Reliability Block Diagram: Redundancy Allocation

Component Reliability

Failure rate λ (per unit, per hour ×10⁻³) 3.0

Unit cost per component 10

Budget cap 140

Subsystem Chain (series)

System Status

R_system(t)

100.0%

MTBF (h)

Cost used / budget

0 / 0

System state

How it works

Each component fails independently following an exponential lifetime model with constant failure rate λ, so a single unit's reliability after time t is:

R_unit(t) = e^(-λt)

A stage with k identical units wired in parallel redundancy (only one needs to survive) fails only if all k fail, so:

R_stage(t) = 1 - (1 - R_unit(t))^k

The stages form a reliability block diagram in series — the whole system works only if every stage works — so the overall reliability multiplies:

R_system(t) = R_stage1(t) × R_stage2(t) × ... × R_stageN(t)

Mean time between failures is the area under the reliability curve, MTBF = ∫₀^∞ R_system(t) dt, approximated here numerically. Adding redundant units raises R_stage(t) but costs budget per unit — this is the classic systems-engineering trade-off between reliability and cost/mass/power constraints when allocating redundancy across a system-of-systems architecture.

+ / − buttons on a stage adjust its redundancy level k (number of parallel units).
Run failure trial runs a Monte Carlo sample: each visible unit is independently marked failed with probability 1 − R_unit(t) at the current simulated time, and the diagram lights up red/green accordingly — a single trial's outcome, not the analytic average.
The small curve (top right) plots the analytic R_system(t) over the next 400 hours so you can see how added redundancy flattens the decay.

Working unit Failed unit (trial) Untested / idle

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