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Fault tree (FTA) templates

Fault Tree — Piped Medical Oxygen

Loss of ward oxygen at an acute hospital: bulk evaporator and emergency manifold in parallel, with the manifold gated by an INHIBIT on unreplaced reserve cylinders, plus three pipeline faults that bypass the redundancy entirely.

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Loss of piped medical oxygen — acute hospitalFault tree (IEC 61025) · 8 basic events · 5 gates · depth 3topWard oxygen supplylost0.010421supply_lostAll oxygen sourcesunavailable1.89e-4vie_lostBulk evaporatorunavailable0.068777vie_emptyBulk deliverymissed, VIE runs dry0.012vaporiser_iceAmbient vaporiserices up in a cold…0.045vie_regulatorVIE line pressureregulator fails0.013054manifold_lostEmergency manifoldunavailablecylinders_stale0.080.002755manifold_regManifold regulatorfails0.034433pipeline_faultDistributionpipeline fault0.010233avsu_closedArea valve serviceunit closed in error0.002pipe_ruptureCopper pipelinerupture during…4.00e-4ward_valveWard isolation valvefails shut0.007853Top event probability (exact)0.010421Minimal cut sets6Smallest cut set order1Single points of failure3Mission time8760 hExact top-event probability 0.010421 · rare-event sum ΣP(cut set) 0.010446The usual approximation overstates this tree by 0.24% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {ward_valve} order 1 P 0.007853 75.4% of the top ← single point of failure2. {avsu_closed} order 1 P 0.002 19.2% of the top ← single point of failure3. {pipe_rupture} order 1 P 4.00e-4 3.8% of the top ← single point of failure4. {vaporiser_ice, manifold_reg, cylinders_stale} order 3 P 1.24e-4 1.2% of the top5. {vie_regulator, manifold_reg, cylinders_stale} order 3 P 3.60e-5 0.3% of the top6. {vie_empty, manifold_reg, cylinders_stale} order 3 P 3.31e-5 0.3% of the topImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)ward_valve — Ward isolation valve fails shut q 0.007853 FV 75.4% B 0.997412 CR 75.2%avsu_closed — Area valve service unit closed in error q 0.002 FV 19.2% B 0.991562 CR 19%pipe_rupture — Copper pipeline rupture during building works q 4.00e-4 FV 3.8% B 0.989975 CR 3.8%manifold_reg — Manifold regulator fails q 0.034433 FV 1.8% B 0.005446 CR 1.8%cylinders_stale — Reserve cylinders not replaced after last use q 0.08 FV 1.8% B 0.002344 CR 1.8%vaporiser_ice — Ambient vaporiser ices up in a cold snap q 0.045 FV 1.2% B 0.002659 CR 1.1%vie_regulator — VIE line pressure regulator fails q 0.013054 FV 0.3% B 0.002573 CR 0.3%vie_empty — Bulk delivery missed, VIE runs dry q 0.012 FV 0.3% B 0.00257 CR 0.3%Rectangle intermediate event · dome AND · shield OR · shield with k/n voting · hexagon INHIBIT with its oval condition · circle basic · diamond undeveloped · triangle transfer

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title "Loss of piped medical oxygen — acute hospital"
mission 8760h

top "Ward oxygen supply lost" = OR(supply_lost, pipeline_fault)

gate supply_lost "All oxygen sources unavailable" = AND(vie_lost, manifold_lost)
gate vie_lost "Bulk evaporator unavailable" = OR(vie_empty, vaporiser_ice, vie_regulator)
gate manifold_lost "Emergency manifold unavailable" = INHIBIT(manifold_reg, condition: cylinders_stale)
gate pipeline_fault "Distribution pipeline fault" = OR(avsu_closed, pipe_rupture, ward_valve)

event vie_empty "Bulk delivery missed, VIE runs dry" p=0.012
event vaporiser_ice "Ambient vaporiser ices up in a cold snap" p=0.045
event vie_regulator "VIE line pressure regulator fails" rate=1.5e-6
event manifold_reg "Manifold regulator fails" rate=4.0e-6
condition cylinders_stale "Reserve cylinders not replaced after last use" p=0.08
event avsu_closed "Area valve service unit closed in error" p=0.002
undeveloped pipe_rupture "Copper pipeline rupture during building works" p=0.0004
event ward_valve "Ward isolation valve fails shut" rate=9.0e-7