MTBF & availability
The three numbers that describe uptime — mean time between failures, mean time to repair, and the availability they produce — from operating hours, failure count, and total repair time.
MTBF, MTTR & inherent availability · reliability from run hours
A = MTBF / (MTBF + MTTR)
What this gives you
Three numbers describe how much of the time an asset is actually available to run, and this calculator produces all three from a single window of history: total operating hours, the number of failures in that window, and the total hours spent down for repair. MTBF (mean time between failures) is the average run time between stoppages, MTTR (mean time to repair) is the average time to get it back, and inherent availability is the fraction of time it would be up given only those two: A = MTBF ÷ (MTBF + MTTR). Use it to turn a year of work-order data into a defensible reliability figure for a line, a pump, or a whole plant.
How the three numbers relate
MTBF and MTTR are just totals divided by the failure count — MTBF = operating hours ÷ failures and MTTR = repair hours ÷ failures — so the failure count is the hinge both pivot on. Availability then falls straight out of their ratio and is unitless: a machine that runs 1,600 hours between failures and takes 4 hours to fix is available 1600 ÷ 1604 = 99.75 percent of the time. Because availability depends on the ratio of uptime to repair time, halving your repair time buys the same availability gain as doubling the time between failures — often the cheaper lever to pull.
Field note — this is inherent availability, not what operations sees
The A this computes is inherent availability: it counts only failures and active repair time. It deliberately ignores the wait for parts, the shift that had no technician, the permit that took an hour, and planned maintenance. Real operational availability is always lower because those delays are real downtime. Treat this figure as the ceiling the equipment is capable of — if your operational uptime is far below it, the problem is in your logistics and staffing, not the machine.
Worked example
A packaging line logs 8,760 hours in a year with 12 breakdowns totalling 48 hours of repair. MTBF is 8,760 ÷ 12 = 730 hours between failures; MTTR is 48 ÷ 12 = 4 hours per repair; and inherent availability is 730 ÷ (730 + 4) = 99.46 percent. Cut the average repair to 2 hours — better spares staging, a documented procedure — and MTTR halves while availability climbs to 730 ÷ 732 = 99.73 percent, all without touching the failure rate itself.
Reliability over a mission, and how failures pile up
Availability tells you the long-run fraction of uptime, but it says nothing about the odds of finishing a specific run. For that, assume a constant failure rate — the standard bathtub-midlife model — and reliability decays exponentially: R(t) = e−t ÷ MTBF, the probability of running t hours with no failure. With MTBF = 1,600 hours, the chance of clearing a 720-hour month untouched is e−0.45 = 63.8 percent; stretch the mission to a full 1,600 hours and it falls to e−1 = 36.8 percent. The same MTBF also fixes the failure rate λ = 1 ÷ MTBF — here 0.000625 per hour, or λ × 8,760 = 5.48 failures per year — and the annual downtime = (1 − A) × 8,760, which for A = 99.75 percent is about 21.8 hours a year the asset is down for repair.