In practice, several qualitative frameworks [12; 13] and quantitative methods [14] have been proposed to assess uncertainty in the field of maritime risk analysis.  
There are typically two types of uncertainty: randomness resulting from inherent variability and cognitive imprecision resulting from expert opinions. The former type of uncertainty is often referred to as aleatory uncertainty whereas the latter is often referred to as epistemic uncertainty [15]. As vessel traffic accidents are random events, the number of accidents can be considered as a random number generated from a random event [16]. Thus, the vessel traffic accident frequency calculated by the number of accidents is often taken as a variable with aleatory uncertainty due to inherent variability [17]. With regards to the vessel traffic accident consequence, it can be taken as the result of many factors affecting one another through an ambiguous development process. In the field of maritime risk analysis, the number of fatalities is generally far less than the number of vessel traffic accidents. The accident consequence is often considered as a variable with epistemic uncertainty, as the available information is usually scarce and expert judgements are often incorporated in the process of analyzing the accident consequence [18].  
Different mathematical methods are required in order to quantify different types of uncertainty. Aleatory uncertainty is often quantified by probability distributions [19]. For the quantification of epistemic uncertainty, a number of methods can be used, such as possibility theory and evidence theory [20]. In this study, possibility theory is selected to quantify epistemic uncertainty due to its mathematical simplicity [21]. It should be noted that the time window used for the inclusion of data has a major effect on the quantification of uncertainty [22]. Without considering the time window selection, uncertainties will be measured too conservatively or too optimistically. Therefore, it is considered necessary to propose an algorithm for time window selection.  
When selecting the time window, the aleatory uncertainty of vessel traffic accident occurrences should be taken into account. In addition, it should be noted that the vessel traffic accident frequency changes over time due to maritime rules becoming operative on the vessel traffic being analyzed [23]. In other words, the time series of the accident frequency may reveal certain trends. Due to uncertainties and variation trends of the vessel traffic accident frequency, the time window selection comes down to constructing and splitting the uncertain time series. In this study, the aleatory uncertainty of the vessel traffic accident frequency is quantified by the Poisson distribution [18], so that the confidence intervals of the accident frequency can be obtained each year. When the confidence intervals are arranged in chronological order, the uncertain time series of the accident frequency is built up. Based on the orderliness of time series, the sliding window method [24] is used to split the uncertain time series, which aggregates the relatively concentrative confidence intervals. The latest segmentation is selected as the statistical time window.  
The rest of the paper is organized as follows. Section 2 describes the algorithm for the quantification of the two types of uncertainty identified in the risk assessment process. In Section 3, the time window selection algorithm is described. The case study is carried out and comparisons are made to verify the superiority of the proposed algorithms in Section 4. Conclusions are provided in Section 5.