Ordering Properties of the Smallest and Largest Order Statistics from Exponentiated Location-Scale Models Under Random Shocks

Abstract

In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems when the components are exponentiated location-scale models under random shocks. The results established here are developed in two directions. First, the comparisons are carried out with respect to usual stochastic ordering by using the concept of vector majorization for series and parallel systems. Next, when the matrix of parameters changes to another matrix of parameters in the sense of multivariate chain majorization, we study the usual stochastic order of the smallest order statistics when each component receives a random shock.

Keywords

• exponentiated location-scale family
• matrix majorization
• random shock
• usual stochastic order
• vector majorization