Hello,

I have a question on what would be the proper way to calculate FPY for an end item audit step?

Example: 200 units are produced in a run. 5 samples are taken. 1 sample is found to be nonconforming. Would you say your FPY rate is .995 or .8?

Thanks for you help and opinions.

Rick

Just so that we are all on the same page, FPY is what?

Just so that we are all on the same page, FPY is what?

First Piece Yield?

First Piece Yield?

probably, but better to be sure of what we are commenting on.:agree:

probably, but better to be sure of what we are commenting on.:agree:

Yes! :bonk::bonk:

First Pass Yield (http://en.wikipedia.org/wiki/FPY).

Stijloor.

Hello,

I have a question on what would be the proper way to calculate FPY for an end item audit step?

Example: 200 units are produced in a run. 5 samples are taken. 1 sample is found to be nonconforming. Would you say your FPY rate is .995 or .8?

Thanks for you help and opinions.

Rick

Neither would be correct; your example demonstrates that there is at least one defective in the lot of 200, but there might be more. Until you know how many there were, you can't calculate FPY and have it mean anything.

Yes FPY = First Pass Yield

Neither would be correct; your example demonstrates that there is at least one defective in the lot of 200, but there might be more. Until you know how many there were, you can't calculate FPY and have it mean anything.

Ok I would see the logic in that. So you would take another sample, let's say 5 more and if there were no further defects found?

Rick

Ok I would see the logic in that. So you would take another sample, let's say 5 more and if there were no further defects found?

Rick

If you want to know what the actual FPY is, you need to know how many defectives there are. In your example you have evidence that 20% (or more) of the lot could be bad. On the other hand, except for the defective found in the first five-piece sample, there might be no defects in the lot. Taking another five-piece sample isn't going to help much.

I would say:


a lot with 1.3% defective will yield a sample with one in five bad 5% of the time (if you happen to select a bad item more often than average)
a lot with 53% defective will yield a sample with one in five bad 5% of the time(if you happen to select a bad item less often than average)

Therefore, the lot has FPY of 20% +23%/-18.7% with a 95% confidence level.


Tim F

If you want to know what the actual FPY is, you need to know how many defectives there are. In your example you have evidence that 20% (or more) of the lot could be bad. On the other hand, except for the defective found in the first five-piece sample, there might be no defects in the lot. Taking another five-piece sample isn't going to help much.

Ok so in other words trying to calculate FPY for this is probably not the way to go?

Ok so in other words trying to calculate FPY for this is probably not the way to go?

Well, it depends on what you want to know. As Tim's post suggests, you might be able to get a reasonable estimate of the number of defects in the lot by statistical sampling, but it'll only be an estimate. On the other hand, 100% inspection of the lot might not yield 100% accurate results either, depending on circumstances.

First-Pass Yield is about how many things went through the process and how many came out "good." How you actually reach the FPY number depends on a number of factors--lot size, time available, ease of differentiation between good and bad, and the criticality of having results as accurate as possible, among others.

I should probably mention that my earlier calculations are based on the binomial distribution, in case anyone wants to check the calculations. (To be really precise, we should probably use a hypergeometric distribution since we are sampling without replacement, but the difference will be very minor here.)

As Jim mentioned, my results are estimates. The main lesson to take away is that with such a small sample, the uncertainties are huge. About all we can say statistically is


20% of the items actually were defective.
the defect rate for the whole lot could easily fall anywhere within a wide range ... from around 1% to around 50%.

Tim F