不完全共因失效系统可靠性预测贝叶斯更新

Bayesian update of system reliability prediction based on incomplete common cause failures

利用泊松过程描述了系统共因失效(common cause failures,CCF)的发生规律,证明了共因发生可表示为所有多重失效过程的叠加。给出了共因发生率和多重失效率的数学关系,并利用Jeffreys原则求解多重失效率的贝叶斯估计值。解析了不完全CCF机制,并推导出系统可靠度表达式。以一种飞行数据记录系统为例,基于独立失效和不完全CCF建立了可靠度函数,并与完全CCF和不考虑CCF的假设结果进行对比,说明了该模型能更合理地对系统可靠性进行预测。另外,通过参数的贝叶斯更新,动态地反映了系统可靠性的变化规律,为系统检修周期的确定等问题提供了依据。

Poisson process is used to describe the occurrence of the common cause failure(CCF).It is proved that the Poisson process of common cause can be expressed as the superposition of all multiple failures.The mathematical relationship between the common cause occurrence rate and the multiple failure rate is given,and the Bayesian estimate of the multiple failure rate is solved by using the Jeffreys principle.The failure mechanism of incomplete common-cause is analyzed,and the reliability expression of the system is derived accordingly.The system reliability function is derived.An analytical example is provided,where both the independent failure and the incomplete CCF are considered to establish the system reliability function.In addition,a comparison with the complete CCF system and the normal system without CCF is made to illustrate that this model predicts system reliability more properly.Moreover,through the Bayesian updating of the parameters,the change pattern of the system reliability is dynamically reflected,which provides the basis for the determination of the system maintenance cycle.