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Fault tree (FTA) templates

Fault Tree — Total Loss of Vehicle Braking

Dual diagonal hydraulic circuits backed by an electric park brake over 300 driving hours, showing how the shared master cylinder and reservoir turn two independent-looking circuits into one, and the 12 V supply into a common mode.

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Total loss of service brakingFault tree (IEC 61025) · 9 basic events · 6 gates · depth 4topDriver cannot retardthe vehicle4.70e-6hydraulic_lostBoth hydrauliccircuits lost9.36e-4master_cylTandem mastercylinder fails3.60e-5fluid_lossReservoir drainedbelow both ports9.00e-4circuit_pairFront and rearcircuits both fail2.02e-7front_circuitFront circuit fails4.50e-4front_hoseFront flexible hoseruptures1.80e-4front_caliperFront caliper seizesthe fluid path2.70e-4rear_circuitRear circuit fails4.50e-4rear_hoseRear flexible hoseruptures1.80e-4rear_caliperRear caliper seizesthe fluid path2.70e-4parking_lostElectric park brakeunavailable0.005015epb_actuatorEPB caliper motorfails6.00e-4epb_ecuEPB control unitfault4.20e-4veh_batteryVehicle 12 V supplylost0.004Top event probability (exact)4.70e-6Minimal cut sets18Smallest cut set order2Single points of failurenoneMission time300 hExact top-event probability 4.70e-6 · rare-event sum ΣP(cut set) 4.70e-6The usual approximation overstates this tree by 0.09% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {fluid_loss, veh_battery} order 2 P 3.60e-6 76.7% of the top2. {fluid_loss, epb_actuator} order 2 P 5.40e-7 11.5% of the top3. {fluid_loss, epb_ecu} order 2 P 3.78e-7 8% of the top4. {master_cyl, veh_battery} order 2 P 1.44e-7 3.1% of the top5. {master_cyl, epb_actuator} order 2 P 2.16e-8 0.5% of the top6. {master_cyl, epb_ecu} order 2 P 1.51e-8 0.3% of the top7. {front_caliper, rear_caliper, veh_battery} order 3 P 2.92e-10 0% of the top8. {front_hose, rear_caliper, veh_battery} order 3 P 1.94e-10 0% of the top9. {front_caliper, rear_hose, veh_battery} order 3 P 1.94e-10 0% of the top10. {front_hose, rear_hose, veh_battery} order 3 P 1.30e-10 0% of the top+ 8 further cut sets not listedImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)fluid_loss — Reservoir drained below both ports q 9.00e-4 FV 96.1% B 0.005015 CR 96.1%veh_battery — Vehicle 12 V supply lost q 0.004 FV 79.8% B 9.35e-4 CR 79.7%epb_actuator — EPB caliper motor fails q 6.00e-4 FV 12% B 9.32e-4 CR 11.9%epb_ecu — EPB control unit fault q 4.20e-4 FV 8.4% B 9.32e-4 CR 8.3%master_cyl — Tandem master cylinder fails q 3.60e-5 FV 3.8% B 0.005011 CR 3.8%front_caliper — Front caliper seizes the fluid path q 2.70e-4 FV 0% B 2.25e-6 CR 0%rear_caliper — Rear caliper seizes the fluid path q 2.70e-4 FV 0% B 2.25e-6 CR 0%front_hose — Front flexible hose ruptures q 1.80e-4 FV 0% B 2.25e-6 CR 0%Rectangle intermediate event · dome AND · shield OR · shield with k/n voting · hexagon INHIBIT with its oval condition · circle basic · diamond undeveloped · triangle transfer

Make it your own.

title "Total loss of service braking"
mission 300h                      # roughly one year of driving

top "Driver cannot retard the vehicle" = AND(hydraulic_lost, parking_lost)

gate hydraulic_lost "Both hydraulic circuits lost" = OR(master_cyl, fluid_loss, circuit_pair)
gate circuit_pair "Front and rear circuits both fail" = AND(front_circuit, rear_circuit)
gate front_circuit "Front circuit fails" = OR(front_hose, front_caliper)
gate rear_circuit "Rear circuit fails" = OR(rear_hose, rear_caliper)
gate parking_lost "Electric park brake unavailable" = OR(epb_actuator, epb_ecu, veh_battery)

event master_cyl "Tandem master cylinder fails" rate=1.2e-7
event fluid_loss "Reservoir drained below both ports" p=0.0009
event front_hose "Front flexible hose ruptures" rate=6.0e-7
event rear_hose "Rear flexible hose ruptures" rate=6.0e-7
event front_caliper "Front caliper seizes the fluid path" rate=9.0e-7
event rear_caliper "Rear caliper seizes the fluid path" rate=9.0e-7
event epb_actuator "EPB caliper motor fails" rate=2.0e-6
event epb_ecu "EPB control unit fault" rate=1.4e-6
event veh_battery "Vehicle 12 V supply lost" p=0.004