Thank you for that, as it confirms many things that the manufacturers are less explicit about. One issue tho, when multiple LEDs are operating in series (e.g. home light bulb), my understanding is that the MTBF (for the whole device) is actually closer to LED_MTBF/n, where n is the number in series. String enough of them together, and run them close to the limits, and you end up with a device MTBF much shorter than the LED MTBF.
Correct. Perhaps a more intuitive approach is to convert the MTBF into a failure rate by inverting it. A component with an MTBF of 1000 hours has a failure rate of 1 / 1000 = 0.001 failures per hour. If you have three of these components in series, simply add the failures per hour. Thus you'd get a system failure rate of 0.003 failures per hour. Invert that again to give a system MTBF of 333.3 hours.
Why on earth bother with failure rates when you can use the formula you suggested (MTBF/n)? Because that only works when the components are all the same. Suppose you had a switching transistor, a current limiting resistor and an LED in series. The MTBFs are:
Transistor: 500 hours
Resistor: 10000 hours
LED: 1000 hours
The failure rates are:
Transistor: 1/500 = 0.002 failures per hour
Resistor: 1/10000 = 0.0001 fph
LED: 1/1000 = 0.001 fph
Now add the failure rates:
System failure rate = 0.002 + 0.0001 + 0.001 = 0.0031 failures per hour
System MTBF = 1 / 0.0031 = 323 hours
Thus you can see that using failure rates makes it very easy to calculate a system failure rate and MTBF, even when the system comprises all sorts of different components.
Two points. Firstly, the MTBFs I've used are ridiculously low and not realistic, so don't quote them! Secondly,
MTBF has nothing to do with ageing or lifespan. MTBF refers
only to random failures. Items like LEDs, with predictable ageing mechanisms, usually have an MTBF many times longer than the actual lifespan of the LED. Take incandescent bulbs: they have a predictable lifespan of around 1000 hours (they're designed that way), but it is very rare for a bulb to suffer a failure before it has worn out, so the MTBF is probably orders of magnitude longer than the lifespan.