# Mean Time Between Failures - MTBF

## Description

Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The terms is used in both plant and equipment maintenance contexts. The MTBF is typically part of a model that assumes the failed system is immediately repaired (mean time to repair, or MTTR), as a part of a renewal process. This is in contrast to the mean time to failure (MTTF), which measures average time to failures with the modeling assumption that the failed system is not repaired (infinite repair time).

The definition of MTBF depends on the definition of what is considered a system failure. For complex, repairable systems, failures are considered to be those out of design conditions which place the system out of service and into a state for repair. Failures which occur that can be left or maintained in an unrepaired condition, and do not place the system out of service, are not considered failures under this definition. In addition, units that are taken down for routine scheduled maintenance or inventory control are not considered within the definition of failure.

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

By referring to the figure above, the MTBF is the sum of lengths 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 as shown here.

Related formulas## Variables

MTBF | mean time between failures (h) |

downtime_{start} | start of "downtime" (h) |

uptime_{start} | start of "uptime" (h) |

failures | number of observed failures (dimensionless) |