Engineering
Series vs Parallel System Reliability & active redundancy formula (PRODUCT)
Compare series and active-parallel mission reliability under independent failures and a common mission horizon.
Compare independent series and active-parallel mission reliability
All component reliabilities must refer to the same mission duration and conditions. For independent component survival events, series reliability is their product; the system requires all components. This value is no greater than the least reliable component, though equality is possible.
The active-parallel expression assumes statistically independent failures and that any one surviving component can meet the full requirement. Shared power, common software, correlated environment, insufficient surviving capacity and failed switching violate this simple model. Mission survival probability is not an uptime SLA or repaired-system availability.
| Subsystem / Node (A) | Reliability R_i (B) | Failure Prob 1 - R_i (C) | Architecture Outcome |
|---|---|---|---|
| Node-A | 0.95 | 0.05 | 5% individual failure risk |
| Node-B | 0.90 | 0.10 | Weakest single link |
| Node-C | 0.98 | 0.02 | 2% individual failure risk |
| 3-Node System | Series = 0.8379 | Parallel = 0.9999 | 16.21% versus 0.01% modeled mission failure probability |
Series chain reliability PRODUCT(B2:B4)
Every single-point-of-failure stage compounds failure risk multiplicatively.
=IF(OR(COUNT(B2:B4)<>3,MIN(B2:B4)<0,MAX(B2:B4)>1),"Invalid inputs",ROUND(PRODUCT(B2:B4), 4))Active parallel redundancy reliability 1 - PRODUCT(C2:C4)
C2:C4 contains failure probabilities over the common mission. Their product is the probability all independent components have failed by that time; failures need not occur at the same instant.
=IF(OR(COUNT(B2:B4)<>3,MIN(B2:B4)<0,MAX(B2:B4)>1),"Invalid inputs",ROUND(1 - PRODUCT(C2:C4), 4))Try the example
Use the original values or change them to test your understanding.