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MTBF Calculator: MTTR, Availability and Failure Rate
Calculate mean time between failures, mean time to repair, and inherent availability from your maintenance records, or enter known MTBF and MTTR. Add a mission time to see the probability of running it without failure.
MTBF, MTTR and availability calculator
Mission reliability assumes a constant failure rate (exponential model).
| Step | Formula | Value |
|---|---|---|
| Mean time between failures | MTBF = operating time / failures = 2000 / 5 | 400 h |
| Mean time to repair | MTTR = repair time / repairs = 15 / 5 | 3 h |
| Inherent availability | Aᵢ = MTBF / (MTBF + MTTR) = 400 / (400 + 3) | 99.2556 % |
| Failure rate | λ = 1 / MTBF = 1 / 400 | 0.0025 /h |
| Expected downtime per year | (1 − Aᵢ) × 8760 h | 65.21 h |
| Reliability over mission time | R(t) = e^(−t / MTBF) = e^(−40 / 400) | 90.484 % |
Formulas used
- Mean time between failures
- MTBF = total operating time / number of failures
- Mean time to repair
- MTTR = total repair time / number of repairs
- Inherent availability
- Aᵢ = MTBF / (MTBF + MTTR)
- Failure rate
- λ = 1 / MTBF
- Mission reliability (constant λ)
- R(t) = e^(−t / MTBF)
- Expected downtime per year
- (1 − Aᵢ) × 8760 h
Assumptions and limits
- Operating time counts only time the equipment was running, not calendar time or planned shutdowns.
- Every failure is repaired, so the number of repairs equals the number of failures.
- Inherent availability counts active repair time only. Waiting for parts, technicians, or approvals is excluded; including it gives operational availability, which is lower.
- Mission reliability assumes a constant failure rate (exponential model). It does not describe wear-out or infant-mortality behaviour.
- Annual downtime assumes continuous operation, 8,760 hours per year.
Worked example
A packaging line logged 2,000 running hours last quarter with 5 breakdowns and 15 hours of total repair time. What are MTBF, MTTR, availability, and the chance of getting through a 40-hour week without a breakdown?
| Step | Formula | Value |
|---|---|---|
| Mean time between failures | MTBF = operating time / failures = 2000 / 5 | 400 h |
| Mean time to repair | MTTR = repair time / repairs = 15 / 5 | 3 h |
| Inherent availability | Aᵢ = MTBF / (MTBF + MTTR) = 400 / (400 + 3) | 99.2556 % |
| Failure rate | λ = 1 / MTBF = 1 / 400 | 0.0025 /h |
| Expected downtime per year | (1 − Aᵢ) × 8760 h | 65.21 h |
| Reliability over mission time | R(t) = e^(−t / MTBF) = e^(−40 / 400) | 90.484 % |
Result: MTBF 400 h, MTTR 3 h, inherent availability 99.26%, and a 90.5% chance of completing a 40-hour week without failure.
How to use MTBF, MTTR and availability
Collect the right data
You need three numbers for the period: running hours, number of failures, and total hands-on repair time. Pull them from your CMMS or downtime log, and decide up front what counts as a failure, such as any unplanned stop over five minutes.
MTBF is an average, not a guarantee
Under a constant failure rate, only about 37% of units run as long as the MTBF without failing, because R(MTBF) = e^(−1). Use mission reliability, R(t), to answer "will it survive this shift or week?"
Improving availability
Availability can be raised by failing less often (higher MTBF) or by recovering faster (lower MTTR). Standard work for changeovers and repairs, kitted spares, and clear troubleshooting job aids reduce MTTR, often faster than reliability engineering raises MTBF.
Link to OEE
Breakdowns are one of the losses in OEE availability. MTBF and MTTR tell you how often you stop and for how long, which shows where an OEE availability loss comes from.
Common mistakes
- Using calendar time instead of operating time. Counting nights and weekends the machine was idle inflates MTBF.
- Including waiting time in MTTR for inherent availability. Logistic delays belong in operational availability. Mixing them in hides where the downtime comes from.
- Calculating MTBF from zero failures. With no failures there is no point estimate. Use a confidence bound instead (see the FAQ).
- Treating MTBF as service life. MTBF describes the random-failure period. Parts that wear out need life data (for example a Weibull analysis), not MTBF.
- Mixing failure definitions across lines. If one line logs every micro-stop and another only major breakdowns, their MTBFs cannot be compared.
Frequently asked questions
How do you calculate MTBF?
Divide total operating time by the number of failures in that time. For example, 2,000 running hours with 5 failures gives an MTBF of 400 hours.
What is the difference between MTBF and MTTR?
MTBF is the average running time between failures. MTTR is the average time to repair a failure. Together they set inherent availability: MTBF / (MTBF + MTTR).
What is a good availability figure?
It depends on the process and its cost of downtime. The calculator shows the annual downtime each availability implies, which is often easier to judge than a percentage.
What if there were no failures?
You can only state a lower confidence bound. For a time-terminated test with r failures, MTBF_lower = 2T / χ²(C; 2r + 2), where T is total operating time and χ²(C; 2r + 2) is the chi-square value with 2r + 2 degrees of freedom whose cumulative probability equals the confidence level C. With r = 0 at 90% confidence, this is about T / 2.3.
Is MTBF the same as MTTF?
MTTF (mean time to failure) is used for items that are not repaired. MTBF is used for repairable items. Under a constant failure rate the arithmetic is the same.
Sources
- IEC 60050-192:2015, International Electrotechnical Vocabulary — Part 192: Dependability — definitions of MTBF, MTTR and availability.
- MIL-HDBK-338B, Electronic Reliability Design Handbook, 1998 — inherent and operational availability, exponential reliability model.
- NIST/SEMATECH e-Handbook of Statistical Methods, Chapter 8: Assessing Product Reliability — exponential model and chi-square confidence bounds for MTBF.
Results are computed in your browser from the published formulas named above. They are an engineering aid, not a substitute for the governing standard, your drawing, or your customer's requirements.