Fault Tree and Reliability Block Diagram Analysis
Fault Tree and Reliability Block Diagram Analysis
This domain tests deductive fault tree analysis (FTA) and inductive reliability block diagrams (RBD), including Boolean reduction and minimal cut sets.
Core rules
- FTA starts from a top event and works down through AND/OR gates. AND gate: all inputs needed; P=∏P_i if independent. OR gate: any input; P=1-∏(1-P_i).
- RBD models success paths: series blocks are all required; parallel blocks are redundant.
- An AND gate in a fault tree corresponds to parallel redundancy in an RBD; an OR gate corresponds to a series dependency.
- Minimal cut sets are the smallest combinations that cause the top event; single-element cut sets dominate risk.
Worked example
An RBD has two parallel branches, each with A=0.9 in series with B=0.8. Branch reliability=0.72. System reliability=1-(1-0.72)^2=0.9216. The equivalent fault tree has a top event that occurs if both branches fail. Each branch failure probability is 0.28, so top=0.28^2=0.0784, and success=1-0.0784=0.9216. Consistency checks like this catch gate errors.
Traps
- Swapping AND and OR probabilities.
- Multiplying probabilities for non-independent common-cause events.
- Missing minimal cut sets that contain repeated events.
- Treating a fault tree as a success diagram.