Stochastic comparisons of lifetimes of series and parallel systems with dependent and heterogeneous components

Reliability study of series and parallel systems of heterogeneous component lifetimes under proportional odds model

In this paper, we investigate various stochastic orderings for series and parallel systems with independent and heterogeneous components having lifetimes following the proportional odds model. We also investigate comparisons between system with heterogeneous components and that with homogeneous components. This paper also studies relative ageing orders for two systems in the framework of components having lifetimes following the proportional odds model.

Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas

In this paper, we compare the lifetimes of two series and two parallel systems stochastically where the lifetime of each component follows location-scale (LS) family of distributions. The comparison is carried out under two scenarios: one, that the components of the systems have a dependent structure sharing Archimedean copula and two, that the components are independently distributed. It is shown that the systems with components in series or parallel sharing Archimedean copula with more dispersion in the location or scale parameters results in better performance in the sense of the usual stoc…

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are assumed to follow heterogeneous general exponentiated location-scale models. In this communication, the usual stochastic and reversed hazard rate orders between the systems' lifetimes are established under two cases. For the case of independent random lifetimes, the usual stochastic order and the reversed hazard rate order between the second-largest order s…

Stochastic comparisons of series and parallel systems with heterogeneous components

In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the likelihood ratio order. In the presence of the Archimedean copula, we study stochastic comparison of series dependent systems in terms of the usual stochastic order.

随机冲击下Archimedean copula中串联与并联系统寿命的随机比较

Stochastic comparison of series and parallel systems lifetime in Archimedean copula under random shock

本文研究了经历随机冲击的异质相依组件构成的串联与并联系统寿命的随机排序，基于Archimedean copulas和组件生存函数的对数凹凸性建立条件，利用通常的随机序框架比较两系统寿命，并辅以实例和图形阐明理论发现。

Equivalence of the Hazard Rate and Usual Stochastic Orders for Parallel Systems

In this paper, we investigate stochastic comparisons of parallel systems, and obtain two characterization results in this regard. First, we compare a parallel system with independent heterogeneous components to a parallel system with homogeneous components, and establish some certain assumptions under which the hazard rate and usual stochastic orders between the lifetimes of two parallel systems are equivalent. Next, we turn our attention to two parallel systems with their component lifetimes following multiple-outlier model and prove that under some specified assumptions, the $p$-larger order…