Reliability Allocation in Series Systems

When a system reliability goal is set (e.g., R_system = 0.95 at 1000 hours), reliability allocation distributes that goal across subsystems so each design team has a target to work toward.

Series system formula

For n subsystems in series: R_sys = R₁ × R₂ × ... × Rₙ To achieve R_sys = 0.95 with 4 equal subsystems: R_each = (0.95)^(1/4) = 0.9873

Equal apportionment method

All subsystems get the same reliability target: Rᵢ = R_sys^(1/n) For R_sys = 0.90, n = 3: Rᵢ = (0.90)^(1/3) = 0.9655 each

ARINC method (complexity-weighted)

The ARINC method allocates failure rates proportional to complexity (number of parts). Simpler subsystems get a better (lower) failure rate target; complex ones get a higher allowed failure rate.

λᵢ_allocated = λ_system × (complexity_i / total complexity) Subsystem A: 100 parts, B: 200 parts, C: 300 parts Total = 600 parts If λ_system = 0.001 failures/hour: λ_A = 0.001 × 100/600 = 0.0001667/h λ_B = 0.001 × 200/600 = 0.0003333/h λ_C = 0.001 × 300/600 = 0.0005000/h

CQE exam tips

Equal apportionment is simple but ignores complexity — ARINC is more realistic.
Reliability allocation is iterative: initial targets drive design, then achieved values feed back into the model.

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