We manufacture product on an automatic line with a predetermined lot size. QA selects samples approximately every 30 minutes of production. Often times, they have met their sample size prior to the completion of the full production run. Rather then stop sampling, they continue to test samples on 30 minute time intervals until the production run is complete, exceeding the required sample size.

example: Lot size 4400, sample size 80, A=2, 2 rejects found in SS=80 therefore lot is acceptable. Continue to sample, since production run is not yet complete, and find a reject at sample 90. 3 rejects have now been found in sample size of 90 even though lot passed with only 2 rejects in required sample size of 80.

My questions are:
1) Should they stop sampling once the sample size has been met?
2) If the accept level is exceeded with samples selected AFTER the full sample size has been evaluated, strictly speaking, is this cause for failure of the lot?

Thanks in advance for your inputs.

I'm no expert on sample sizes but if this is a critical item shouldn't the sample size for a lot of 4400 be 200? If you are only required to sample 80 items then I'd stop at 80. I would suggest expanding the length of time between samples (go 35 minutes instead of 30) so that you get a good representation during the entire production run or use "% of run completed" to determine when to sample instead of time.

Quest,

Are you using Z1.4 (the old MIL-STD-105) sampling plans? That is pretty standard and seems to fit the general nature of your question. For instance, you might be doing a Level I, normal inspection plan with AQL 1.

I agree with Julianna that you can't change the plan in the middle of the process. If your plan says collect 80, then you need to collect 80. On the other hand, I would hate to quit drawing samples half way through the run, just because you have enough. Sampling plans are most effective when the sample is random, and drawing all the parts from the earlier parts of he run is definitely not random.


You could wait until the end to collect them all (the best way to get a random sample, but the worst for detecting problems early) or collect them at a rate proportional to production (good from a statistical perspective, but tougher for the inspectors since they have to adjust the collection to match production), or just stop when you get to 80 (the worst choice statistically). In any case, the extra defect after 90 can't be counted against the sample size of 80.




A couple of brainstorming thoughts.
Can you switch to a variable measurement rather than a pass/fail measurement? You could use a much smaller sample size and still get the same protection.
Can you switch to SPC? If you collect samples every hour for example, you could plot them on a control chart. This also should be more effective at spotting problems
It sounds like you are effectively doing a multiple sampling plan. For Code J (which you appear to be using for Level I, normal inspection, AQL1) the multiple plan calls for collecting samples of 20. The plan would be
collect 20: R=2 (and there is no accepting yet)
collect 20 more: A = 0, R =3
collect 20 more: A = 0, R =3
collect 20 more: A = 1, R =4
collect 20 more: A = 2, R =4
collect 20 more: A = 3, R =5
collect 20 more: A = 4, R =5You still have the statistically questionable practice of a non-random sample. On the other hand, this seems to fit more closely with your collection practice. The one downside is that you might get to the end and still have neither accepted nor rejected the lot. In this case you might have to draw a couple extra sets of 20 until you reach a definite conclusion.
Tim F

Thank you for your inputs. I will be discussing them with the QA manager.

Tim touched on the real issue: the sampling as done now is not statistically random. the Randomnesss is absolutely essential to the validity of the sampling plan.

what are they trying to do?

if they are sampling to release the whole lot - they need to sample randomly from the whole lot.

if they are trying to limit the amount of bad prouct that is made by sampling on a regular interval then they are accepting - or rejecting - all of the material made in that time interval - that material is now an inspection lot by itself. adn teh sample size shodul be calculated accordingly.

Bev,

Great job cutting to the heart of the issue. I gave a brilliant :notme: statistically-based answer, but you focused in on the two key issues. :agree1:

What is the sampling used for? until we know this, there is no way to choose a plan
The sample here is not random. This means the conclusions will quite possibly be invalid.
Tim


P.S. If the defects are randomly distributed, then the sample doesn't have to be random. If the defects aren't randomly distributed, then the sample must be random. However, you usually don't know if the defects will be random, so the safe approach is to make sure the sampling is random.

What we are really doing is trying to elimiate having to 100% inspect an entire production run of approx 4000 by dividing it into sublots.

We have decided to sample approximately every 30 minutes and treat all the product made in that interval as an inspection sublot. The sample size will be calculated according to how many parts are made in that time interval which is a very consistent. If the sample fails, then we only need to sequester and test the sublot. If we wait until the whole lot is complete, random sample and fail, we are forced to test the 4000.

The sampling is not completely random. Instead, samples produced one right after the other are chosen at the approximately 30 minute intervals and production continues to run until the pass-fail determination is made. At this point, the 'bin' containing that time interval parts is moved either to quarantine or the next production step.

Are we following ANSI Z.4 even though what we are doing is not trully random sampling? Does what we are doing have a different name or is it defined by a different standard?

By the way, we have looked into contiuous sampling plans but the sample sizes that must be evaluated were not feasible for us. It takes us about 5 minutes to test 8 samples and we produce product at a rate of 1 every 7 seconds.

Lastly, we are fortunate that our overall reject rate is pretty low, about 0.3% of the samples tested fail.

Anyway, that is it for this week. I look forward to reading your responses on Monday.:thanx:

well if the sampling isn't random you aren't following the standard. and if you have an isolated set of defects then your sample may not be providing good protection either.

How does the majority of the severe or major defects behave? are they random isloated defects? or do they shift/trend?

If isolated (come and go by themselves) you must randomize.

if they shift or trend - endpoint sampling of the time period will be helpful. However, if your data is continuous and not categorical (pass/fail) I woudl recommend using SPC to detect changes that can be corrected BEFORE you produce any defects - that way you don't even have to 100% inspect the time period.

If isolated - are the defects caused by errors? then investigate error proofing or at elast some form of error proof inspection.

A 0.3% rejection rate is a relatively small rate. What is the defect rate? Defects can tend to 'cluster' with rare events. what is the time sequence of your defect rate? if it actually does cluster, then an endpoint sample plan can be even more ineffective as you might get unlucky enought ot sample during a 'quiet' period.

you are not stuck with having to use ANSI standards (unless your customer unfortunately imposes it) You can use the Binomial or Poisson approach (a search of this site will turn up the formulas...) What defect rate are you trying to protect your Customer from??

You confirmed what I thought that ANSI Z.4 is based upon a purely random sample. This is especially interesting to me as our process control procedures all say that we utilize ANSI Z.4 sampling.

Our reject rate and defect rate are the same as we only test for 1 pass fail attribute. SPC is not feasible at this time.

We experience some randomly isolated rejects but very rarely. Never enough to cause us to fail a .65AQL. The rejects are more likely to occur due to a minor change in raw material or machine conditions over time. Unfortunately, we have not correlated machine conditions with rejects. (This is an open engineering project!!)

Thank you for your thoughts. :thanks:

I will pass our discussion along to the QA Manager.