# understanding the use of MTBF

I have on a few occasions calculated the MTBF using the FITS of all the components on a BOM and something like the telcordia standard in some spreadsheet tool I was given. We get a number say 1 Million hours, and everyone nods approvingly because 1 Million is a very big number.

I have trouble understanding the practical use of this number though. Doing some reading I understand this is supposed to be the average time between failures, but does not mean 1 unit will run for 1 million hours. If however I had 1 Million units I think it means I should expect a failure once an hour?

Can I then extrapolate that and say if I ran my 1 million units for a year or 8760 hours I should expect 8760 failures? Would it then make sense to say that's a 0.9% failure rate?

The final thing I don't quite get is MTTF vs MTBF. I understand that MTTF is when the unit can't or won't be repaired, but I don't really understand the difference. For electronic designs at least no one has ever wanted to talk about MTTF even though most of my products are throw away if they break.

The essential thing to understand is that it's statistics - which you graze with the statement:

does not mean 1 unit will run for 1 million hours. If however I had 1 Million units I think it means I should expect a failure once an hour?

Statistics tell you NOTHING about what an individual item (or event) will do, but a great deal about what a population of them will do - subject, of course, to the "garbage in, garbage out" rule - if the data they are based on is accurate, they are accurate for a population - if the data is flawed, the statistics based on it are flawed.

In practical terms there are other factors of how real life behaves, such as the "bathtub curve" - there's a disproportionate number of failures early (from e.g. manufacturing defects), fewer over the major lifespan of the product, and a disproportionate number of failures late in life from aging (all of which are reflected in the MTBF, but the bathtub curve is normally seen when looking at the actual failures that make up the mean.) If you've heard of products being "burned in" that's effectively trying to catch the first part of the bathtub curve before the product hits the marketplace, which makes the perceived failures in the wild look better (and you get less bad press of the "I bought a brand new XYZ widget and it broke the first day I used it" sort.)

If most of your products are "throw away if they break" then MTBF is MTTF. Or MTFF is MTTF (where MTFF would be "first failure")

FIT as a unit is failures per billion hours. So your system of 1 million hours calculated MTBF came from a calculation of 1000 FITs. That means, if you keep one and only one of the system continuously operating for 1 billion hours, replace, repair or correct any failure immediately, the system would have failed 1000 times on average.

If you keep one of the system continuously operating for 1 million hours, it would have failed 1 time on average. But sometimes, a system could have lasted the 1 million hours without failure. But other times, a system could have experience 2, 3 or more failures (and fixes). And it balances out to 1 failure per million hours on average. (But of course, if you indeed operate a system for 1 million hours, some of the assumptions in the original calculation are bound to be incorrect.)

Similarly, if 1 million units are running, you should expect a failure per hour on average.

You 0.9% failure rate looks to be correct.

As for the last question, I think some people apply a literal interpretation of the name "Mean Time Between Failure" and therefore come up with MTBF = MTTF + MTTR. I don't know the history of the terms, but I would guess that the FIT to MTBF calculation (which implies MTTR = 0) exists long before there were such things as MTTF (I can easily be wrong on this). Therefore, manufacturers stay with what they have done for a long time, use the term MTBF.