Ageing Orders of Series-Parallel and Parallel-Series Systems with Independent Subsystems Consisting of Dependent Components

Balakrishnan, Narayanaswamy; Barmalzan, Ghobad; Hosseinzadeh, Ali Akbar

doi:10.52547/jirss.20.1.83

Ageing Orders of Series-Parallel and Parallel-Series Systems with Independent Subsystems Consisting of Dependent Components

Authors

Narayanaswamy Balakrishnan ¹

Ghobad Barmalzan ²

Ali Akbar Hosseinzadeh ³

¹ Department of Mathematics and Statistics, McMaster University, Hamilton, CANADA

² Department of Statistics, University of Zabol, Sistan and Baluchestan, IRAN

³ Department of Mathematics, University of Zabol, Sistan and Baluchestan, IRAN

10.52547/jirss.20.1.83

Abstract

In this paper, we consider series-parallel and parallel-series systems with independent subsystems consisting of dependent homogeneous components whose joint lifetimes are modeled by an Archimedean copula. Then, by considering two such systems with different numbers of components within each subsystem, we establish hazard rate and reversed hazard rate orderings between the two system lifetimes, and also discuss how these systems age relative to each other in terms of hazard rate and reversed hazard rate functions.

Keywords

Relative Ageing Orders

hazard rate order

Reversed Hazard Rate Order

Series-Parallel Systems

Parallel-Series Systems

Archimedean Copulas

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