Comparisons of series and parallel systems with heterogeneous exponentiated geometric components

Abstract

This article examines the problem of stochastic comparisons of series and parallel systems with independent heterogeneous exponentiated geometric (EG) components. Suppose and are independent non negative random variables with and In this article, we present under some restrictions on the involved parameters that is greater than with respect to the usual stochastic order, when is weakly supermajorized by and is weakly supermajorized by We also establish the usual stochastic order between and by using the unordered majorization between and and the p-majorization order between and For the series systems, in the case and some restrictions on the involved parameters, we establish is greater than with respect to the usual stochastic order, when is weakly supermajorized by On the other hand, sufficient conditions are given for the comparison of and when is weakly submajorized by