Fault Tree Analysis Probability Calculator

Estimate operating reliability and failure probability for a fixed series-and-parallel fault-tree topology.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Event reliabilities

Enter the operating reliability R(t) of each independent binary event at the same mission time.

System result

Probabilities are dimensionless and refer to the same mission time.

Operating reliability R(t)0.677

Probability that the complete system operates successfully.

Failure probability F(t)0.323

D/E branch RDE0.985

F/G branch RFG0.998

How to use

This calculator has one fixed topology: A, B and C are required series events; D/E and F/G are parallel-success pairs.
Enter A–G as operating reliabilities from 0 to 1, all evaluated at the same mission time and under compatible conditions.
Select Calculate to update the system and branch results. Select Reset to restore the worked-example defaults.
Interpret R(t) as system success probability and F(t) as system failure probability. Branch values show the equivalent reliability of each parallel pair.
Correct any warning before using results. Do not use this model for dependent events, common-cause failures, repairable systems, changing topology, or time-varying hazards without an appropriate reliability model.

Equations used

Each symbol A–G is the dimensionless operating reliability R(t) of the correspondingly labeled independent event. All values use the same mission time. Parallel success means the branch operates when at least one event succeeds.

RDE = 1 − (1 − D)(1 − E)

RFG = 1 − (1 − F)(1 − G)

R(t) = A · B · C · RDE · RFG

F(t) = 1 − R(t)

RDE and RFG are intermediate branch reliabilities. R(t) and F(t) are independently displayed to three decimals. There is no sign convention because all quantities are probabilities constrained to 0 ≤ value ≤ 1.

Worked example

Use A=0.90, B=0.85, C=0.90, D=0.70, E=0.95, F=0.80 and G=0.99.
The parallel branches are RDE=0.985 and RFG=0.998.
The expected outputs are R(t)=0.677 and F(t)=0.323. Under the independence assumption, this topology has about a 67.7% probability of successful operation over the selected mission time.

Theory and method

The model combines statistically independent binary events. Reliabilities multiply for required series events. For a two-event parallel-success branch, the only branch-failure condition is simultaneous failure, giving one minus the product of event failure probabilities. The calculation therefore represents exactly the topology shown above.

Assumptions and limits

Events are independent, binary, and evaluated over the same mission time.
Input probabilities are known and representative of the intended environment and duty.
No common-cause failure, conditional dependence, repair, sequence logic, standby switching, or uncertainty propagation is included.
The model is unsuitable when those effects materially influence system reliability.