Letters to the Editor
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@Electro Robot
wrote: 50 or a 100 thousand hours are great. If you are >+4STD in the quality control area. But if the bulb fails early you are hosed. This is the tradeoff we learn from 6-Sigma; the cost to push from 5 to 6 sigma can be almost asymptotic for certain processes. And since no one will pay for that the actual failure distribution is far less than 5 or 6 STD, often less than 4, which sounds great until you churn out a billion units of something.
I do not see what you mean. To say anything sensible about light bulb failure, you need the failure distribution curve for each of the light bulbs being compared. It is very easy to get confused. Remember this: "Consider two idealized light bulbs in use simultaneously--what is the difference in their failure times? It will be true that once one of the bulbs fails, the remaining bulb, being as good as new, will have a remaining failure lifetime given by the standard waiting time distribution." (Mantel and Pasternak, ASAJ, Sep 1966).
That statement was written by a statistician, and ignores the obvious physics about real light bulbs, which shows that an old light bulb is more likely to fail than a new one. (evaporation from the filament, etc.)
So, can you explain what it is you mean, and actually show that it is true?