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MTBF and availability calculator

Assumes a constant failure rate (the flat part of the bathtub curve). Add up operating time across all units if you tested more than one.

How it is calculated

MTBF = operating time / failures = 12,000 / 4 = 3,000 h Failure rate λ = 1 / MTBF = 0.000333 per hour MTTR = repair time / failures = 30 / 4 = 7.5 h Inherent availability = MTBF / (MTBF + MTTR) = 99.751% Reliability R(t) = e^(−t/MTBF) = e^(−500/3000) = 84.6% Lower 90% bound on MTBF = 2T / χ²(0.9, 2r + 2) = 24,000 / χ²(0.9, 10) = 1,501 h

The bound uses 2r + 2 degrees of freedom for a test stopped at a fixed time (time-terminated). For a test stopped at the r-th failure (failure-terminated), use 2r.

Read more: Bathtub curve and MTBF · Availability and maintainability · Weibull analysis · Redundancy

FAQ

What is the difference between MTBF and MTTF?

MTBF (mean time between failures) is for repairable items: the average operating time between one failure and the next. MTTF (mean time to failure) is for items that are replaced, not repaired. The arithmetic is the same: total operating time divided by the number of failures.

Does an MTBF of 1,000 hours mean it lasts 1,000 hours?

No. With a constant failure rate, the chance of running a full MTBF without a failure is e^(−1), about 37%. MTBF is an average rate, not a guaranteed life.

Why is the lower confidence bound so much lower than MTBF?

With only a few failures, the true MTBF is uncertain. The chi-square bound says, with the chosen confidence, that the true MTBF is at least this value. More operating time and more failures narrow the gap.

What is inherent availability?

MTBF / (MTBF + MTTR): the share of time the equipment is up, counting only repair time. Operational availability also counts waiting for parts, technicians and logistics, so it is lower.

What if there were zero failures?

MTBF cannot be estimated as a number, but the lower bound still can: with zero failures the bound is 2T / χ²(CL, 2). That is the basis of success-run (zero-failure) test planning.

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