## 3 Algorithm for Time Window Selection  
The vessel traffic accident frequency is chosen as the index in the process of time window selection because accident consequences are generated through a fuzzy development process after accidents occur and are considered as variables with epistemic uncertainty. Based on Equation (1), the limits of the confidence interval for the number of accidents can be calculated. Then the confidence interval for the vessel traffic accident frequency can be measured in the number of accidents per ship year. When the confidence intervals for the accident frequency each year are arranged in chronological order, the uncertain time series is formed [27].  
According to the orderliness of time series, the closer the time interval is to the current time, the nearer the vessel traffic accident frequency measured over the time interval approximates to the current accident frequency. In order to reflect the variation trend of the vessel traffic accident frequency due to maritime rules becoming operative on the vessel traffic being analyzed, it is considered necessary to split the uncertain time series of the vessel traffic accident frequency calculated above.  
The sliding window approach is applied in the process of splitting the uncertain time series. It regards the first year as the first segmentation and continues to expand until the vessel traffic accident frequency in certain years exceeds the confidence interval of the former segmentation. Then the next segmentation starts with this year. The aforementioned splitting procedure is repeated until the last year in the uncertain time series. It should be noted that whether the accident frequency in certain years exceeds the confidence interval of the former segmentation is used as the criterion for splitting the uncertain time series. The criterion is reasonable because it can aggregate relatively concentrative confidence intervals at a certain level of confidence. When the accident frequency exceeds the confidence interval of the former segmentation, it means that the accident frequency still changes under the influence of outside factors after overcoming the randomness of the accident data. In other words, different segmentations show different levels of the vessel traffic accident frequency. Changes in levels of the vessel traffic accident frequency reflect the effects of technical or operational developments, new requirements, or specific arrangements on the vessel traffic being analyzed. The above developments are often carried out along with maritime rules becoming operative. To represent the splitting process of the uncertain time series more clearly, the flowchart is shown in Figure 1.  
Figure 1: Flowchart for splitting uncertain time series.  
After the preliminary segmentation, there is one more step to obtain the final segmentation result. When one segmentation only contains one year and there is no remarkable change between its adjacent segmentations, it means that the large random fluctuation of data from the year leads to the segmentation. In order to avoid excessive segmentation, the segmentation and its adjacent segmentations should be merged. It should be noted that the condition for the segmentation, as can be seen in Figure 1, is used to judge if there is a remarkable change. Finally, the latest segmentation is considered to be the statistical time window.