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

Ghobad Barmalzan, Sajad Kosari and Narayanaswamy Balakrishnan

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 14, 4781-4806

Abstract: In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let X1,⋯,Xn and Y1,⋯,Yn be independent non-negative random variables with Xi∼F(x;αi,βi) and Yi∼F(x;θi,λi),i=1,⋯,n, where F(.) is an absolutely continuous distribution function with reversed hazard rate function r˜(·). 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.

Date: 2022
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DOI: 10.1080/03610926.2020.1823415

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