When reading a question about testing a Java program several times with random seeds the word testing sparked of the association with unit testing in my mind, but that might not have been the kind of testing going on there.
In my opinion introducing randomness in a unit test would be considered bad practice, but then I started considering the case where a (small) percentage of failure might be acceptable for the moment.
For example, the code fails to pass the unit test once every 10^n for n > 3 and gradually you want n to go to infinity without the test going red, maybe yellowish.
Another example might be a system-wide test where most of the time things go right, but you still want to limit/know how often they might go wrong.
So my question is, are there any frameworks (full spectrum of testing) out there that can be persuaded to allow a percentage of failure in an huge/excessive amount of repeated tests?