System Reliability Calculator
Calculate system reliability for series, parallel, and k-out-of-n configurations
System Reliability Calculator
Guide to System Reliability Configurations
Series System
R = R₁ × R₂ × ... × RₙAll components must work. System reliability is always lower than the weakest component. Like a chain — it breaks at its weakest link.
Parallel System
R = 1 - ∏(1 - Rᵢ)Only one needs to work. System reliability is always higher than the best component. Redundancy dramatically improves reliability.
k-out-of-n
R = Σ C(n,i) × pⁱ × (1-p)ⁿ⁻ⁱAt least k of n must work. Common with voting systems, engine configurations (2-of-3), and RAID arrays.
Configuration Comparison Example
Three identical components, each with R = 0.90:
| Configuration | System Reliability | Interpretation |
|---|---|---|
| Series (all 3 must work) | 72.9% | 0.9 × 0.9 × 0.9 |
| 2-out-of-3 | 97.2% | One can fail |
| Parallel (any 1 works) | 99.9% | 1 - (0.1)³ |
FAQ
When should I use redundancy?
When the cost of failure exceeds the cost of adding redundant components. Common in safety systems (dual brakes), critical infrastructure (backup generators), and high-availability IT (RAID, load balancers).
What is the difference between active and standby redundancy?
Active redundancy: all units run simultaneously (hot standby). Standby redundancy: backup units activate only when the primary fails (cold/warm standby). Active is simpler but ages all units; standby preserves backup life but requires switching logic.