[chbot] Is there a statistician in the house?

[Stephen Irons]

I seem to remember doing calculations like this a long time ago...there 
are a number of variations which are probably all related. I have not 
been able to find any Google search terms that give me anything useful.

A factory produces a batch of 10_000 units.
I test 100 units; there are 3 failures. What failure rate can I expect 
from the whole batch? What is my confidence in that estimate?I test 100 
units; there are 0 failures. What failure rate can I expect from the 
whole batch? What is my confidence in that estimate?How many units do I 
need to test to have 99% confidence that there will be less than 1% 
failure rate from the whole batch?
Can someone tell me what you call this type of calculation? Point me to 
a suitable reference site?

All of the examples I find online are of the form: a factory produces 
widgets with x% failure rate; out of a sample of y units, what is the 
probability of finding z defective units...this is probably the same 
calculation from the other direction.

This is just for interest. In my specific case, I had 36 failures out 
of a sample of 50 taken from a batch of a few thousand -- this is 
clearly not acceptable. But we now have a repeatable test that causes 
the failure.

Stephen Irons

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