I did decide to think about this question a little more, since some of the calculations I had yesterday troubled me, in terms of LEDs at least. I suppose the thing about radioactive decay is that the effective variance around the half-life of an individual atom is so large that you can't really ask the question "when will
this atom decay?" and expect a sensible answer. That single atom will decay now, or next week, or in a million years, and you would learn very little about the half-life -- it's only when you have a huge collection, around billions of billions or more, that you can start saying "how long until about a third of the atoms have decayed?" or some such. The resulting exponential decay curve is robust experimentally, to be sure. But I was wondering if it really was appropriate for LEDs after all. They aren't, after all, quite as unstable as atoms (and if you had seen the calculations above you would see that an LEDs could fail in about half a second if 5000 hours was a radioactive half-life).
Instead, the decay curve I had in mind was something that was largely flat and linear until around 5000 hours or so, before falling off fairly sharply afterwards until maybe twice or three times that, by which time virtually all, if not all, LEDs would have failed. A curve that, incidentally, looks not unlike this one (the blue curve)...
http://www.aaxatech.com/articles/UHPversusLED_Curve.jpg
A not unreasonable fit to that curve is something like the following:
N = N0 ArcTan[-(t-t_max)/la] / (ArcTan[t_max/la])
Where the last bit is just to ensure that it normalises correctly, t_max is the absolute maximum time any one LED can be expected to last, and then "la" is some factor that scales the decay rate appropriately -- probably it can be chosen to fix the value of time at which about 10% or so of the LEDs can be expected to have decayed.
I've made up a couple of parameters to give an idea of behaviour -- roughly speaking, though, if no LED lasts more than 15,000 hours and la is about 4,300, then around 10% of LEDs fail after 5,000 hours, 33% after 10,000 hours and -- to answer the question in the OP -- if you have 60 LEDs to start with then the first one would probably fail after 1,100 hours in this model.
I think it's preferable to a radioactive decay model, and certainly seems to fit LED reality better -- although I suspect there's an even more accurate model out there. I was pleased to find the ArcTan fit though.