基于证据理论的共因失效因子不确定性分析

Uncertainty analysis of common cause factor using the evidence theory

安全仪表系统常通过计算其平均要求时失效概率(PFD(avg))来验证其是否满足目标安全完整性水平。计算PFD(avg)的众多参数中,共因失效因子β的变化对输出结果的影响是最大的。然而,由于共因失效的复杂性,β的估算十分困难。标准IEC61508中通过专家对一系列问题的评分来估算β,却没有考虑评分本身存在的不确定性以及多专家评分的影响,难以得到十分可信的β。针对以上问题,本文提出一种基于证据理论的β因子不确定性分析方法,以解决专家评分不确定性和多专家评分融合的问题。此方法将专家、专家评分和得分区间分别视为证据理论中的证据源、证据和焦元,并定义了焦元的权值(WFE)概念,最后将各焦元权值与对应的基本β值相乘后求总和得到新的考虑了不确定性的β。文章最后通过实例验证了方法的实用性和可行性,并且由分析知增加证据源会改变融合结果的不确定度,并且融合结果的不确定度与证据间总的冲突程度成正比。

Average probability of failure on demand always used in safety instrumented system to verify that the design achieves the target safety integrity level. Common cause factor, among the numerous parameters used to calculate PFDavg, leads to the greatest impact of result. However, the calculation offl is rather difficult due to the complexity of common cause failure. An expert scoring approach is introduced in IEC 61508 to estimate the value of/？. But this approach cannot achieve the reliable value offl since the uncertainty of scoring process and the fusion of multi-expert scoring are not considered. In order to solve the above problems, a new method based on the evidence theory is proposed to analysis the uncertainty of/？ in this paper. Experts, scores and score intervals are regarded as evidence source, evidence and focus elements in evidence theory, respectively. The concept of weight of focus element （WFE） is defined in this paper and the final/？ can be calculated as the summation of product of each focus element＇s WFE and its corresponding interval basic/？. At the end of this paper, an example is studies to prove the validity of this method. A conclusion that the uncertainty of result is proportional to the total conflict degree of evidence is also achieved by this numerical example.