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Fault tree (FTA) templates

Fault Tree — Wrong-Side Signalling Failure

A conflicting movement authority issued at a junction: interlocking logic, a two-of-three train-detection vote and the downstream protection layer, quantifying how much of the residual risk sits with the signaller rather than the equipment.

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Wrong-side signalling failure at a junctionFault tree (IEC 61025) · 7 basic events · 4 gates · depth 3topConflicting movementauthority issued6.57e-8interlock_wrongInterlocking grantsa conflicting route0.002606logic_faultInterlocking logicdata fault8.76e-4detection_wrongTrack vacancywrongly reported2/30.001132axle_count_aAxle counter head Amiscounts0.021662axle_count_bAxle counter head Bmiscounts0.021662track_circuitTrack circuit failsto detect a vehicle0.015644panel_errorSignaller sets anunsafe route by…6.00e-4protection_absentNothing downstreamstops the train2.52e-5tpws_failTrain protectionsystem inactive on…0.0021driver_missDriver fails toreact to the aspect0.012Top event probability (exact)6.57e-8Minimal cut sets5Smallest cut set order3Single points of failurenoneMission time8760 hExact top-event probability 6.57e-8 · rare-event sum ΣP(cut set) 6.61e-8The usual approximation overstates this tree by 0.65% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {logic_fault, tpws_fail, driver_miss} order 3 P 2.21e-8 33.6% of the top2. {panel_error, tpws_fail, driver_miss} order 3 P 1.51e-8 23% of the top3. {axle_count_a, axle_count_b, tpws_fail, driver_miss} order 4 P 1.18e-8 18% of the top4. {axle_count_a, track_circuit, tpws_fail, driver_miss} order 4 P 8.54e-9 13% of the top5. {axle_count_b, track_circuit, tpws_fail, driver_miss} order 4 P 8.54e-9 13% of the topImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)tpws_fail — Train protection system inactive on the approach q 0.0021 FV 100% B 3.13e-5 CR 100%driver_miss — Driver fails to react to the aspect q 0.012 FV 100% B 5.47e-6 CR 100%logic_fault — Interlocking logic data fault q 8.76e-4 FV 33.6% B 2.52e-5 CR 33.5%axle_count_a — Axle counter head A miscounts q 0.021662 FV 30.7% B 9.22e-7 CR 30.4%axle_count_b — Axle counter head B miscounts q 0.021662 FV 30.7% B 9.22e-7 CR 30.4%track_circuit — Track circuit fails to detect a vehicle q 0.015644 FV 25.7% B 1.07e-6 CR 25.4%panel_error — Signaller sets an unsafe route by override q 6.00e-4 FV 23% B 2.51e-5 CR 23%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 "Wrong-side signalling failure at a junction"
mission 8760h

top "Conflicting movement authority issued" = AND(interlock_wrong, protection_absent)

gate interlock_wrong "Interlocking grants a conflicting route" = OR(logic_fault, detection_wrong, panel_error)
gate detection_wrong "Track vacancy wrongly reported" = KOFN(2, axle_count_a, axle_count_b, track_circuit)
gate protection_absent "Nothing downstream stops the train" = AND(tpws_fail, driver_miss)

event logic_fault "Interlocking logic data fault" rate=1.0e-7
event panel_error "Signaller sets an unsafe route by override" p=0.0006
event axle_count_a "Axle counter head A miscounts" rate=2.5e-6
event axle_count_b "Axle counter head B miscounts" rate=2.5e-6
event track_circuit "Track circuit fails to detect a vehicle" rate=1.8e-6
event tpws_fail "Train protection system inactive on the approach" p=0.0021
undeveloped driver_miss "Driver fails to react to the aspect" p=0.012