Usual stochastic and reversed hazard orders of parallel systems with independent heterogeneous components

In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let and be independent non-negative random variables with and where is an absolutely continuous distribution function with reversed hazard rate function 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.