Stochastic comparison of the second-largest order statistics from heterogeneous models

Abstract

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 component lifetimes, following a general family of exponentiated location-scale distributions. In this article, usual stochastic order between the lifetimes of systems has been established when the components are interdependent. For the independent heterogeneous distributions, sufficient conditions under which reversed hazard rate order between the second-largest order statistics holds are investigated. To illustrate theoretical findings, some examples are considered.