There is a possibility that accidents of oil tankers cause human loss and/or marine environmental pollution. Therefore, it is important to examine safety measures to prevent the accidents or to reduce subsequent damages. “Risk” is an index to quantitatively evaluate the effectiveness of such measures. One of the methods to express the risk is F – T (frequency vs. tons of spilt oil) curve. Some approximation functions have been proposed so far by the application of power-law distributions to express exceedance frequency curves of consequence severity, corresponding to F – T curve. However, there are some technical issues to be resolved in these approximation functions. Hence, the authors developed approximation functions to express the exceedance frequency curve of consequence severity by applying power-law distributions. In this study, these functions have been modified further to approximate F – T curve. It has been found that the present functions nicely reproduce F – T curve obtained from historical database. Furthermore, in the application of the present functions, it has been shown that the approximation of F – T curve by these functions enables us to identify a volume range of spilt oil with higher risk.

中文翻译：

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使用增强的幂律分布函数的油轮的频率与溢油吨数曲线

油轮事故有可能造成人员伤亡和/或海洋环境污染。因此，检查安全措施以防止事故或减少后续损害非常重要。“风险”是量化评估此类措施有效性的指标。表达风险的方法之一是 F-T（频率与溢油吨数）曲线。到目前为止，已经提出了一些近似函数，通过应用幂律分布来表达后果严重程度的超出频率曲线，对应于 F-T 曲线。然而，在这些近似函数中还有一些技术问题需要解决。因此，作者开发了近似函数，通过应用幂律分布来表达后果严重程度的超出频率曲线。在这项研究中，这些函数已进一步修改以近似 F-T 曲线。已经发现，目前的函数很好地再现了从历史数据库中获得的 F-T 曲线。此外，在本函数的应用中，已经表明这些函数对 F-T 曲线的近似使我们能够识别具有更高风险的溢油体积范围。