Editing Mean time between failures (section)

==Overview==
Mean time between failures (MTBF) describes the expected time between two failures for a repairable system. For example, three identical systems starting to function properly at time 0 are working until all of them fail. The first system fails after 100 hours, the second after 120 hours and the third after 130 hours. The MTBF of the systems is the average of the three failure times, which is 116.667 hours. If the systems were non-repairable, then their [[#Variations of MTBF|MTTF]] would be 116.667 hours.

In general, MTBF is the "up-time" between two failure states of a repairable system during operation as outlined here:

[[File:Time between failures.svg]]

For each observation, the "down time" is the instantaneous time it went down, which is after (i.e. greater than) the moment it went up, the "up time". The difference ("down time" minus "up time") is the amount of time it was operating between these two events.

By referring to the figure above, the MTBF of a component is the sum of the lengths of the operational periods divided by the number of observed failures:
:<math>
\text{MTBF} = \frac{\sum{(\text{start of downtime} - \text{start of uptime})}}{\text{number of failures}}.
</math>

In a similar manner, mean down time (MDT) can be defined as
:<math>
\text{MDT} = \frac{\sum{(\text{start of uptime} - \text{start of downtime})}}{\text{number of failures}}.
</math>