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Concept
Mean time between failures
Summary
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The term is used for repairable systems while mean time to failure (MTTF) denotes the expected time to failure for a non-repairable system.
The definition of MTBF depends on the definition of what is considered a 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. The higher the MTBF, the longer a system is likely to work before failing.
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 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:
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:
In a similar manner, mean down time (MDT) can be defined as
The MTBF is the expected value of the random variable indicating the time until failure.
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Related courses (2)
CS-487: Industrial automation
This course consists of two parts:
- architecture of automation systems, hands-on lab
- handling of faults and failures in real-time systems, including fault-tolerant computing
MSE-424: Fracture of materials
This course covers elementary fracture mechanics and its application to the fracture of engineering materials.
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SPRINGER INTERNATIONAL PUBLISHING AG2022Immunizing Systems from Distant Failures by Limiting Lamport Exposure
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Weibull distribution
In probability theory and statistics, the Weibull distribution ˈwaɪbʊl is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page. The distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939, although it was first identified by Maurice René Fréchet and first applied by to describe a particle size distribution.