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.

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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.

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 hours, the second after hours and the third after hours.

The MTBF of the systems is the average of the three failure times, which is If the systems were non-repairable, then their MTTF would be 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. 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:. Any practically-relevant calculation of MTBF or probabilistic failure prediction based on MTBF requires that the system is working within its "useful life period", which is characterized by a relatively constant failure rate the middle part of the " bathtub curve " when only random failures are occurring.

The units used are typically hours or lifecycles. The MTBF is the expected value, average or mean of the exponential distribution.

The MTBF value can be used as a system reliability parameter or to compare different systems or designs. This inaccuracy can lead to bad design decisions. Furthermore, probabilistic failure prediction based on MTBF implies the total absence of systematic failures i. MTBF value prediction is an important element in the development of products. MDT can be defined as mean time which the system is down after the failure. The terminology is here used by close analogy to electrical circuits, but has a slightly different meaning.

We say that the two components are in series if the failure of either causes the failure of the network, and that they are in parallel if only the failure of both causes the network to fail. The MTBF of the resulting two-component network with repairable components can be computed according to the following formulae, assuming that the MTBF of both individual components is known: [6] [7]. Then, assuming that MDTs are negligible compared to MTBFs which usually stands in practice , the MTBF for the parallel system consisting from two parallel repairable components can be written as follows: [6] [7].

Intuitively, both these formulae can be explained from the point of view of failure probabilities. First of all, let's note that the probability of a system failing within a certain timeframe is the inverse of its MTBF.

Then, when considering series of components, failure of any component leads to the failure of the whole system, so assuming that failure probabilities are small, which is usually the case probability of the failure of the whole system within a given interval can be approximated as a sum of failure probabilities of the components.

With parallel components the situation is a bit more complicated: the whole system will fail if and only if after one of the components fails, the other component fails while the first component is being repaired; this is where MDT comes into play: the faster the first component is repaired, the less is the "vulnerability window" for the other component to fail.

Using similar logic, MDT for a system out of two serial components can be calculated as: [6]. In a special but all-important case of several serial components, MTBF calculation can be easily generalised into.

Such nomenclature is used when it is desirable to differentiate among types of failures, such as critical and non-critical failures. For example, in an automobile, the failure of the FM radio does not prevent the primary operation of the vehicle. It can be calculated as follows:. From Wikipedia, the free encyclopedia. Lienig, H. Bruemmer Fundamentals of Electronic Systems Design. Springer International Publishing. Stephen Foskett, Pack Rat.

Retrieved Vicor Reliability Engineering. Retrieved 1 June Lin ". David J. Smith Reliability, Maintainability and Risk eighth ed. Retrieved 7 July Categories : Engineering failures Survival analysis Reliability analysis. Namespaces Article Talk. Views Read Edit View history.

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## Mean Time Before Failure (MTBF), Mean Time To Repair(MTTR) and Reliability Calculators

Usually people think of it as the average time that something works until it fails and needs to be repaired again. As reliable production processes are crucial in a Lean Manufacturing environment, MTBF is vital for all lean initiatives. In other words, the mean time between failures is the time from one failure to another. This distinction is important if the repair time is a significant fraction of MTTF. Here is an example.

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## MTTR, MTBF, or MTTF? – A Simple Guide To Failure Metrics

The MTBF, or mean time between failure, is a statistical measure used to predict the behavior of a large group of samples, or units. For example, the MTBF may be used to determine maintenance schedules, to determine how many spares should be kept on hand to compensate for failures in a group of units, or as an indicator of system reliability. In order to calculate MTBF, you need to know the total unit hours of testing conducted during the trial in question and the number of failures that occurred. Whether you're evaluating the reliability of new software or trying to decide how many spare widgets to keep on hand in your warehouse, the process for calculating MTBF is the same. The first metric you must know is the total "unit hours" of testing that took place in your reliability study. Imagine that your subject is warehouse widgets, and that 50 of them were tested for hours each.