MP
MTBF
MTBF (acronym for Mean Time Between Failures) is the arithmetic mean (average) time between failures of a system. The MTBF is typically part of a model which assumes that the failed system is repaired immediately (time zero), as part of a renewal process. Instead, the MTTF (mean time to failure) measured the mean time between failure by assuming a model in which the failed system is not repaired.
Formal definition of MTBF
The MTBF is simply the reciprocal of the rate of failure.
The MTBF is often denoted by the symbol 
Or
Since the rate of failures and the MTBF is reciprocal, both notations are found in the literature, depending on which is best suited for your application.
The MTBF can be defined in terms of expected value of the failure density function f (t)
with
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