Mean Time Between Failures - Formal Definition of MTBF

Formal Definition of MTBF

By referring to the figure above, the MTBF is the sum of the operational periods divided by the number of observed failures. If the "Down time" (with space) refers to the start of "downtime" (without space) and "up time" (with space) refers to the start of "uptime" (without space), the formula will be:

\text{Mean time between failures}
= \text{MTBF} =\frac{\sum{(\text{start of downtime} - \text{start of uptime})}}\text{number of failures}. \!

The MTBF is often denoted by the Greek letter θ, or

The MTBF can be defined in terms of the expected value of the density function ƒ(t)

where ƒ is the density function of time until failure – satisfying the standard requirement of density functions –

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