Life-Support FMEA Reliability Chain

FMEA Reliability Chain

O₂ Generator λ 400/1000h

CO₂ Scrubber λ 600/1000h

Power Bus λ 250/1000h

Mission duration 2000 h

System reliability

–

Mission risk

–

Weakest link (single point of failure)

–

How it works

Each component's failure follows an exponential reliability model: the probability it is still working after time t is R(t) = e^−λt, where λ is its constant failure rate. Chained (series) components form the classic weak-link system: the whole chain only survives if every link does, so reliabilities multiply and the system is always less reliable than its worst part. A redundant (parallel) path removes that single point of failure — the pair only fails if both units fail — which is why real life-support hardware duplicates its highest-risk component instead of hardening it further.

R_i(t) = e^(−λᵢ·t)
R_series = R₁ · R₂ · … · Rₙ
R_parallel(2 units) = 1 − (1−R)·(1−R)
Mission risk = 1 − R_system(t)

λ sliders — each component's failure rate per 1000 operating hours; higher λ means a shorter expected time-to-failure.
Redundant toggle — duplicates the CO₂ Scrubber into two parallel units so a single failure no longer dooms the mission; switching to "Single path" turns it back into a lone point of failure.
Mission duration — the time horizon t the reliability chain must survive; every component's individual R(t) decays as t grows, dragging the system reliability down with it.
Weakest link — whichever branch currently has the lowest R(t) at mission end is the one worth making redundant first; that's the core output of a real FMEA (Failure Mode and Effects Analysis) pass.

Real-world relevance: this is the actual math behind spacecraft reliability engineering — NASA and ESA FMEA reviews compute exactly this kind of series/parallel reliability tree to decide which life-support components need a backup unit before flight.