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Fault Tree — Metro Signalling Loss

Loss of movement authority on a CBTC metro line over a year, where a shared trackside radio segment sits inside both the primary and the fallback branch and is the tree's only single-point failure.

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Loss of movement authority — CBTC metro lineFault tree (IEC 61025) · 8 basic events · 5 gates · depth 3topTrains lose movementauthority0.026445cbtc_lostCBTC supervisionunavailable0.346067zone_controllerBoth zonecontrollers down0.02128zc_aZone controller Afails0.145877zc_bZone controller Bfails0.145877radio_networkTrackside radionetwork segment…0.009onboard_atpOnboard ATP unitfails to hold a…0.325781fallback_lostFixed-block fallbackunavailable0.060289interlockingSolid-stateinterlocking…0.051203radio_networkTrackside radionetwork segment…0.009track_circuitsTrack circuitdetection lost2/35.83e-4tc_feed_1Track circuit powerfeed 1 fails0.014tc_feed_2Track circuit powerfeed 2 fails0.014tc_feed_3Track circuit powerfeed 3 fails0.014Top event probability (exact)0.026445Minimal cut sets9Smallest cut set order1Single points of failure1Mission time8760 hRepeated basic events1Exact top-event probability 0.026445 · rare-event sum ΣP(cut set) 0.026974The usual approximation overstates this tree by 2% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {radio_network} order 1 P 0.009 34% of the top ← single point of failure2. {onboard_atp, interlocking} order 2 P 0.016681 63.1% of the top3. {zc_a, zc_b, interlocking} order 3 P 0.00109 4.1% of the top4. {onboard_atp, tc_feed_1, tc_feed_2} order 3 P 6.39e-5 0.2% of the top5. {onboard_atp, tc_feed_1, tc_feed_3} order 3 P 6.39e-5 0.2% of the top6. {onboard_atp, tc_feed_2, tc_feed_3} order 3 P 6.39e-5 0.2% of the top7. {zc_a, zc_b, tc_feed_1, tc_feed_2} order 4 P 4.17e-6 0% of the top8. {zc_a, zc_b, tc_feed_1, tc_feed_3} order 4 P 4.17e-6 0% of the top9. {zc_a, zc_b, tc_feed_2, tc_feed_3} order 4 P 4.17e-6 0% of the topImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)interlocking — Solid-state interlocking processor faults q 0.051203 FV 65.9% B 0.336871 CR 65.2%onboard_atp — Onboard ATP unit fails to hold a target q 0.325781 FV 63.8% B 0.050198 CR 61.8%radio_network — Trackside radio network segment fails q 0.009 FV 34% B 0.982397 CR 33.4%zc_a — Zone controller A fails q 0.145877 FV 4.2% B 0.005044 CR 2.8%zc_b — Zone controller B fails q 0.145877 FV 4.2% B 0.005044 CR 2.8%tc_feed_1 — Track circuit power feed 1 fails q 0.014 FV 0.5% B 0.008829 CR 0.5%tc_feed_2 — Track circuit power feed 2 fails q 0.014 FV 0.5% B 0.008829 CR 0.5%tc_feed_3 — Track circuit power feed 3 fails q 0.014 FV 0.5% B 0.008829 CR 0.5%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 movement authority — CBTC metro line"
mission 8760h

top "Trains lose movement authority" = AND(cbtc_lost, fallback_lost)

gate cbtc_lost "CBTC supervision unavailable" = OR(zone_controller, radio_network, onboard_atp)
gate zone_controller "Both zone controllers down" = AND(zc_a, zc_b)
gate fallback_lost "Fixed-block fallback unavailable" = OR(interlocking, radio_network, track_circuits)
gate track_circuits "Track circuit detection lost" = KOFN(2, tc_feed_1, tc_feed_2, tc_feed_3)

event zc_a "Zone controller A fails" rate=1.8e-5
event zc_b "Zone controller B fails" rate=1.8e-5
// The one event that is not independent between the two branches.
event radio_network "Trackside radio network segment fails" p=0.009
event onboard_atp "Onboard ATP unit fails to hold a target" rate=4.5e-5
event interlocking "Solid-state interlocking processor faults" rate=6.0e-6
event tc_feed_1 "Track circuit power feed 1 fails" p=0.014
event tc_feed_2 "Track circuit power feed 2 fails" p=0.014
undeveloped tc_feed_3 "Track circuit power feed 3 fails" p=0.014