# Incandescent light bulb lifetime - exponential distribution?

It's been said that incandescent light bulbs lifetime has exponential distribution. As I understand, this means a 10,000 hours time-to-failure has the same probability no matter how long the light bulb was used until now (i.e. the "memorylessness" property).

On the other hand, Wikipedia says that "(a light bulb's) Lifetime is approximately proportional to $V^{−16}$". Doesn't this mean that if the lifetime is 10,000 hours and 5,000 hours have passed, failure in 10,000 hours is less likely than in 5,000 hours?

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## 2 Answers

I would not expect light bulbs to have an exponential distribution, as there is a wear out mechanism involved-evaporation of the filament material. The Wikipedia statement that the lifetime is proportional to $V^{-16}$ is for steady state conditions. Higher voltage leads to higher operating temperature, which leads to increased evaporation. "Long-life" bulbs have cooler filaments, as you can see because they generate less (and redder) light for the same power consumption. All this ignores the stresses generated in on/off cycles, and the fact that the power when the bulb is turned on is much higher than steady state due to the lower resistance at lower temperature.

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What about a Weibel distribution?

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This does not address the exact question –  Hagen von Eitzen Nov 8 '12 at 22:37
This is not an answer. What is a Weibel distribution? Why would it fit this situation? –  robjohn Nov 9 '12 at 2:35