L10 life conversion to MTBF calculation?

[samuel80]

Is the following logic and calculations correct in applying manufacturer L10 life data to convert to a unit failure rate and MTBF?

Example: A fan manufacturer specifies their fan to have an L10 life of 50,000 hours @ 40 Deg C. L10 life meaning 10 percent of fans are expected to have failed at 50,000 hours in use environments of 40C.

Logic wise if I have 2000 fans in use I can expect 10% or 200 of these fans to have failed by 50,000 hours. If I wanted to get a failure rate I would say: F.R. = (expected failures/total operating time of all units) = 200 failures / (2000 fans * 50,000 hrs) = 2 x 10^-6. Or 2 failures per million hours. Then MTBF = 1 / 2 failure per million hrs = 500,000 MTBF? This seems too high to believe. :eek:

[Pantelis]

Your logic is somewhat correct, with the exception that the failed fans from the 200 population would have failed at a time less than 50K so the answer would be a little less than 500K (~ 475K). To get that you have to make a failure rate assumption. In this case if you make an exponential assumption (i.e. constant failure rate) then,

R=exp(-t/m)
0.9=exp(-50K/m) >> solve for m.

Now you mention that the number seems too high. Well it is! However it is the correct answer based on the model. The problem is that the model assumed a constant failure rate – and I guarantee you that the fans do not have a constant failure rate. In other words the exponential distribution assumption is flawed. To illustrate that assume that you did the same (and used similar numbers and the same assumption) for human beings. Thus say 10% died by the age of 50 (which is a reasonable value), then the MTTF (average lifespan) for humans would be 475 years (a very ureasonable and wrong number)….

The real answer to this is that you should NOT be assuming an exponential model. Having said that, and when only given a single metric such as the L10, and if you do not assume constant failure rate (true life) then you can’t try to infer other metrics from it .

Hope this helped J

[samuel80]

Thanks for the clarification Pantelis.