Yes, when the
sample size gets close to the lot size, then the
hypergeometric distribution is a better at getting the correct probabilities. Unfortunately, the equation is somewhat complicated and involves factorials. Excel does have this functionbuilt in, but factorials for large numbers become huge! Sample sizes much over 100 return an error.
Details about the eqaution can be found at
http://mathworld.wolfram.com/HypergeometricDistribution.html
Part of the challenge is that your error rate is so small. 500 ppm = 1 part per 2000 =
3 parts per 6000. Assuming 500 ppm is the limit on acceptable lots, you are trying to deterine if there are 4 or more defects out of the 6000 pieces.
If you have to use a pass/fail type test and if the test is labor intensive, this might be a good place to consider a continuous sampling plan.
I haven't work the exact numbers, but it would be
something like:
* reject the lot if 1 of 500 is bad
* reject the lot if 2 of 1500 are bad
* reject the lot if 3 of 3000 are bad
* reject the lot if 4 out of any number are bad
* accept the lot if 0 of 2000 is bad
* accept the lot if 1 of 4000 is bad
* accept the lot if 2 of 5000 are bad
* accept the lot if 3 of 5900 are bad
Always note that this assumes a random sample. you shouldn't just take the samples in order because the defects are quite likely to be clustered in many real situations.
Tim F