1. FAULT TREE ANALYSIS: REALISTIC EXAMPLE, MINIMAL CUT SETS

2. Example: Primary Containment Instrument Gas System (Two trains each of a compressor, dryer, and receiver) PLANT INTAKE COMPRESSOR A COMPRESSOR B DRYER A DRYER B RCVR A RCVR B HEADER A HEADER B CROSS-TIE

3. 1/2 2/2 Intake Back Leakage (from receivers) Compressor BDryer BReceiver B Compressor ADryer AReceiver A Intertie Valves Header A Header B Contamination (can disable both trains) Example: Primary Containment Instrument Gas System (Simplified block diagram)

4. FAULT TREE REPRESENTATION

5. * * e.g. relief valve stuck open * e.g. failure to allow flow through *

6. FAULT TREE REPRESENTATION * * e.g. relief valve stuck open * e.g. failure to allow flow through *

7. MINIMUM CUT SET A set of components that is sufficient to cause system failure, But would not be sufficient if any one event were removed Example In the preceding fault tree: Failure of Receiver A and Dryer B is sufficient to cause system failure But failure of Receiver A or Dryer B alone would not be sufficient

8. ALGORITHM FOR MINIMUM CUT SETS Finding minimal cut sets is computationally difficult (NP-complete!) Rules: 1.Each OR gate generates new rows in the table of cut sets (corresponding to new cut sets) 2.Each AND gate generates new columns in the table of cut sets (corresponding to additional elements in existing cut sets) After each of the above steps, you can: 3.Eliminate redundant elements that appear multiple times in a cut set 4.Eliminate non-minimal cut sets

9. A∩C A∩D A∩E B∩C B∩D B∩E C∩C C∩D C∩E 1 2∩3 A∩3 B∩3 C∩3 Rule 2 Rule 1 Example 23 4 1 5 A BC C DE F GH I Rule 3 Rule 4 A∩D A∩E B∩D B∩E C minimal cut sets F∩D G∩D F∩H∩I G∩H∩I B∩D B∩E C F∩D G∩D F∩E G∩E B∩D B∩E C