1. FAULT TREE ANALYSIS

2. NOTATION Series system System fails when either component fails Pump Failure Valve Failure P(system failure) = P(pump failure  valve failure) 2

3. NOTATION Series system System fails when either component fails Pump Failure Valve Failure P(system failure) = P(pump failure  valve failure) 2

4. NOTATION System fails when both components fail (with one-out-of-two success criterion) Parallel system Pump 1 Pump 2 With two-out-of-two success criterion, system fails when either component fails Even though the components are physically in parallel, they are conceptually in series! P(system failure) = P(pump 1 fails ∩ pump 2 fails) 3

5. Example: One-out-of-two success criterion Alternative representation: minimal cut sets 4

6. Example: Two-out-of-two success criterion Alternative representation: minimal cut sets 5

7. Example with IN and OUT events: One-out-of-two success criterion 6

8. Example with an interconnection (cross-tie) or 7

9. Example of a three-train system Three-out-of-three success criterion One-out-of-three success criterion 8

10. Example of a three-train system (continued) Two-out-of-three success criterion Two-out-of-three logic gate 9

11. SUCCESS TREE A success tree is the dual of a failure tree Just apply De Morgan’s Law: Every AND gate turns into an OR gate Every OR gate turns into an AND gate 10

12. QUANTIFYING THE FAILURE PROBABILITY If events are not independent, then we need conditional probabilities Rare-event approximation (OK if the individual component failure probabilities are less than 0.1) 11

13. MINIMAL CUT-SET REPRESENTATION By rare-event approximation: 12

14. MINIMAL CUT-SET REPRESENTATION By rare-event approximation: 12