective is found in the sample, the "lot is withheld" for review and disposition.

All sampling plans are based on probability and statistics. OC curves are one method of showing the probability of acceptance for a given % defective. "AQL" plans still have OC curves. The biggest difference is (as mentioned above) you can't accept a lot with known defects.

If I have a lot size of, say, 1200 and I sample 47 pieces, I read from the chart that I have a 99% probability of accepting a lot with .02% defectives and a 10% probability of accepting a lot with 4.69% defectives.

If I samples 125 pieces, I would have 99% probability of accepting a lot with .01% defectives and a 10% probability of accepting a lot with 2.93% defectives.

Have I read this chart for lot size 501-1200 correctly?

Without looking at the chart, that sounds about right.

Also, I should be able to put some faith into my supplier's capability based upon my study when I approved them as a supplier.

Absolutely. By the way, none of the standards based on ISO 9001 specifically require incoming inspection at all! If you are doing it, it's either a customer requirement or a requirement your organization has imposed on itself...

 

[Karen Whitehead]

Thanks very much for your response. It is so very nice to have someone who has a quality background to ask questions when I am "baffled."

Yes, we sample certain incoming parts because we would like to find problems, if possible, when received rather than later on the production line. We don't want to have to sing "It's a little too late to do the right thing" when we're trying to get the product out the door and find we have bad parts.

Thanks again!

 

[howste]

We don't want to have to sing "It's a little too late to do the right thing"...

I don't know that song. Can you hum a few bars?

 

[Tim Folkerts]

Well, the concept of c=0 is becoming more confusing. My interpretation of Mr. Squeglia's book: (1) the c=0 plans are not AQL plans (just has a table for comparison purposes & uses an "index" #), (2) one goes to an operating curve based on the lot size, (3) if ONE defective is found in the sample, the "lot is withheld" for review and disposition.

I have never read hios book, and in the past I have sometimes expressed doubts about c=0 plans. However, given this summary I am developing a more positive attitude.

Based on "lot is withheld for review and disposition", then this sounds in a sense like a double sampling plan. The "first sample" is designed to see if there might be a problem. If a problem is found, then further review is called for - perhaps a larger sample; perhaps a measurement of a variable instead of simple go/no-go.

I also like the idea of OC curves for making decisions. One complaint I have always had about Z1.4 is the extent to which it is NOT based on OC curves and statistics. Of the c=0 plans, my preference would be to base it on the "reject" end on the curve - decide what level of defects you want to catch 95% of the time and go with the corresponding sample size.

If I have a lot size of, say, 1200 and I sample 47 pieces, I read from the chart that I have a 99% probability of accepting a lot with .02% defectives and a 10% probability of accepting a lot with 4.69% defectives.

If I samples 125 pieces, I would have 99% probability of accepting a lot with .01% defectives and a 10% probability of accepting a lot with 2.93% defectives.

This sounds right. I posted a spreadsheet here a while back. It allows you to set various parameters and see if sampling plan is OK. For a sample of 47; I find that 0.021% defective will be accepted 99% of the time amd 4.79% defects will be rejected 10% of the time. One difference is that I was assuming basically an infinite lot size; a smaller lot size would mean you are more able to detect bad lots.

The biggest difference is (as mentioned above) you can't accept a lot with known defects.

I don't think either allows "known defects". For the AQL plans, when you find a defect it is removed. so if Ac=4 and even if you find 2 defects, those are removed and there are no "known" defects left. There are "suspected defects", but that would be true for the c=0 plans too.


Tim F

 

[howste]

I don't think either allows "known defects". For the AQL plans, when you find a defect it is removed. so if Ac=4 and even if you find 2 defects, those are removed and there are no "known" defects left. There are "suspected defects", but that would be true for the c=0 plans too.

I understand what you're saying, but that's different than the intent of what I was saying. My meaning is that the process definitely produced defects, therefore the rest of the parts/material in the lot must be verified to ensure that there are no others.

 

[Karen Whitehead]

Based on "lot is withheld for review and disposition", then this sounds in a sense like a double sampling plan. The "first sample" is designed to see if there might be a problem. If a problem is found, then further review is called for - perhaps a larger sample; perhaps a measurement of a variable instead of simple go/no-go.


Tim F

This is exactly how we are proceeding. Quality might make a call for more sampling - Engineering may have to make a call - Lot could be rejected - Etc., Etc., Etc.