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System Availability Calculator

Calculate the availability and reliability of a system of components in series, parallel or k-out-of-n. Enter each component’s MTBF (or failure rate) and MTTR — results update instantly.

Failure input

The system is a series chain of the groups below. Each group can be series, parallel (redundant) or k-out-of-n.

ComponentMTBF (h)MTTR (h)Remove

Results

System availability
99.997%
steady state, with repair
Downtime
0.3 h / yr
expected
Reliability R(8,760 h)
60.042%
no repair
System MTTF
13,140 h
no repair

Reliability R(t) — no repair

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Availability vs reliability

Availability is the long-run fraction of time a repairable system is working. For one component with a constant failure rate it is A = MTBF / (MTBF + MTTR). Reliability R(t) is the probability of surviving a mission of length t with no failure and no repair; for a constant failure rate, R(t) = e^(−t / MTBF). The calculator reports both, plus the system MTTF — the mean time to the first system failure.

Series and parallel formulas

Series — every component needed

Rseries = Π Ri

Aseries = Π Ai

Any single failure stops the system, so the result is lower than the weakest component.

Parallel — any one is enough

Rparallel = 1 − Π (1 − Ri)

Aparallel = 1 − Π (1 − Ai)

The system fails only when every redundant unit is down at once.

A k-out-of-n group (for example 2-of-3 compressor trains) is up when at least k of its n components are up; the calculator sums the probabilities of every such combination, so components do not need identical values. Assumes constant failure and repair rates and independent components, each with its own repair crew.

Worked example: two pumps in parallel

Two identical pumps, each with MTBF = 8,760 h and MTTR = 48 h, either of which can carry the duty.

  1. One pump: A = 8,760 / (8,760 + 48) = 99.455%.
  2. Both down at once: (1 − A)² = 2.97e-5.
  3. System availability: 1 − (1 − A)² = 99.9970% — about 0.26 h of downtime a year, versus 48 h for a single pump.
  4. One-year reliability without repair: one pump R = e−1 = 36.8%; the pair R = 1 − (1 − 36.8%)² = 60.0%.
  5. System MTTF (no repair): 1.5 × 8,760 = 13,140 h.

This is the example pre-loaded in the calculator above — change any value to explore.

Frequently asked questions

How do you calculate system availability?

First find each component’s steady-state availability, A = MTBF / (MTBF + MTTR). Then combine them according to how the system is built: for components in series, multiply the availabilities (A = A₁ × A₂ × …); for redundant components in parallel, multiply the unavailabilities and subtract from one (A = 1 − (1 − A₁)(1 − A₂)…). A k-out-of-n group is available when at least k of its n components are up.

What is the difference between series and parallel reliability?

In a series system every component must work, so any single failure stops the system and reliability is the product of the component reliabilities — always lower than the weakest part. In a parallel (redundant) system only one component needs to work, so the system fails only when all of them fail: R = 1 − Π(1 − Rᵢ), which is higher than any single component.

What is the difference between availability and reliability?

Reliability R(t) is the probability of running for a mission time t without any failure, ignoring repair. Availability is the long-run fraction of time the system is up when failed components are repaired, so it depends on MTTR as well as MTBF. A system can have low mission reliability but very high availability if repairs are quick.

When the formulas stop being enough

Closed-form results assume constant rates, independent repairs and no logistics. Real plants have wear-out (Weibull) failures, preventive maintenance, shared spares, limited repair crews and storage buffers — that is what Monte Carlo simulation is for. Read the RAM analysis guide or the Monte Carlo vs analytical explainer, or start a free trial to model your full system.