Answer: MTBF is total operating hours divided by the number of failures. 720 hours with 6 failures gives an MTBF of 120 hours, a failure rate of 8.33 per 1,000 hours, and 97.6% availability if each repair takes 3 hours.
Mean time between failures, plus MTTR, availability, and mission reliability
| MTBF (hrs) | MTTR (hrs) | Ratio | Availability |
|---|---|---|---|
| 100 | 5 | 20:1 | 95.2% |
| 120 | 3 | 40:1 | 97.6% |
| 200 | 10 | 20:1 | 95.2% |
| 250 | 5 | 50:1 | 98.0% |
| 500 | 8 | 63:1 | 98.4% |
| 1,000 | 10 | 100:1 | 99.0% |
| 2,000 | 20 | 100:1 | 99.0% |
Notice the two 95.2% rows and the two 99.0% rows: availability depends on the ratio, not the raw MTBF. A plant that doubles MTBF but lets repairs stretch twice as long gains nothing.
MTBF answers one question: how long does this asset run, on average, between breakdowns? It's the core metric of reliability engineering for repairable systems, and it feeds directly into availability targets, spare-parts decisions, and maintenance planning.
MTBF = operating hours ÷ failures. MTTR = total repair time ÷ repairs. Availability = MTBF ÷ (MTBF + MTTR). Failure rate is the reciprocal of MTBF, shown here per 1,000 hours so the numbers stay readable. Mission reliability uses the exponential model: R(t) = e^(−t/MTBF), the probability the asset survives t hours of operation without a failure.
Pull a period from your maintenance log or CMMS: the hours the asset was scheduled and running, how many unplanned failures stopped it, and the wrench time spent getting it back. Keep one definition of "failure" and stick with it. Most teams count any unplanned stop needing a work order and exclude scheduled maintenance.
A packaging line logs 720 operating hours in a quarter and 6 unplanned failures. MTBF = 720 ÷ 6 = 120 hours. The 6 repairs consumed 18 hours total, so MTTR = 3 hours, and availability = 120 ÷ 123 = 97.6%. The failure rate works out to 8.33 failures per 1,000 operating hours, which at around-the-clock operation is roughly 73 per year (8,760 ÷ 120).
For the mission estimate: the chance of getting through a 24-hour production run without a stop is e^(−24/120) = 81.9%. Stretch the run to a full week, 168 hours, and it drops to 24.7%, which matches what the crew sees: week-long clean runs are rare, not normal. A second asset, a process pump with 3 failures across 8,760 operating hours, works out to MTBF = 2,920 hours and 99.6% availability at 38 total repair hours (MTTR 12.7 hours); the odds of a 30-day (720-hour) clean run are 78.1%.
The mission figure is the one people misread most. Under the constant-failure-rate model this calculator uses, the chance of running t hours with no failure is e^(−t/MTBF). It depends only on how long the mission is compared with the MTBF, so one table covers every asset you'll ever plug in.
| Mission length ÷ MTBF | Example at MTBF = 120 hrs | Chance of no failure |
|---|---|---|
| 0.05 | 6 hrs | 95.1% |
| 0.1 | 12 hrs | 90.5% |
| 0.25 | 30 hrs | 77.9% |
| 0.5 | 60 hrs | 60.7% |
| 0.693 | 83.2 hrs | 50.0% |
| 1 | 120 hrs | 36.8% |
| 2 | 240 hrs | 13.5% |
| 3 | 360 hrs | 5.0% |
Look at the 1× row. An asset asked to run exactly one MTBF only gets through clean 36.8% of the time, so about two runs in three see at least one stop. That isn't a flaw in the math. MTBF is a mean, and the exponential distribution is lopsided: lots of short intervals, a few very long ones. Half of all intervals end before 0.693 × MTBF, which is 83 hours on a 120-hour asset.
If you need a given confidence of finishing a run, flip the formula: t = −MTBF × ln(R). For 90% odds that's about 0.105 × MTBF, for 95% about 0.051 × MTBF, and for 99% about 0.010 × MTBF. On the 120-hour packaging line, that means clean runs of roughly 12.6, 6.2, and 1.2 hours. High targets get expensive fast, which is why critical systems lean on redundancy and spares instead of hoping one machine behaves.
The tool reports failures per 1,000 operating hours. You'll also see λ per hour (simply 1 ÷ MTBF), failures per year, and FIT, the electronics convention of failures per billion device-hours. They're all the same number in different units:
| MTBF (hrs) | λ per hour | Per 1,000 hrs | Per year (8,760 hrs) | FIT |
|---|---|---|---|---|
| 100 | 0.01 | 10 | 87.6 | 10,000,000 |
| 500 | 0.002 | 2 | 17.5 | 2,000,000 |
| 1,000 | 0.001 | 1 | 8.76 | 1,000,000 |
| 10,000 | 0.0001 | 0.1 | 0.88 | 100,000 |
| 100,000 | 0.00001 | 0.01 | 0.09 | 10,000 |
| 1,000,000 | 0.000001 | 0.001 | 0.009 | 1,000 |
The per-year column assumes the asset runs around the clock. A machine on one 8-hour shift, five days a week, logs about 2,080 hours a year, so scale it down to match.
MTTF (mean time to failure) is the same average for things you replace instead of repair: bearings, lamps, sealed modules. The arithmetic is identical, so you can use this calculator for MTTF too. Just set repair time to zero and ignore the availability card. MTTR here is total repair time divided by the number of failures, which assumes one repair per failure. If your log splits response time from wrench time, pick one and say which. Counting travel and waiting on parts gives a more honest availability number.
The availability this tool shows, MTBF ÷ (MTBF + MTTR), is what reliability engineers call inherent availability. It leaves out planned downtime like changeovers and PMs, so it'll usually read higher than the availability term in an OEE calculation. Neither is wrong; they answer different questions.
There is no universal good number, because MTBF scales with how often an asset runs and what you count as a failure. A packaging line at 120 hours and a pump at 2,900 hours can both be healthy. The honest target is the MTBF-to-MTTR ratio, which sets availability: 120 hours between failures with 3-hour repairs gives 97.6% availability, while 200 hours with 10-hour repairs gives 95.2%. Track your own baseline, then drive the ratio up.
No, and this is the most common misreading. MTBF is the average interval between failures of a repairable asset, not how long it lasts. An asset with an MTBF of 120 hours can run for years if each failure is fixed in an hour. Lifetime is a retirement question; MTBF is a breakdown-frequency question.
MTBF measures how often something fails: operating time divided by the number of failures. MTTR measures how long each failure lasts: total repair time divided by the number of repairs. Availability combines the two: MTBF ÷ (MTBF + MTTR). Cutting MTTR is often cheaper than stretching MTBF, which is why spares and repair procedures matter as much as the hardware.
The standard formulas assume a constant failure rate, which only holds during an asset's useful-life period, after infant mortality but before wear-out. In that window, reliability over a mission of t hours follows R(t) = e^(−t/MTBF). If your failures cluster early (bad installs) or late (wear-out), the exponential model understates or overstates the risk, so treat the percentages as estimates, not guarantees.
Add up the hours the asset was actually running, count the failures that stopped it, and divide. Decide up front what counts as a failure; most teams exclude planned maintenance and include any unplanned stop that required a work order. Keep the definition consistent, because a metric that changes definitions every quarter can't show a trend.
The calculator needs at least one failure, because operating hours divided by zero has no meaningful value, so it shows a dash. Zero failures tells you the MTBF is probably longer than your observation window, not what it actually is. For a lower bound, reliability engineers use the chi-squared method: with zero failures in T hours, you can say with 90% confidence that MTBF is at least about T ÷ 2.3. A pump that ran 5,000 hours without failing supports an MTBF of at least roughly 2,170 hours at that confidence.
Because MTBF is an average, not a guarantee. Under the exponential model, R(t) = e^(−t/MTBF), and when t equals MTBF that's e^(−1), or 36.8%. Failure intervals are lopsided: many are short and a few are very long, so the long ones pull the average up. Half of all intervals end before about 0.69 × MTBF. If you want 90% odds of a clean run, keep the mission to about a tenth of the MTBF.
MTBF applies to repairable assets that fail, get fixed, and go back into service. MTTF applies to items you replace after one failure, like a bearing or a light bulb. Both are operating hours divided by failures, so the math in this calculator works for either. For MTTF, set repair time to zero and ignore the availability result.
The calculator shows failures per 1,000 hours, which is 1,000 ÷ MTBF. For failures per hour, divide by 1,000. For FIT (failures per billion hours), multiply the per-1,000-hour figure by 1,000,000. For failures per year, divide the asset's yearly run hours by the MTBF: a 120-hour MTBF on a 24/7 asset means 8,760 ÷ 120 = 73 failures a year, but on a 2,080-hour single-shift schedule it's about 17.