On Probabilistic Risk of Aircraft Collision along Air Corridors

The separation of aircraft in cruising flight in air corridors is based on the assurance of an extremely low probability of collision due to position inaccuracy caused by navigation errors, atmospheric disturbances, or other factors. The appropriate standard is the International Civil Aviation Organization (ICAO) Target Level of Safety (TLS) of frequency of collision less than 5 × 10−9 per flight hour. An upper bound for the collision probability per unit distance is the probability of coincidence, in the case of aircraft flying at the same speed along parallel tracks in the same direction. This leads to the case of two aircraft flying at a constant separation, for which at least three probabilities of coincidence can be calculated: (i) the maximum probability of coincidence at the most likely point; (ii) the cumulative probability of coincidence integrated along the flight path; and (iii) the cumulative probability of coincidence integrated over all space. These three probabilities of coincidence are applied to the old standard and new reduced vertical separations of 2000 ft and 1000 ft respectively, for comparison with the ICAO TLS, and also to assess their suitability as safety metrics. The possibility is raised of complementing the ICAO TLS 5 × 10−9 per hour, which is suitable for the cumulative probability of collision, by two additional safety metrics: (i) one per hour flown squared, which is suitable for comparison with the maximum joint probability density of collision; and (ii) another times hour flown, for comparison with the three-dimensional cumulative probability of coincidence. These three metrics (i) to (iii) have distinct dimensions, give different information, and could be alternatives or supplements.