Availability (MTBF / MTTR)
Steady-state availability of a repairable system from its mean time between failures and mean time to repair.
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The engineering
Steady-state (inherent) availability is the fraction of time a repairable system is up over the long run: it trades total operating time against the repair time it accrues. Reach for it when you need to turn a failure rate and a repair estimate into a single uptime number — an SLA target, a redundancy trade study, or a spares-and-crew sizing argument.
This is inherent availability — it counts only active repair time, not logistics delay, admin lag, or waiting on parts. Real operational availability (Aₒ) is always lower once mean-down-time swallows those queues. Sanity check with the 'nines': 0.999 is ~8.76 h of downtime a year, 0.9999 is ~53 min. If MTTR is an order of magnitude below MTBF you are already past three nines.
MTBF is the reciprocal of the constant failure rate λ from a handbook like MIL-HDBK-217F; MTTR comes from the maintainability analysis, not wishful thinking.
Where this math comes from
Availability as a formal metric grew out of WWII and postwar military electronics, where 'does it work when we flip it on?' mattered as much as 'how long until it breaks.' The distinction between reliability (staying up) and maintainability (getting back up fast) crystallized in the 1950s and 60s as the Department of Defense built out reliability engineering as a discipline, culminating in the MIL-HDBK-217 series of part-level failure-rate models first issued in 1965.
The clean A = MTBF/(MTBF+MTTR) form is the equilibrium solution of a two-state up/down Markov process, work that traces to Andrey Markov's chains and the renewal-theory treatments formalized by reliability theorists like Barlow and Proschan in their 1965 Mathematical Theory of Reliability. Today the same expression underwrites cloud SLAs and the 'five nines' telecom benchmark.
- 1906Andrey MarkovIntroduces Markov chains — the two-state up/down model behind steady-state availability.
- 1962AGREE / DoD reliability communityFormalizes availability alongside reliability and maintainability for military systems.
- 1965Barlow & ProschanPublish Mathematical Theory of Reliability, giving the renewal-theory basis for A.
- 1991U.S. DoDReleases MIL-HDBK-217F, the standard source for the failure rates feeding MTBF.
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