Imagine that your “component test and guesswork” is launching shuttle after shuttle, and seeing how many blow up. You could get the 1% figure by
launching 100 shuttles, and observing that only one blew up
launching 100.000 shuttles, and observing that 1000 of them blew up.
Even though both could be described as “1% likely to fail”, it’s clear that you have much more confidence in that figure in the second scenario; observing one extra successful launch will shift your confidence around more in the first scenario than in the second.
As others said, you should have a probability distribution over the frequency of failure (a Beta distribution I believe), that should peak near 1%, but the peak will be much sharper in the second scenario than in the first.
Imagine that your “component test and guesswork” is launching shuttle after shuttle, and seeing how many blow up. You could get the 1% figure by
launching 100 shuttles, and observing that only one blew up
launching 100.000 shuttles, and observing that 1000 of them blew up.
Even though both could be described as “1% likely to fail”, it’s clear that you have much more confidence in that figure in the second scenario; observing one extra successful launch will shift your confidence around more in the first scenario than in the second.
As others said, you should have a probability distribution over the frequency of failure (a Beta distribution I believe), that should peak near 1%, but the peak will be much sharper in the second scenario than in the first.