Mean time between failure

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Mean-time-between-failure (MTBF) is the "average" time between failures, the reciprocal of the failure rate in the special case when 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 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 true. In particular, for an exponential failure distribution, the probability that an item will fail by the MTBF is approximately 0.63. For typical distributions with some variance, MTBF only represents a top-level statistic, thus is not suitable for predicting detailed time of failure, as the uncertainty in actual failure distribution manifests itself in variability in the time to failure distribution.

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Formal definition of MTBF

The MTBF is simply the reciprocal of the failure rate,

<math>MTBF=\frac{1}{\lambda} \!</math>.

The MTBF is often denoted by the symbol, <math>\! \theta</math>, or,

<math>MTBF=\theta \!</math>.

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,

<math>MTBF=E(t)=\int_{0}^{\infty} xf(x)\, dx \!</math>
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Variations of MTBF

There are many variations of MTBF, such as mean-time-between-system-abort (MTBSA) or mean-time-between-critical-failure (MTBCF). Such nomenclature is used when it is desirable to differentiate among types of failures. For example, in an automobile, the failure of the FM radio does not prevent the primary operation of vehicle, so that it may be desirable to differentiate the failure rates of critical versus non-critical failures. Mean-time-to-failure (MTTF) is sometimes used instead of MTBF in cases where a system is replaced after a failure, whereas MTBF denotes time between failures where the system is repaired.

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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 that it engenders - many component MTBFs are given in databases, and often these values are very inaccurate; its use has led to the negative exponential distribution being used much more than it should have been - it has been estimated 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).

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