{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T02:51:17Z","timestamp":1771987877508,"version":"3.50.1"},"reference-count":64,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T00:00:00Z","timestamp":1611705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Aerospace"],"abstract":"<jats:p>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 \u00d7 10\u22129 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 \u00d7 10\u22129 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.<\/jats:p>","DOI":"10.3390\/aerospace8020031","type":"journal-article","created":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T06:10:54Z","timestamp":1611727854000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On Probabilistic Risk of Aircraft Collision along Air Corridors"],"prefix":"10.3390","volume":"8","author":[{"given":"Lu\u00eds M. B. C.","family":"Campos","sequence":"first","affiliation":[{"name":"CCTAE, IDMEC, Departamento de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2395-2920","authenticated-orcid":false,"given":"Joaquim M. G.","family":"Marques","sequence":"additional","affiliation":[{"name":"CCTAE, IDMEC, Departamento de Engenharia Mecatr\u00f3nica, Escola de Ci\u00eancias e Tecnologia, Universidade de \u00c9vora, Col\u00e9gio Lu\u00eds Ant\u00f3nio Verney, Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,27]]},"reference":[{"key":"ref_1","unstructured":"Eurocontrol (2020, December 20). EUROCONTROL Seven-Year Forecast February 2018. 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