MTBF Calculator Widget
Give maintenance and reliability readers a quick MTBF and MTTR calculator. From operating hours, the number of failures and the repair time it reports the failure rate, inherent availability and the probability of completing a mission of a given length without a failure.
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<iframe src="https://a2z.tools/embed/w/mtbf-calculator" title="MTBF Calculator by A2Z Tools" width="100%" height="560" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>
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<div data-a2z-widget="mtbf-calculator" data-height="560"></div> <script async src="https://a2z.tools/embed.js"></script>
Adds a small script (what it does) that sizes the widget to fit its content, loads it lazily and keeps it isolated from your page's CSS.
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How it works
Mean time between failures is the total operating time divided by the number of failures; repair time is excluded from the numerator, so enter running hours only. Mean time to repair is the total active repair time divided by the same number of failures. The failure rate is the reciprocal of MTBF, shown per hour and per million hours. Inherent availability, MTBF / (MTBF + MTTR), is the share of time the equipment would be up if repairs started instantly and spares were always on hand; real operational availability is lower because it also counts waiting for parts and people. For a mission time t the widget gives reliability R(t) = e^(-t / MTBF), which assumes a constant failure rate - the flat bottom of the bathtub curve. With 10,000 hours, 4 failures and 20 hours of repairs, MTBF is 2,500 hours, MTTR 5 hours, availability 99.80% and the chance of a 100-hour run without failure 96.08%. Zero failures is refused: MTBF then needs a chi-square confidence bound, not a point estimate.
Calculation method
- MTBF = total operating time / number of failures
- MTTR = total repair time / number of failures
- Failure rate lambda = 1 / MTBF
- Inherent availability Ai = MTBF / (MTBF + MTTR)
- Reliability for mission time t: R(t) = exp(-t / MTBF) (constant failure rate, exponential model)
Worked examples
Handbook case
Inputs: 1,000 operating hours; 5 failures; 10 hours of repairs; mission 200 h
Result: MTBF 200 h; MTTR 2 h; failure rate 5,000 per million hours; availability 99.010%; R(200 h) 36.79%
Five failures per thousand hours is the Reliability Analysis Center's own example of an MTBF of 200 hours.
Pump fleet
Inputs: 10,000 operating hours; 4 failures; 20 hours of repairs; mission 100 h
Result: MTBF 2,500 h; MTTR 5 h; 400 per million hours; availability 99.800%; R(100 h) 96.08%
e^(-100 / 2,500) = e^-0.04 = 0.9608.
Limitations
- Reliability uses the exponential (constant failure rate) model; early-life and wear-out failures need a Weibull analysis.
- Availability is inherent availability - logistics delays, preventive maintenance and waiting time are excluded.
- Small failure counts give very uncertain estimates; no confidence interval is shown.
Where publishers use it
- A CMMS or maintenance-software vendor's metrics glossary
- Reliability-engineering coursework on exponential failure models
- Data-centre and IT operations pages comparing redundant hardware
- Equipment manufacturers publishing reliability claims for pumps, drives or sensors
- Fleet and facilities managers justifying preventive maintenance budgets
Questions
Does an MTBF of 2,500 hours mean the machine lasts 2,500 hours?
No. Under a constant failure rate only e^-1 = 36.8% of units survive to the MTBF without a failure. MTBF is an average rate figure: 2,500 hours means 400 failures per million operating hours across a population, not a life expectancy.
What is the difference between MTBF and MTTF?
MTBF is used for repairable equipment that goes back into service after each failure; MTTF, mean time to failure, is used for items that are replaced rather than repaired, such as bulbs or bearings. Under the exponential model both equal 1 / lambda.
Why is availability so high when there were four breakdowns?
Because inherent availability only counts active repair time. Four 5-hour repairs in 10,000 hours is 99.8%. If each breakdown also waited 2 days for a spare part, operational availability would be about 10,000 / (10,000 + 212) = 97.9%.
What if nothing has failed yet?
A point estimate of MTBF is undefined with zero failures. Reliability engineers quote a lower confidence bound instead, for example the 60% bound 2T / chi-square(0.6, 2), roughly T / 0.92 for T operating hours. The widget asks for at least one failure.
Should I add up hours across several identical machines?
Yes, if they run under similar conditions. Ten pumps running 1,000 hours each with 4 failures between them give 10,000 operating hours and an MTBF of 2,500 hours.
Sources
- Exponential distribution (e-Handbook 8.1.6.1) - NIST/SEMATECH e-Handbook of Statistical Methods . R(t) = e^(-lambda t), constant failure rate h(t) = lambda, mean = 1 / lambda. Checked 2026-10-01.
- Operational Availability Handbook, Section 1: Introduction to Operational Availability - Reliability Analysis Center (US DoD information analysis center), hosted by AcqNotes . Defines inherent availability Ai = MTBF / (MTBF + MTTR) and gives the 5 failures per 1,000 hours = 200-hour MTBF example. Checked 2026-10-01.
Cite or recommend this tool
If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.
A2Z Tools MTBF Calculator https://a2z.tools/mtbf-mttr-calculator
<a href="https://a2z.tools/mtbf-mttr-calculator">A2Z Tools MTBF Calculator</a>
[A2Z Tools MTBF Calculator](https://a2z.tools/mtbf-mttr-calculator)
MTBF Calculator by A2Z Tools - https://a2z.tools/mtbf-mttr-calculator
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