Denominator-Conditioned Functional Coverage Assessment of Rear-End Automated Emergency Braking Using Naturalistic- Trajectory-Derived Hazard Scenarios

This study presents a denominator-conditioned functional-coverage framework for rear-end automated emergency braking (AEB). The framework estimates what share of a declared modeled rear-end hazard denominator is controllable at a given intervention lead time. Ego–lead episodes come from NGSIM US-101 and I-80; the default D0 denominator is a modeled no-action counterfactual from episode-entry states, not a replay of observed future motion or a crash-rate estimator. A longitudinal brake-only replay model estimates policy-specific required lead times for transparent reference policies: a brake-only upper envelope, TTC-family references, a stopping-distance reference, and an RSS-style baseline. Under the default pipeline, the upper envelope saturates near 99%, the weak TTC anchor covers roughly half of the denominator, and stronger references reach about 95–96% frequency-weighted saturation. Duration filters change the saturation by at most 4.00 percentage points, and increasing physical-uncertainty realizations from R = 3 to R = 30 changes the saturation by at most 0.33 percentage points. An extended TTC-family audit shows that a coverage-only candidate reaches 99.00% saturation but 30.70% nuisance intervention, whereas a burden-constrained candidate reaches 97.88% saturation with 9.23% nuisance. The reported values are conditional controllability measures, not certification evidence or deployment-level crash-rate estimates.