{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:35Z","timestamp":1760241155928,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T00:00:00Z","timestamp":1574899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Heinrich\u2019s pyramid theory is one of the most influential theories in accident and incident prevention, especially for industries with high safety requirements. Originally, this theory established a quantitative correlation between major injury accidents, minor injury accidents and no-injury accidents. Nowadays, researchers from different fields of engineering also apply this theory in establishing quantitatively the correlation between accidents and incidents. In this work, on the one hand, we have detected the applicability of this theory by studying incident reports of different severities occurred in air traffic management. On the other hand, we have deepened the analysis of this theory from a qualitative perspective. For this purpose, we have applied the convolution operator in identifying correlations between contributing causes to different incident severities, also known as precursors to accidents, and system failures. The results suggested that system failures are mechanisms by which the causes are manifested. In particular, the same underlying cause can be manifested through different failures which contribute to incidents with different severities. Finally, deriving from this result, an artificial neuronal network model is proposed to recognize future causes and their possible associated incident severities.<\/jats:p>","DOI":"10.3390\/e21121166","type":"journal-article","created":{"date-parts":[[2019,11,28]],"date-time":"2019-11-28T10:54:10Z","timestamp":1574938450000},"page":"1166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Detection of Common Causes between Air Traffic Serious and Major Incidents in Applying the Convolution Operator to Heinrich Pyramid Theory"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8701-9059","authenticated-orcid":false,"given":"Schon Z. Y.","family":"Liang Cheng","sequence":"first","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3., 28040 Madrid, Spain"},{"name":"Aeronautic, Space &amp; Defence Division, ALTRAN Innovation S.L., Calle Campezo 1, 28022 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6639-6819","authenticated-orcid":false,"given":"Rosa Maria","family":"Arnaldo Vald\u00e9s","sequence":"additional","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3., 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0961-2188","authenticated-orcid":false,"given":"V\u00edctor Fernando","family":"G\u00f3mez Comendador","sequence":"additional","affiliation":[{"name":"Department of Sistemas Aeroespaciales, Transporte A\u00e9reo y Aeropuertos, School of Aerospace Engineering, Universidad Polit\u00e9cnica de Madrid (UPM), Plaza Cardenal Cisneros n3., 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco Javier","family":"S\u00e1ez Nieto","sequence":"additional","affiliation":[{"name":"Centre for Aeronautics, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, Bedford MK43 0AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Reason, J. 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