![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
In this article, we study the hazard rate ordering of lifetimes of two-component systems (series and parallel) by considering some bivariate distributions for the joint distribution of component lifetimes. Such that, we aim to investigate the lifetimes of systems with stochastically dependent and with stochastically independent components, the lifetimes of the components, and a stochastic ordering relation between these lifetimes. In addition to these, the mononotonicity of the hazard rates of the parallel and the series systems for the bivariate Farlie–Gumbel–Morgenstern (FGM) family is studied.
Mathematics Subject Classification:
Acknowledgments
The author is grateful to the referees for their invaluable comments and suggestions. In particular, the present form of the condition (i) of Lemmas 4.1 and 5.1 was generously suggested to the author by an anonymous referee. The author also thanks the Associate Editor for his contributions which helped to improve the readability of this article.