MTBF vs MTTR vs MTTF: reliability metrics explained

MTBF, MTTR and MTTF are the three numbers most maintenance teams use to describe how often equipment fails and how quickly it comes back. MTBF, mean time between failures, is the average running time between breakdowns of something that gets repaired. MTTR, mean time to repair, is the average time each repair takes. MTTF, mean time to failure, is the average life of something that is thrown away and replaced when it fails. This article explains what each one measures, how to calculate them from your own records, how they combine into availability, why a large MTBF figure on a datasheet does not mean a part will last that long, and how connected sensors change both the numbers and how they are collected.

MTBF: mean time between failures

MTBF applies to repairable equipment: a pump, a conveyor, a compressor, a gateway that gets rebooted or has a board swapped. It is the average operating time between one failure and the next.

The calculation is total operating time divided by the number of failures in the same period:

MTBF = total operating time / number of failures

Operating time means time the equipment was meant to be running and was running. Planned shutdowns, weekends when the line is off, and the repair time itself are left out. A higher MTBF means the equipment fails less often.

What counts as a failure has to be agreed before the number means anything. A failure is usually any event that stops the equipment doing its job and needs unplanned work to fix. Planned maintenance is not a failure. Whether a two-minute jam cleared by an operator counts is a local decision, and it moves the result a lot, so write the rule down and keep it.

MTTR: mean time to repair

MTTR measures how quickly equipment comes back after a failure. It is total repair time divided by the number of repairs:

MTTR = total repair time / number of repairs

In maintenance, repair time usually runs from the moment the equipment fails to the moment it is back in service. That includes noticing the failure, getting a technician there, finding the cause, waiting for parts, doing the repair, and testing. Some teams measure only the hands-on repair; the number then looks better and says less about the downtime the plant actually suffers. A lower MTTR is better.

The R is ambiguous. In IT and incident management, MTTR is often mean time to recover, restore, respond or resolve, each with a different start and end point. When comparing figures from different teams or tools, check which one is meant.

MTTF: mean time to failure

MTTF applies to non-repairable items: a bearing, a fuse, a sensor, a battery, a disk. When they fail they are replaced, so there is no “between”. MTTF is the average time such items run before they fail, calculated across a population:

MTTF = total operating time of all units / number of units that failed

In practice MTTF and MTBF are worked out the same way and are often used loosely for each other, especially on component datasheets. The distinction that matters is whether the thing is repaired and goes back into service, which makes MTTR relevant, or is replaced, which makes the replacement time the equivalent of MTTR.

A worked example

A packaging line’s main pump was scheduled to run for 2,000 hours over a quarter. It failed four times. The four repairs took 3, 7, 4 and 6 hours, 20 hours in total.

• Operating time is 2,000 minus the 20 hours it spent broken: 1,980 hours.
• MTBF = 1,980 / 4 = 495 hours.
• MTTR = 20 / 4 = 5 hours.
• Availability = 495 / (495 + 5) = 99.0 per cent.

Two cautions about the example. Four failures is a small sample, and one unusual breakdown would move the MTBF by a quarter; the figures settle down only over many failures or many machines. And the averages hide the spread: an MTTR of 5 hours might be four quick fixes or three ten-minute resets and one long wait for a part. Keep the individual records, because the long repairs are usually where the improvement is.

Availability: putting MTBF and MTTR together

Availability is the fraction of the time equipment is able to work when it is needed:

Availability = MTBF / (MTBF + MTTR)

This form, often called inherent availability, counts only failures and repairs. It shows why the two metrics are managed together. The same 99 per cent can come from a machine that fails rarely and takes a long time to fix, or one that fails often and is fixed in minutes. The first needs spare parts and skills on hand for a rare event; the second needs the causes of its frequent small failures removed. Availability is also the first of the three factors in overall equipment effectiveness, alongside performance and quality.

What an MTBF figure does not tell you

Datasheets for drives, power supplies and industrial PCs often quote MTBF figures of hundreds of thousands or millions of hours. A million hours is more than a hundred years, and nobody expects the part to last a century. The figure is a statement about a large population during its normal working life, and two pieces of arithmetic make that clear.

First, with a constant failure rate, the chance that one unit is still working at time t is e to the power of minus t divided by the MTBF. At t equal to the MTBF, that is about 37 per cent. So even taken at face value, most units fail before reaching their MTBF.

Second, MTBF converts into an annual failure rate. A year is 8,760 hours, so a part with an MTBF of 1,000,000 hours has an annual failure rate of about 8,760 divided by 1,000,000, or 0.9 per cent. In a fleet of 1,000 such parts, about nine a year would be expected to fail during their working life. That is the useful reading: it tells you how many spares to stock, and nothing about when a particular one will go.

The constant failure rate behind both calculations holds only for part of a product’s life. Failure rates over a whole life usually follow the bathtub curve.

Early failures, sometimes called infant mortality, come from manufacturing defects, damage in transit and installation mistakes, and fall away as the weak units are weeded out; burn-in testing and careful commissioning target them. Useful life has a low, roughly constant rate of random failures, and this is the region datasheet MTBF figures describe. Wear-out is where bearings, seals, brushes, capacitors and batteries reach the end of their life and the failure rate climbs. Preventive replacement and condition monitoring target that region.

Predicted MTBF and measured MTBF

A datasheet MTBF is usually predicted, not observed. It is calculated by adding up failure rates for every component on the board, from a handbook method such as MIL-HDBK-217 or Telcordia SR-332, at a stated temperature and duty. The result depends heavily on the method and the assumed temperature, so two figures for similar products are only comparable when both are known.

A measured MTBF comes from your own failure records, for your equipment in your conditions. It is the one to plan maintenance with. Use the predicted figure for comparing designs and estimating spares before you have field data, and replace it with measured data as soon as you have enough failures to trust it.

MTTD, MTTA and the parts of downtime

Downtime splits into stages, and two more metrics measure the early ones:

• MTTD, mean time to detect: from the failure to someone or something noticing it.
• MTTA, mean time to acknowledge: from the alert to a person taking ownership of it.

After that come diagnosis, waiting for parts and the repair itself. Splitting MTTR into these stages shows where the time goes. In many plants the repair is quick and the waiting is not: a fault on a night shift goes unnoticed until morning, or a technician arrives and then waits a day for a part.

How IoT monitoring changes the numbers

Connected sensors and machines affect these metrics in three ways.

Better data. Calculating MTBF needs accurate operating hours and failure times. Many plants reconstruct them from handwritten logs and work orders, which miss short stops and blur the timing. A PLC or gateway that records run state, stops and fault codes gives exact operating time and an exact timestamp for every failure, as described in the articles on what a PLC is and what an industrial IoT system is made of.

Shorter MTTR. Automatic alerts cut detection time to seconds. A fault code and the readings leading up to the stop shorten diagnosis. For connected devices themselves, remote diagnostics and over-the-air firmware updates can fix some faults without a site visit at all.

Longer MTBF. Condition monitoring finds wear before it causes a breakdown, so the work happens as a planned repair instead of a failure. The predictive maintenance article covers the vibration and temperature sensors that do this for rotating machines. Expect the measured MTBF to rise for that reason, and expect planned maintenance hours to rise with it; both belong in the report, or the improvement looks free.

One warning when introducing monitoring: the new data will often show more failures than the old records did, because short stops that nobody wrote down are now counted. MTBF can appear to drop in the first months. Compare like with like, or start a fresh baseline when the measurement changes.