# Mean Time Between Failures (Mtbf)

**Mean Time Between Failures (MTBF)**

Reliability is quantified as MTBF (Mean Time Between Failures) for repairable product and MTTF (Mean Time To Failure) for non-repairable product. A correct understanding of MTBF is important. A power supply with an MTBF of 40,000 hours does not mean that the power supply should last for an average of 40,000 hours. According to the theory behind the statistics of confidence intervals, the statistical average becomes the true average as the number of samples increase. An MTBF of 40,000 hours, or 1 year for 1 module, becomes 40,000/2 for two modules and 40,000/4 for four modules. Sometimes failure rates are measured in percent failed per million hours of operation instead of MTBF. The FIT is equivalent to one failure per billion device hours, which is equivalent to a MTBF of 1,000,000,000 hours. The formula for calculating the MTBF is

MTTF is stands for Mean Time To Failure. To distinguish between the two, the concept of suspensions must first be understood. In reliability calculations, a suspension occurs when a destructive test or observation has been completed without observing a failure. MTBF calculations do not consider suspensions whereas MTTF does. MTTF is the number of total hours of service of all devices divided by the number of devices. It is only when all the parts fail with the same failure mode that MTBF converges to MTTF.

**Example:** Suppose 10 devices are tested for 500 hours. During the test 2 failures occur. The estimate of the MTBF is:

Whereas for MTTF

If the MTBF is known, one can calculate the failure rate as the inverse of the MTBF. The formula for (λ) is:

Once a MTBF is calculated, what is the probability that any one particular Vicor module will be operational at time equal to the MTBF? We have the following equation:

This tells us that the probability that any one particular module will survive to its calculated MTBF is only 36.8%.