具有4个相异指数随机变量的串联系统的条件样本间隔

The Conditional Sample Spacings of Series Systems with Four Divergence Components Random Variables

基于具有4个独立不同指数分布元件的串联系统在某时刻失效时的元件剩余寿命,引入条件样本间隔概念,借助概率论与随机过程得到了其生存函数、期望和协方差等。然后,证明出了第一个条件样本间隔的生存函数关于元件的失效率是舒尔凸的。最后得到了第二个条件样本间隔在普通随机序意义下小于等于第三个条件样本间隔。所得结论将为设计最优系统和寿命检验提供理论依据。

When a series system with four independent components distributed as exponential fails at some time,the con⁃ditional spacings are introduced.By probability and stochastic process,the survival functions,the expectation and covari⁃ance of conditional sample spacings are obtained.Then,the first spacing is proved to be Schur convex about the hazard rates of components lifetimes.In the end,a stochastic comparison between the second conditional spacing and the third one is investigated.The results obtained will provide theory basis for designing optimal system and life tests.