Life-Support Standby Switchover Reliability

Redundancy Level

Standby Mode

Switch reliability p 90%

Unit MTBF (hours) 2000 h

Mission duration 3000 h

Live Mission Run

RUNNING

Elapsed / mission

0 / 3000 h

Active module

Analytic R(T)

—

Switchovers used

How it works

Each life-support module (e.g. a CO₂ scrubber cartridge) fails after a random time drawn from an exponential distribution with rate λ = 1/MTBF — the memoryless failure model standard in reliability engineering. With N modules (1 active + N−1 standby) and an automatic switchover that succeeds with probability p each time it fires, the classic standby-redundancy reliability formula gives the probability the system is still delivering life support at mission time t:

λ = 1 / MTBF
R_sys(t) = e^(-λt) · Σ_{k=0}^{N-1} (p·λ·t)^k / k!

The k=0 term is "the first module simply never fails." Each further term is the shrinking probability that exactly k switchovers were needed and every one of them succeeded — a real switch failure (a stuck relay or a valve that won't seat) ends the mission on the spot, it does not retry the next unit.

Cold standby — idle modules draw no load and accrue essentially no wear, so the formula above applies directly; the cost is that p also has to cover the cartridge's own start-up (purge, warm-up, valve seat).
Hot standby — idle modules are already spun up and switch over instantly, but they run "hot" the whole time and can fail before their turn, which this sim approximates with a modest effective-p penalty rather than a second failure clock.
The 3D rack shows the real stochastic process: each module's actual lifetime is sampled live from Exp(λ), not just the analytic curve — over many restarts the fraction of runs ending "MISSION SUCCESS" converges to R_sys(T) above.

This is the same math NASA and Roscosmos use to size ISS ECLSS spares: cranking N up has diminishing returns once switch reliability p is the weak link, because every added standby module still has to pass through the same imperfect switch.

Active module Standby module Failed module

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