What hypothesis test?

I have a population of Z items, where X must pass and Y must fail. The population is huge, so I'm trying to find a sample size to test that is statistically significant to prove that all items that are supposed to fail actually do fail. The thing is that it is not just a count or proportion. So I can't say that 60% of the population fails, because it could be the items that aren't supposed to fail that have failed.

How do I figure out the sample size/what test should I use to test this? Also, how would I test it? Just have a sample size of items to fail? It needs to be risk-based, so ensuring all the failing items will fail with 90% confidence.

This may be super easy, but I can't seem to get my head around it having specific pass/fail items rather than just a 1 proportion test.

Thanks!!

So you have "Y" items that are predicted to fail and you want to test whether they really did? I don't see any reason then to look at the other "X" items. This is just a binomial distribution on "Y" things. If Y is very large, you can use the normal approximation to the binomial distribution.

Re

But if I want to test it with 90% confidence that all of them will fail, do I need to test 90% of the Y as my sample size? Basically having a null of p=1 (or 0 depending how you're defining a success).