Last updated: 2026-07-13

MTBF, MTTR, and Availability

Three numbers summarize how dependable a repairable system is: how long it runs between failures, how long it takes to bring back, and what fraction of time it is actually available. MTBF (mean time between failures) captures the first, MTTR (mean time to repair) the second, and availability combines them into the single figure that most operational targets and SLAs are written against. Feeding real field data — total operating time, the count of failures, and the total repair time — into these formulas turns a maintenance log into the reliability metrics used across hardware, IT infrastructure, and manufacturing.

Formulas

For a repairable system observed over a window, with $n$ failures, total operating time $T$, and total repair time $T_r$:

Steady-state availability is the share of time the system is up across a full failure-and-repair cycle:

During the useful-life portion of the bathtub curve, the failure rate is constant and equal to the reciprocal of MTBF:

Because availability is a ratio, the choice of time unit cancels — MTBF and MTTR only have to be expressed in the same unit. The downtime expected over one year follows directly as $(1 - A)$ multiplied by the hours in a year.

Worked Example

A server logs 10,000 operating hours with 5 failures and a total repair time of 10 hours:

At 99.9001% availability the system is expected to be down about 8.76 hours over a full year. Shortening the average repair from 2 hours to 30 minutes — without touching MTBF — raises availability to roughly 99.975% and cuts annual downtime to about 2.2 hours, which is why maintainability is as important as durability.

MTBF vs MTTF

The two terms are often confused. MTBF is defined for repairable systems and measures the average time between successive failures, implicitly assuming the item is fixed and returned to service. MTTF (mean time to failure) is defined for non-repairable items — a fuse, a bearing, a disk you replace rather than repair — and measures the average time until the single failure that ends the item's life. When repair time is small next to operating time, the numbers are close, but they answer different questions: MTBF is about how often you repair, MTTF about how long one unit lasts.

Interpreting the Failure Rate

The failure rate $\lambda$ is the number of failures expected per unit of time. The reciprocal relationship $\lambda = 1 / \text{MTBF}$ holds under the exponential model, which assumes a constant hazard — failures are equally likely at any instant. That assumption is realistic only in the flat middle of the bathtub curve, between early-life "infant mortality" and end-of-life wear-out. Component datasheets often quote the rate in FITs (failures in time), one FIT being one failure per billion device-hours, which is convenient for the very reliable parts used in electronics.

Limitations

These formulas describe long-run averages, not guarantees: an MTBF of 2,000 hours does not promise that any single unit runs 2,000 hours before failing. The steady-state availability figure also ignores when downtime occurs — one long outage and many short ones can produce the same number yet very different user impact. Availability here counts only unplanned failure and repair; scheduled maintenance windows, spare-part lead times, and detection delays may need to be folded into MTTR or handled separately depending on how the target is defined. For systems built from several components in series or parallel, combine each part's availability with a composition model rather than averaging these single-system figures.