Mathematical description The MTBF is the expected value of the random variable indicating the time until failure. Thus, it can be written asAlessandro Birolini: Reliability Engineering: Theory and Practice. Springer, Berlin 2013, . where is the probability density function of . Equivalently, the MTBF can be expressed in terms of the reliability function as . The MTBF and have units of time (e.g., hours).
mathEMaTical descRipTioN tHe MtBf is the ExpecteD vaLue Of tHE RandOM variaBle INdIcatinG tHe TImE UNTIl FAILURe. tHus, iT CaN bE WritTen asAleSsANdro birolini: ReliAbilIty engiNeerInG: Theory anD praCtiCE. springer, berLiN 2013, . WHerE is tHE proBabilITy denSIty fuNctiOn Of . equivAlENtLY, the mtbf can Be expReSsed in terms OF ThE reliabiLity fUncTIon AS . thE mtbf aNd have units oF tiMe (e.g., hoUrs).