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MTBF, MTTR and reliability calculator

Enter period totals or a list of times between failures to get MTBF, MTTR, availability, the probability of running failure-free over the mission time and the failure pattern from the Weibull shape factor.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimate
Failure data
Model and horizon

With period totals, enter a known or typical β: bearings 1.1 to 1.5; mechanical seals 0.8 to 1.8; belts 1.2 to 2.5; abrasive wear 2 to 4.

—Reliability over the mission time
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Reliability over time

Probability of running without failure up to each time; the dashed line is the exponential model with the same MTBF.

Tap the chart to see the values.

Failure rate versus age

Instantaneous failure risk. Rising means wear-out: age-based preventive replacement can pay off.

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Weibull probability plot

Points from Bernard’s median ranks and a least-squares fit. Aligned points mean a good fit.

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Method, assumptions and references

Equations used

MTBF = operating time ÷ number of failures; MTTR = total repair time ÷ number of failures
Inherent availability Ai = MTBF ÷ (MTBF + MTTR); λ = 1 ÷ MTBF
Exponential: R(t) = e^(−λt); Weibull: R(t) = e^(−(t/η)^β), h(t) = (β/η)(t/η)^(β−1)
Weibull MTBF = η · Γ(1 + 1/β); B10 life = η · (−ln 0.9)^(1/β)
Fit: Bernard median ranks F = (i − 0.3) ÷ (n + 0.4); regression of ln(−ln(1 − F)) on ln t: slope β, η = e^(x̄ − ȳ/β)

Assumptions and limits

  • Repairs leave the equipment “as good as new” for the Weibull fit; for repairable systems that degrade, use process models (Crow-AMSAA).
  • All times are failures of the same mode; censored data (units still running) are not included, which tends to understate life.
  • With period totals and Weibull, η is derived from the MTBF and the β entered.
  • Validation: the regression fit reproduces the ln–ln least-squares method used by IEC 61649 and statistical packages.

Standards and technical documents

  • IEC 60050-192:2015: International Electrotechnical Vocabulary — Dependability
  • ABNT NBR 5462:1994: Confiabilidade e mantenabilidade — Terminologia
  • IEC 61703:2016: Mathematical expressions for reliability, availability, maintainability and maintenance support terms
  • IEC 61649:2008: Weibull analysis
  • ISO 14224:2016: Collection and exchange of reliability and maintenance data for equipment
  • Abernethy, R. B. The New Weibull Handbook, 5th ed.

U.S. regulations

  • OSHA 29 CFR 1910.119(j): mechanical integrity, including inspection and testing frequency based on prior operating experience
  • OSHA 29 CFR 1910.147: energy control during repairs

Frequently asked questions

How do you calculate MTBF?

Divide the period’s operating time by the number of failures. 8,000 h with 6 failures gives an MTBF of about 1,333 h. Do not include downtime in the numerator.

What does β mean in Weibull analysis?

It is the shape factor. Below 1, failures are infant mortality (assembly, startup); near 1, random; above 1, wear-out. Only in wear-out does age-based preventive replacement reduce failures.

What is the difference between inherent and operational availability?

Inherent availability uses only MTBF and MTTR. Operational availability includes waiting for parts, labor and logistics, and is usually much lower.