Orderings of extremes dependent modified proportional hazard and modified proportional reversed hazard variables under Archimedean copula

Abstract

In this paper, we discuss the hazard rate order and reversed hazard rate order of series and parallel systems with dependent components following either modified proportional reversed hazard models or modified proportional hazard models under Archimedean copula. These results generalize some known results in the literature.

Keywords:

• Archimedean copula
• hazard rate order
• reversed hazard rate order
• modified proportional hazard model
• modified proportional reversed hazard model

Acknowledgements

Thanks are due to the Editor and 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 Numbers: [UOZ-GR-9517-61] and [UOZ-GR-9618-14].