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.
[2] In addition, units that are taken down for routine scheduled maintenance or inventory control are not considered within the definition of failure.
[3] The higher the MTBF, the longer a system is likely to work before failing.
For example, three identical systems starting to function properly at time 0 are working until all of them fail.
The MTBF of the systems is the average of the three failure times, which is 116.667 hours.
In general, MTBF is the "up-time" between two failure states of a repairable system during operation as outlined here:
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
Any practically-relevant calculation of the MTBF assumes 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.
[1] In other words, it is assumed that the system has survived initial setup stresses and has not yet approached its expected end of life, both of which often increase the failure rate.
This value should only be understood conditionally as the “mean lifetime” (an average value), and not as a quantitative identity between working and failed units.
[4] Assuming no systematic errors, the probability the system survives during a duration, T, is calculated as exp^(-T/MTBF).
MTBF value prediction is an important element in the development of products.
Reliability engineers and design engineers often use reliability software to calculate a product's MTBF according to various methods and standards (MIL-HDBK-217F, Telcordia SR332, Siemens SN 29500, FIDES, UTE 80-810 (RDF2000), etc.).
The Mil-HDBK-217 reliability calculator manual in combination with RelCalc software (or other comparable tool) enables MTBF reliability rates to be predicted based on design.
MDT can be defined as mean time which the system is down after the failure.
Usually, MDT is considered different from MTTR (Mean Time To Repair); in particular, MDT usually includes organizational and logistical factors (such as business days or waiting for components to arrive) while MTTR is usually understood as more narrow and more technical.
MTBF serves as a crucial metric for managing machinery and equipment reliability.
MTBF provides a quantitative measure of the time elapsed between failures of a system during normal operation, offering insights into the reliability and performance of manufacturing equipment.
[6] By integrating MTBF with TPM principles, manufacturers can achieve a more proactive maintenance approach.
This synergy allows for the identification of patterns and potential failures before they occur, enabling preventive maintenance and reducing unplanned downtime.
As a result, MTBF becomes a key performance indicator (KPI) within TPM, guiding decisions on maintenance schedules, spare parts inventory, and ultimately, optimizing the lifespan and efficiency of machinery.
[7] This strategic use of MTBF within TPM frameworks enhances overall production efficiency, reduces costs associated with breakdowns, and contributes to the continuous improvement of manufacturing processes.
The terminology is here used by close analogy to electrical circuits, but has a slightly different meaning.
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:[8][9]
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.
For example, in an automobile, the failure of the FM radio does not prevent the primary operation of the vehicle.
[1] MTTFd is an extension of MTTF, and is only concerned about failures which would result in a dangerous condition.
In fact with a parametric model of the lifetime, the likelihood for the experience on any given day is as follows: where For a constant exponential distribution, the hazard,