Redundancy: Active Parallel vs Standby Systems

Redundancy adds backup components to improve system reliability. Active (parallel) redundancy runs all components simultaneously; standby redundancy keeps backups idle until needed. The reliability calculations differ significantly.

Active parallel redundancy

Two components in active parallel, each with reliability R: R_sys = 1 − (1 − R)² = 1 − (1 − R)(1 − R) Example: R = 0.90 for each R_sys = 1 − (0.10)² = 1 − 0.01 = 0.99 n components in parallel: R_sys = 1 − (1 − R)ⁿ

Standby redundancy (cold standby)

Primary component + one cold standby, constant failure rate λ: R_sys(t) = e^(−λt)(1 + λt) Example: λ = 0.001/h, t = 100 h λt = 0.001 × 100 = 0.10 R_sys = e^(−0.10)(1 + 0.10) = 0.9048 × 1.10 = 0.995

Comparison

	Active parallel	Cold standby
Both units fail together?	Possible	Standby is protected until primary fails
Switching required?	No	Yes — switching reliability matters
Higher reliability?	Good	Better (if switching is reliable)
Example	Dual power supplies, load sharing	Spare tire, backup generator

CQE exam tips

Standby reliability formula assumes perfect switching; if switching has probability p_s, multiply by p_s.
Active parallel is simpler to implement; standby avoids shared stress degradation.

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