中国安全科学学报 ›› 2019, Vol. 29 ›› Issue (10): 38-42.doi: 10.16265/j.cnki.issn1003-3033.2019.10.007

• 安全系统学 • 上一篇    下一篇

等幂律在求解概率重要度时的失真分析

尹小贝1,2 讲师, 华成杰2, 王浩泽2, 赵睿3   

  1. 1 上海海事大学 物流与风险控制研究中心,上海 201306;
    2 上海海事大学 海洋科学与工程学院,上海 201306;
    3 上海海事大学 商船学院,上海 201306
  • 收稿日期:2019-07-13 修回日期:2019-09-03 出版日期:2019-10-28 发布日期:2020-10-27
  • 作者简介:尹小贝 (1977—),男,湖北荆州人,博士,讲师,主要从事风险分析与风险评价等方面的研究。E-mail:xbyin@shmtu.edu.cn。

A distortion analysis of probability importance formed by equal power law

YIN Xiaobei 1,2, HUA Chengjie2, WANG Haoze2, ZHAO Rui3   

  1. 1 Logistics and Risk Control Research Center, Shanghai Maritime University, Shanghai 201306, China;
    2 College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China;
    3 College of Merchant Marine,Shanghai Maritime University, Shanghai 201306, China
  • Received:2019-07-13 Revised:2019-09-03 Online:2019-10-28 Published:2020-10-27

摘要: 为解决事故树重复事件的概率重要度系数准确性不高的问题,以数学推导为基础,通过复合多元函数的偏导法则,论证使用等幂律会消除重复事件概率对顶上事件概率的影响。首先介绍等幂律在事故树分析技术中的应用基础,顶上事件的概率函数、概率重要度的定义及其数学本质;然后利用复合多元函数的偏导公式推导出基本事件概率重要度求解的一般公式;最后通过例题演示失真所导致的3种偏差规律。结果表明:该一般公式能退化到无重复事件时的概率重要度求解公式;同时也证明有重复事件时,使用等幂律会导致重复事件概率重要度系数的求解失真。

关键词: 概率重要度, 复合多元函数, 等幂律, 失真, 偏差

Abstract: For the sake of improving accurancy of probability importance of repeated events, it was demonstrated that the use of equal power law would eliminate the influence of repeated events probability on the top event probability. Firstly, the equal power law of Boolean algebra, the probability function of the top event, the definition of probability importance and its mathematical essence were introduced in detail. Then a general formula for probability importance of basic events was derived by using the partial derivative formula of compound multivariate function. Finally, three kinds of deviation laws caused by distortion were demonstrated through examples. The results show that for non-repetitive events, the formula can be degraded to the existing probability importance formula, and that for repeated events, the application of equal power law to the solution of probability importance will lead to distortion of results.

Key words: probability importance, compound multivariate function, equal power law, distortion, deviation

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