{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:15Z","timestamp":1760241555765,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T00:00:00Z","timestamp":1525305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51509031"],"award-info":[{"award-number":["51509031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Uncertainty analysis is considered to be a necessary step in the process of vessel traffic risk assessment. The purpose of this study is to propose the uncertainty analysis algorithm which can be used to investigate the reliability of the risk assessment result. Probability and possibility distributions are used to quantify the two types of uncertainty identified in the risk assessment process. In addition, the algorithm for appropriate time window selection is chosen by considering the uncertainty of vessel traffic accident occurrence and the variation trend of the vessel traffic risk caused by maritime rules becoming operative. Vessel traffic accident data from the United Kingdom\u2019s marine accident investigation branch are used for the case study. Based on a comparison with the common method of estimating the vessel traffic risk and the algorithm for uncertainty quantification without considering the time window selection, the availability of the proposed algorithms is verified, which can provide guidance for vessel traffic risk management.<\/jats:p>","DOI":"10.3390\/a11050060","type":"journal-article","created":{"date-parts":[[2018,5,4]],"date-time":"2018-05-04T03:08:21Z","timestamp":1525403301000},"page":"60","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Vessel Traffic Risk Assessment Based on Uncertainty Analysis in the Risk Matrix"],"prefix":"10.3390","volume":"11","author":[{"given":"Molin","family":"Sun","sequence":"first","affiliation":[{"name":"Navigation College, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Zhongyi","family":"Zheng","sequence":"additional","affiliation":[{"name":"Navigation College, Dalian Maritime University, Dalian 116026, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,3]]},"reference":[{"key":"ref_1","unstructured":"International Maritime Organization (IMO) (2018, April 02). Revised Guidelines for Formal Safety Assessment (FSA) for Use in the IMO Rule-Making Process. Available online: http:\/\/research.dnv.com\/skj\/IMO\/MSC-MEPC%202_Circ%2012%20FSA%20Guidelines%20Rev%20III.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.oceaneng.2018.01.038","article-title":"Risk analysis for RoPax vessels: A case of study for the Strait of Gibraltar","volume":"151","author":"Endrina","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.ssci.2015.02.014","article-title":"Recommendations on the use and design of risk matrices","volume":"76","author":"Duijm","year":"2015","journal-title":"Saf. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.ress.2017.05.006","article-title":"Improving risk characterisations in practical situations by highlighting knowledge aspects, with applications to risk matrices","volume":"167","author":"Aven","year":"2017","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.ssci.2015.12.001","article-title":"On the assessment of uncertainty in risk diagrams","volume":"84","author":"Goerlandt","year":"2016","journal-title":"Saf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1111\/j.1539-6924.2011.01697.x","article-title":"An overview of maritime waterway quantitative risk assessment models","volume":"32","author":"Li","year":"2012","journal-title":"Risk Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ress.2015.01.025","article-title":"Maritime transportation risk analysis: Review and analysis in light of some foundational issues","volume":"138","author":"Goerlandt","year":"2015","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_8","first-page":"1","article-title":"Models and computational algorithms for maritime risk analysis: A review","volume":"265","author":"Lim","year":"2018","journal-title":"Ann. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"285","DOI":"10.5194\/os-12-285-2016","article-title":"Combining operational models and data into a dynamic vessel risk assessment tool for coastal regions","volume":"12","author":"Fernandes","year":"2016","journal-title":"Ocean Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.strusafe.2014.10.004","article-title":"Probabilistic ship collision risk and sustainability assessment considering risk attitudes","volume":"53","author":"Dong","year":"2015","journal-title":"Struct. Saf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1016\/j.ssci.2013.09.010","article-title":"On the reliability and validity of ship-ship collision risk analysis in light of different perspectives on risk","volume":"62","author":"Goerlandt","year":"2014","journal-title":"Saf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.ress.2014.03.009","article-title":"On a systematic perspective on risk for formal safety assessment (FSA)","volume":"127","author":"Montewka","year":"2014","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_13","first-page":"303","article-title":"Uncertainty in maritime risk analysis: Extended case study on chemical tanker collisions","volume":"229","author":"Sormunen","year":"2015","journal-title":"P. I. Mech. Eng. M-J. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/j.1539-6924.2006.00708.x","article-title":"Speaking the truth in maritime risk assessment","volume":"26","author":"Merrick","year":"2006","journal-title":"Risk Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1111\/j.1539-6924.2008.01085.x","article-title":"A combined Monte Carlo and possibilistic approach to uncertainty propagation","volume":"28","author":"Baraldi","year":"2008","journal-title":"Risk Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1080\/03081060.2016.1231901","article-title":"Comparing prediction methods for maritime accidents","volume":"39","author":"Zhao","year":"2016","journal-title":"Transp. Plan. Technol."},{"key":"ref_17","unstructured":"International Maritime Organization (IMO) (2018, April 02). Formal Safety Assessment: FSA-Cruise Ships. Available online: http:\/\/www.safedor.org\/resources\/MSC_85-INF-2.pdf."},{"key":"ref_18","unstructured":"European Maritime Safety Agency (EMSA) (2018, February 10). Risk Acceptance Criteria and Risk Based Damage Stability, Final Report, Part 2: Formal Safety Assessment. Available online: http:\/\/emsa.europa.eu\/publications\/technical-reports-studies-and-plans.html."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.ress.2012.11.024","article-title":"Separating the contributions of variability and parameter uncertainty in probability distributions","volume":"112","author":"Sankararaman","year":"2013","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.ress.2012.10.007","article-title":"Application of Dempster-Shafer theory for the quantification and propagation of uncertainty caused by the use of AIS data","volume":"111","author":"Talavera","year":"2013","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s11069-010-9578-6","article-title":"The use of the possibility theory to investigate the epistemic uncertainties within scenario-based earthquake risk assessments","volume":"56","author":"Rohmer","year":"2011","journal-title":"Nat. Hazards"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.apenergy.2015.10.135","article-title":"Optimization of combined heat and power production with heat storage based on sliding time window method","volume":"162","author":"Fang","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.marpol.2015.06.003","article-title":"A proactive approach for maritime safety policy making for the Gulf of Finland: Seeking best practices","volume":"60","author":"Haapasaari","year":"2015","journal-title":"Mar. Policy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/671589","article-title":"Time series outlier detection based on sliding window prediction","volume":"2014","author":"Yu","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1080\/03610926.2013.821486","article-title":"Modified large sample confidence intervals for Poisson distributions: Ratio, weighted average, and product of means","volume":"45","author":"Krishnamoorthy","year":"2016","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1007\/s11367-011-0364-9","article-title":"On the use of possibility theory in uncertainty analysis of life cycle inventory","volume":"17","author":"Andre","year":"2012","journal-title":"Int. J. Life Cycle Assess."},{"key":"ref_27","first-page":"1","article-title":"Chebyshev similarity match between uncertain time series","volume":"5","author":"Wang","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_28","unstructured":"Marine Accident Investigation Branch (MAIB) (2018, January 23). MAIB Annual Report 2016, Available online: https:\/\/www.gov.uk\/government\/publications\/maib-annual-report-2016."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1175\/JHM-D-15-0131.1","article-title":"Probabilistic inference coupled with possibilistic reasoning for robust estimation of hydrologic parameters and piecewise characterization of interactive uncertainties","volume":"17","author":"Wang","year":"2016","journal-title":"J. Hydrometeorol."},{"key":"ref_30","first-page":"163","article-title":"Marine traffic, accidents, and underreporting in the Baltic Sea","volume":"46","author":"Sormunen","year":"2016","journal-title":"Sci. J.-Marit. Univ. Szczec."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.aap.2009.10.008","article-title":"Under-reporting of maritime accidents","volume":"42","author":"Psarros","year":"2010","journal-title":"Accid. Anal. Prev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1016\/j.aap.2011.05.027","article-title":"Underreporting of maritime accidents to vessel accident databases","volume":"43","author":"Hassel","year":"2011","journal-title":"Accid. Anal. Prev."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/5\/60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:03:11Z","timestamp":1760194991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/5\/60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,3]]},"references-count":32,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["a11050060"],"URL":"https:\/\/doi.org\/10.3390\/a11050060","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2018,5,3]]}}}