I think you are utterly doomed trying to get to MTBF of 250000 hours on any usefully complex product, but then you haven't said what it is, so it might be very simple.
LEDs tend to age faster if they're hotter / driven at higher currents, and the failure mechanism is different for white leds (which are fluorescent) and natural-coloured LEDs. But generally they get dimmer as they age.
I would expect that you would get very long life if you significantly under-drove the LED (modern traditional-colour (red, etc)) LEDs are incredibly bright and tend to need very little current to act as a useful indicator, and if you weren't too fussy about the specific output you could play faster-and-looser about the failure condition.
But if I was trying to make a fantastically reliable product, one way I'd do that is to dispense with absolutely every component I possibly could. I expect the power-on LED would fail to make the cut in that regard.
Update: Well, clearly I know even less about reliability than I thought I did - it seems lots of diskdrives claim MTBFs well over 250k hours - so good luck with your product!