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

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