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Fault tree (FTA) templates

Fault Tree — Blowout Preventer on Demand

Subsea BOP failing to seal a well over one section, with the blue and yellow control pods feeding BOTH the shear rams and the annular preventer — a shared gate drawn once and transferred, and the reason the two seals are not independent.

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BOP fails to seal the well on demandFault tree (IEC 61025) · 6 basic events · 4 gates · depth 3topWell not sealed ondemand0.001638shear_failsBlind shear ramsfail to seal0.039402shear_ram_bodyShear ram fails toclose0.008control_podsBoth control podsunavailable6.76e-4pod_blueBlue control podinoperable0.026pod_yellowYellow control podinoperable0.026tool_jointDrill pipe tooljoint across the…0.031annular_failsAnnular preventerfails to seal0.025505annular_elementAnnular packingelement fails0.011accumulatorAccumulator pressurebelow shear…0.014control_pods (transfer)Both control podsunavailable6.76e-4Top event probability (exact)0.001638Minimal cut sets5Smallest cut set order2Single points of failurenoneMission time720 hExact top-event probability 0.001638 · rare-event sum ΣP(cut set) 0.001651The usual approximation overstates this tree by 0.78% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {pod_blue, pod_yellow} order 2 P 6.76e-4 41.3% of the top2. {tool_joint, accumulator} order 2 P 4.34e-4 26.5% of the top3. {tool_joint, annular_element} order 2 P 3.41e-4 20.8% of the top4. {shear_ram_body, accumulator} order 2 P 1.12e-4 6.8% of the top5. {shear_ram_body, annular_element} order 2 P 8.80e-5 5.4% of the topImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)tool_joint — Drill pipe tool joint across the shear plane q 0.031 FV 47% B 0.024631 CR 46.6%pod_blue — Blue control pod inoperable q 0.026 FV 41.3% B 0.025975 CR 41.2%pod_yellow — Yellow control pod inoperable q 0.026 FV 41.3% B 0.025975 CR 41.2%accumulator — Accumulator pressure below shear requirement q 0.014 FV 33.1% B 0.0383 CR 32.7%annular_element — Annular packing element fails q 0.011 FV 26% B 0.038184 CR 25.6%shear_ram_body — Shear ram fails to close q 0.008 FV 12.1% B 0.024059 CR 11.7%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 "BOP fails to seal the well on demand"
mission 720h                      # one well section

top "Well not sealed on demand" = AND(shear_fails, annular_fails)

gate shear_fails "Blind shear rams fail to seal" = OR(shear_ram_body, control_pods, tool_joint)
gate annular_fails "Annular preventer fails to seal" = OR(annular_element, accumulator, control_pods)
gate control_pods "Both control pods unavailable" = AND(pod_blue, pod_yellow)

event shear_ram_body "Shear ram fails to close" p=0.008
event tool_joint "Drill pipe tool joint across the shear plane" p=0.031
event pod_blue "Blue control pod inoperable" p=0.026
event pod_yellow "Yellow control pod inoperable" p=0.026
event annular_element "Annular packing element fails" p=0.011
undeveloped accumulator "Accumulator pressure below shear requirement" p=0.014