Yeah, safe-life is a older design philosophy. Fail safe and fault-tolerant came out as alternatives to it.
My understanding is that safe-life can work, but it's extremely tricky to do it and as you've already guessed, there is uncertainty built in. I remember one time I toured a Boeing plant and saw where they did some of their testing. One of the things that they do with some components like a landing gear is that they put it through a machine and torques it, compresses it, sheers it etc. And they keep doing that 24/7 365 days a year until it breaks. Basically what they're doing is running the component through all the stresses that it is expected to undergo during its life cycle and see how long till it fails. Do that a few times, assuming that the components are consistent in how they were made and you can get a good idea of the life cycle.
The problem however, is as my dad puts it is that your life cycle estimates are only reasonable if and only if that component during its service does not endure anything that you did not test for. So if you test say a structural beam and assumed that the plane would always steer well clear of severe storms, but during the actual service that plane has flown right through a severe thunderstorm or two then your estimate may or may not be valid anymore.
"Don't confuse facts with reality."
-Robert D. Ballard