Stochastic comparisons of residual lives of series-parallel and parallel-series systems with independent subsystems consisting of dependent components

Abstract

In this article, we consider residual lives of series-parallel and parallel-series systems with independent subsystems consisting of dependent homogeneous components with the joint distribution of their lifetimes being modeled by an Archimedean copula. By considering two such systems with different numbers of components within each subsystem, we establish various stochastic orderings and aging results for the residual lives of series-parallel and parallel-series systems. The results established here are quite general. Several examples are presented to illustrate all the established results and their reliability implications.

Keywords:

• Relative aging orders
• hazard rate order
• reversed hazard rate order
• series-parallel
• systems
• parallel-series systems
• Archimedean copulas

Acknowledgements

The authors express their sincere thanks to the Editor and the anonymous reviewers for their useful comments and suggestions on an earlier version of this manuscript, which led to this improved version.

Additional information

Funding

This work has been conducted by University of Zabol, Grant Number: GR-UOZ-3389.