Mean time between failures
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Mean time between failures (MTBF) is the mean (average) time between failures of a system, the reciprocal of the failure rate in the special case when the failure rate is constant. Calculations of MTBF assume that a system is "renewed", i.e. fixed, after each failure, and then returned to service immediately after failure. A related term, mean distance between failures, with a similar and more intuitive sense, is widely used in transport industries such as railways and trucking. The average time between failing and being returned to service is termed mean down time (MDT).
A common misconception about the MTBF is that it specifies the time (on average) when the likelihood of failure equals the likelihood of not having a failure. This is only true for certain symmetric distributions. In many cases, such as the (non-symmetric) exponential distribution, this is not the case. In particular, for an exponential failure distribution, the probability that an item will fail after a MTBF is approximately 0.63. For typical distributions with some variance, MTBF only represents a top-level aggregate statistic, and thus is not suitable for predicting specific time to failure, the uncertainty arising from the variability in the time-to-failure distribution.
On commercial product descriptions, the "MTTF lifetime" is the amount of time the product should last, assuming that it is used properly.
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[edit] Formal definition of MTBF
The MTBF is simply the reciprocal of the failure rate,
The MTBF is often denoted by the symbol 
, or
Since failure rate and MTBF are simply reciprocals, both notations are found in the literature, depending on which notation is most convenient for the application.
The MTBF can be defined in terms of the expected value of the failure density function f(t)
with
[edit] Variations of MTBF
There are many variations of MTBF, such as mean time between system aborts (MTBSA) or mean time between critical failures (MTBCF). Such nomenclature is used when it is desirable to differentiate among types of failures, such as critical and non-critical failures. For example, in an automobile, the failure of the FM radio does not prevent the primary operation of vehicle. Mean time to failure (MTTF) is sometimes used instead of MTBF in cases where a system is replaced after a failure, since MTBF denotes time between failures in a system which is repaired.
[edit] Problems with MTBF
As of 1995, the use of MTBF in the aeronautical industry (and others) has been called into question due to the inaccuracy of its application to real systems and the nature of the culture which it engenders. Many component MTBFs are given in databases, and often these values are very inaccurate.
This has led to the negative exponential distribution being used much more than it should have been. Some estimates say that only 40% of components have failure rates described by this. It has also been corrupted into the notion of an "acceptable" level of failures, which removes the desire to get to the root cause of a problem and take measures to erase it. The British Royal Air Force is looking at other methods to describe reliability, such as Maintenance-Free Operating Period (MFOP).
[edit] Exaggeration of MTBF
Many manufacturers seem to exaggerate the MTBF of their products (e.g. Hard Drives), in order to either sell more product or sell for a higher price. A common way that this is done is to define the MTBF as counting only those failures that occur before the expected "wear-out" time of the device. Continuing with the example of hard drives, these devices have a definite wear-out mechanism as their spindle bearings wear down, perhaps limiting the life of the drive to five or 10 years (say 50,000-100,000 hours). But the stated MTBF is often many hundreds of thousands of hours and only considers those other failures that occur before the expected wear-out of the spindle bearings.
