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MTBF Calculator
Estimate mean time between failures from field or test data. Enter the operating hours (or units times hours) and the number of failures to get MTBF, failure rate in FPMH and FIT, chi-square confidence limits, inherent availability from MTTR, and the probability of surviving a mission without failure.
Last updated:
Operating time and failures
Operating time
h
h
h
Optional, for availability
Mission and confidence
h
Period you want the reliability for
Enter your values to see the result.
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How to use the MTBF Calculator
- Enter the operating time: total hours, or the number of units and the hours each one ran.
- Enter the number of failures observed in that time, and the MTTR if you want availability.
- Set the mission time you care about (for example one year = 8,760 h) and a confidence level.
- Choose how the test ended: at a fixed time, or right at the last failure.
- Read MTBF, failure rate, availability and reliability, and use the lower confidence limit for conservative planning.
MTBF and reliability formulas
| Quantity | Formula |
|---|---|
| Mean time between failures | MTBF = T ÷ r (total operating time ÷ failures) |
| Failure rate | λ = 1 ÷ MTBF; FPMH = λ × 10⁶; FIT = λ × 10⁹ |
| Reliability for time t | R(t) = e−λt = e−t ÷ MTBF |
| Probability of failure by t | F(t) = 1 − R(t) |
| Inherent availability | Ai = MTBF ÷ (MTBF + MTTR) |
| Lower confidence limit (time-terminated) | MTBFL = 2T ÷ χ²C, 2r+2 |
| Lower confidence limit (failure-terminated) | MTBFL = 2T ÷ χ²C, 2r |
| Two-sided upper limit | MTBFU = 2T ÷ χ²(1−C)/2, 2r |
| Systems in series | λsystem = λ₁ + λ₂ + … (MTBFsystem = 1 ÷ Σλ) |
These formulas assume a constant failure rate (the flat "useful life" part of the bathtub curve, exponential distribution). Early-life failures and wear-out need a Weibull analysis instead.
Reliability at multiples of MTBF
| Mission time | Reliability R(t) | Failure probability |
|---|---|---|
| 1% of MTBF | 99.00% | 1.00% |
| 10% of MTBF | 90.48% | 9.52% |
| 50% of MTBF | 60.65% | 39.35% |
| 69.3% of MTBF (median) | 50.00% | 50.00% |
| 100% of MTBF | 36.79% | 63.21% |
| 200% of MTBF | 13.53% | 86.47% |
Tips for using MTBF
- MTBF is not a lifetime. A drive with a 1,000,000 h MTBF will not last 114 years; it means that in a large population roughly 0.9% fail per year of continuous use during their service life.
- Use consistent time. Count powered-on or operating hours, not calendar time, unless the item fails while idle too.
- Plan with the lower limit. With few failures the point estimate is uncertain; the one-sided lower confidence limit is the safer number for spares and warranty planning.
- Cut MTTR to raise availability. Halving repair time has the same effect on availability as doubling MTBF.
Frequently asked questions
How do you calculate MTBF?
MTBF = total operating time ÷ number of failures. Twenty units that each ran 2,500 hours (50,000 unit-hours) with 4 failures have an MTBF of 12,500 hours. Count only the time the items were actually operating.
How do I convert MTBF to failure rate?
For a constant failure rate, λ = 1 ÷ MTBF. An MTBF of 12,500 h is 0.00008 failures per hour, 80 failures per million hours (FPMH) or 80,000 FIT (failures per billion hours).
What is the probability of surviving a mission?
With a constant failure rate, reliability R(t) = e^(−t ÷ MTBF). A unit with a 12,500 h MTBF has a 92.3% chance of running 1,000 h without failure. At t = MTBF only about 36.8% survive, which is why MTBF is not the same as expected life.
How is availability calculated from MTBF and MTTR?
Inherent availability A = MTBF ÷ (MTBF + MTTR). With MTBF 12,500 h and MTTR 6 h, A = 99.952%, about 4.2 hours of downtime per year of continuous operation. Operational availability is lower when it includes logistics and waiting time.
What is the MTBF confidence interval?
Because failures are random, the observed MTBF is only an estimate. The lower limit at confidence C is 2T ÷ χ²(C, 2r + 2) for a time-terminated test (2r degrees of freedom if the test stopped at a failure). With 4 failures in 50,000 h you can be 90% confident the MTBF is at least about 6,255 h.
What if there were no failures?
You cannot compute a point estimate, but you can state a demonstrated minimum: MTBF ≥ T ÷ −ln(1 − C). 10,000 failure-free hours demonstrate an MTBF of at least about 4,343 h at 90% confidence.
What is the difference between MTBF and MTTF?
MTBF applies to repairable items that are restored after each failure; MTTF (mean time to failure) is used for non-repairable items that are replaced. For a constant failure rate both are calculated the same way, total time ÷ failures.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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