Space Life Support Risk Matrix (2D)

Subsystem

Component reliability

Component MTBF (hours) 10000

Consequence severity (1–5) 3

Redundant standby units 0

Mission duration (days) 180

Live risk readout

LOW RISK

Unit failure P

0.0%

System failure P

0.0%

Risk score

0.0

Grid cell

P1 · S3

How it works

Each life-support subsystem is treated as a repairable component with an exponential (constant hazard-rate) failure model — the standard first-order reliability approximation used in spacecraft FMEA/PRA work:

p_unit = 1 - e^(-t / MTBF)

t     = mission duration (hours)
MTBF  = mean time between failures (hours)

Adding n redundant standby units means the whole line only fails if every unit fails independently, so the system failure probability drops geometrically:

p_system = p_unit^(n + 1)

risk_score = p_system × severity   (severity 1–5)

The 5×5 grid on the right is a probability-vs-severity risk matrix — the classic tool mission-assurance teams use to triage hazards. The probability axis is bucketed on a log scale (each column is a decade of p_system), the severity axis is the 1–5 consequence rating, and cell colour is the resulting risk score: green (acceptable) → yellow (monitor) → orange (mitigate) → red (unacceptable without action). Each glowing marker is one subsystem, positioned live from its own p_system and severity; dragging the redundancy slider up walks a marker left across the grid as extra standby hardware buys down probability — the same trade mission-assurance engineers make between spare mass and residual risk.

Low risk Monitor Mitigate Unacceptable Selected subsystem