独立不同分布的n中取(n-k+1)系统存活元件的剩余寿命

Residual Lifetimes of Surviving Components in(n-k+1)-out-of-n system with Independent but not Identically Distributed Components

n中取(n-k+1)系统在可靠性、生存分析和其他生命科学中扮演着非常重要的角色.研究了由n个独立但不同分布元件构成的n中取(n-k+1)系统在t时刻失效的状态下,可存活元件的剩余寿命即(X_(k∶n)-t|X_(j∶n)<t)(1≤j<k≤n),借助于permanent函数得到了可存活元件剩余寿命的可靠度函数的混合表达式和平均剩余寿命函数的混合表达式.在混合表达式的基础上,对不同的n中取(n-k+1)系统进行了普通随机序比较.

(n-k+1)-out-of-n systems are very important in reliability,survival analysis and other life sciences.In this paper,the residual lifetimes of surviving components in(n-k+1)-out-of-n system with independent but not identically distributed components that failed at is investigated.A mixture representation of reliability function and mean residual lifetimes function of the residual lifetimes is established in term of the permanent function.Based on the mixture representations,some stochastic ordering properties for different(n-k+1)-out-of-n system are obtained.