Abstract

In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let $X_1,\cdots ,X_n$ and $Y_1,\cdots ,Y_n$ be independent non-negative random variables with $X_i\sim F(x;{\alpha }_i,{\beta }_i)$ and $Y_i\sim F(x;{\theta }_i,{\lambda }_i),i=1,\cdots ,n,$ where $F(.)$ is an absolutely continuous distribution function with reversed hazard rate function $\tilde{r}(·).$ In this paper, under certain conditions, by using the concept of vector majorization, unordered order, p-majorization and related orders, we discuss stochastic comparisons between parallel systems in the sense of usual stochastic and reversed hazard rate orders. The results developed in this paper generalize some known results in the literature.

摘要

在本文中，我们提出了两个包含通用独立异构组件的并行系统之间的一些新排序属性。更准确地说，让$X_1,\cdots ,X_n$和${是}_1,\cdots ,{是}_n$是独立的非负随机变量$X_{\mathrm{一世}}～F(X;{\alpha }_{\mathrm{一世}},{\beta }_{\mathrm{一世}})$和${是}_{\mathrm{一世}}～F(X;{\theta }_{\mathrm{一世}},{\lambda }_{\mathrm{一世}}),\mathrm{一世}=1,\cdots ,n,$在哪里$F(.)$是具有反向危险率函数的绝对连续分布函数$\stackrel{～}{r}(·).$在本文中，在一定条件下，通过使用向量主要化、无序顺序、p-主要化和相关顺序的概念，我们讨论了通常随机和反向危险率顺序意义上的并行系统之间的随机比较。本文开发的结果概括了文献中的一些已知结果。