二维联合概率分布函数构造方法对结构串联系统可靠度影响分析

Effect of bivariate distribution construction methods on series system reliability

简要介绍了两种构造联合分布函数近似方法:基于Pearson相关系数的近似方法P和基于Spearman相关系数的近似方法S。推导了基于直接积分方法的串联系统失效概率计算公式,提出了两构件功能函数间负相关时串联结构系统失效概率上限值的计算公式。以理论联合概率分布函数是二维极值分布为例研究了两种近似方法在串联系统可靠度计算中的精度。结果表明,两种近似方法能够有效地计算串联结构系统可靠度,且精度很高,为不完备概率信息条件下串联结构系统可靠度分析提供了一条有效的途径。当两构件的功能函数正相关时,两种近似方法误差随串联系统失效概率的减小而增加,但近似方法与精确方法系统失效概率的差别最大也不会超过2倍;当两构件的功能函数负相关时,两种近似方法误差随系统失效概率的减小而减小,但两种近似方法的失效概率几乎与精确解一样。此外,两种近似方法误差不是随构件间相关性的增加而单调增加,而是存在一极大值。

The two approximate methods for constructing bivariate distributions,namely method P and method S,are briefly introduced first.Thereafter,the closed-form expressions for calculating the series system probability of failure using direct integration are derived.For two negatively correlated performance functions underlying a series system,a formula for calculating the upper bound of probability of failure for a series system is derived.Then,an illustrative example is presented to demonstrate the capability and validity of two approximate methods.The results indicate that the methods P and S are effectively the same from a numerical viewpoint.Both two approximate methods can produce sufficiently accurate probabilities of failure for series systems.The two approximate methods provide a tool for series system reliability analysis under incomplete probability information.The errors in series system probability of failure increase with decreasing system probability of failure when the two performance functions underlying two components are positively correlated.They will decrease with decreasing system probability of failure when the two performance functions underlying two components are negatively correlated.The maximum error in the series system probability of failure may not be associated with a large correlation.It can happen at an intermediate correlation.