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Fault Tree — AV Pedestrian Detection

An automated vehicle failing to detect a crossing pedestrian across 1000 urban hours: camera, lidar and radar pipelines must all miss AND the fusion layer must fail to recover, ranking sensor modality against software by Fussell–Vesely.

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Automated vehicle fails to detect a crossing pedestrianFault tree (IEC 61025) · 11 basic events · 6 gates · depth 3topPedestrian notdetected in time4.43e-6sensing_lostNo sensor reportsthe pedestrian4.40e-5camera_missCamera pipelinemisses the target0.023829low_sunLow sun saturatesthe forward camera0.014camera_hwCamera modulefailure0.003992classifier_missClassifier misses anoccluded pedestrian0.006lidar_missLidar pipelinemisses the target0.033652heavy_rainHeavy rainattenuates the lida…0.021lidar_hwLidar module failure0.00896cluster_missClustering mergesthe target into…0.004radar_missRadar pipelinemisses the target0.05484radar_hwRadar module failure0.002996radar_clutterRadar return lost inground clutter0.052fusion_no_recoveryFusion and planningdo not recover0.10073fusion_rejectFusion rejects asingle-sensor track0.09track_droppedTrack associationdrops across frames0.011compute_overrunPerception framebudget overrun8.00e-4Top event probability (exact)4.43e-6Minimal cut sets54Smallest cut set order4Single points of failurenoneMission time1000 hExact top-event probability 4.43e-6 · rare-event sum ΣP(cut set) 4.56e-6The usual approximation overstates this tree by 2.98% — that gap is the overlap between cut sets, which only the exact evaluation removes.Minimal cut sets — by order, then probability1. {low_sun, heavy_rain, radar_clutter, fusion_reject} order 4 P 1.38e-6 31.1% of the top2. {classifier_miss, heavy_rain, radar_clutter, fusion_reject} order 4 P 5.90e-7 13.3% of the top3. {low_sun, lidar_hw, radar_clutter, fusion_reject} order 4 P 5.87e-7 13.3% of the top4. {camera_hw, heavy_rain, radar_clutter, fusion_reject} order 4 P 3.92e-7 8.9% of the top5. {low_sun, cluster_miss, radar_clutter, fusion_reject} order 4 P 2.62e-7 5.9% of the top6. {classifier_miss, lidar_hw, radar_clutter, fusion_reject} order 4 P 2.52e-7 5.7% of the top7. {low_sun, heavy_rain, radar_clutter, track_dropped} order 4 P 1.68e-7 3.8% of the top8. {camera_hw, lidar_hw, radar_clutter, fusion_reject} order 4 P 1.67e-7 3.8% of the top9. {classifier_miss, cluster_miss, radar_clutter, fusion_reject} order 4 P 1.12e-7 2.5% of the top10. {low_sun, heavy_rain, radar_hw, fusion_reject} order 4 P 7.93e-8 1.8% of the top+ 44 further cut sets not listedImportance — Fussell–Vesely (share of current risk) and Birnbaum (potential swing)radar_clutter — Radar return lost in ground clutter q 0.052 FV 94.8% B 8.05e-5 CR 94.5%fusion_reject — Fusion rejects a single-sensor track q 0.09 FV 89.3% B 4.35e-5 CR 88.3%heavy_rain — Heavy rain attenuates the lidar return q 0.021 FV 62.4% B 1.30e-4 CR 61.6%low_sun — Low sun saturates the forward camera q 0.014 FV 58.8% B 1.84e-4 CR 58.2%lidar_hw — Lidar module failure q 0.00896 FV 26.6% B 1.28e-4 CR 26%classifier_miss — Classifier misses an occluded pedestrian q 0.006 FV 25.2% B 1.83e-4 CR 24.7%camera_hw — Camera module failure q 0.003992 FV 16.8% B 1.82e-4 CR 16.4%cluster_miss — Clustering merges the target into clutter q 0.004 FV 11.9% B 1.28e-4 CR 11.5%Rectangle intermediate event · dome AND · shield OR · shield with k/n voting · hexagon INHIBIT with its oval condition · circle basic · diamond undeveloped · triangle transfer

Make it your own.

title "Automated vehicle fails to detect a crossing pedestrian"
mission 1000h                     # urban operational design domain

top "Pedestrian not detected in time" = AND(sensing_lost, fusion_no_recovery)

gate sensing_lost "No sensor reports the pedestrian" = AND(camera_miss, lidar_miss, radar_miss)
gate camera_miss "Camera pipeline misses the target" = OR(low_sun, camera_hw, classifier_miss)
gate lidar_miss "Lidar pipeline misses the target" = OR(heavy_rain, lidar_hw, cluster_miss)
gate radar_miss "Radar pipeline misses the target" = OR(radar_hw, radar_clutter)
gate fusion_no_recovery "Fusion and planning do not recover" = OR(fusion_reject, track_dropped, compute_overrun)

event low_sun "Low sun saturates the forward camera" p=0.014
event heavy_rain "Heavy rain attenuates the lidar return" p=0.021
event camera_hw "Camera module failure" rate=4.0e-6
event lidar_hw "Lidar module failure" rate=9.0e-6
event radar_hw "Radar module failure" rate=3.0e-6
event classifier_miss "Classifier misses an occluded pedestrian" p=0.006
event cluster_miss "Clustering merges the target into clutter" p=0.004
event radar_clutter "Radar return lost in ground clutter" p=0.052
event fusion_reject "Fusion rejects a single-sensor track" p=0.09
event track_dropped "Track association drops across frames" p=0.011
undeveloped compute_overrun "Perception frame budget overrun" p=0.0008