Ordering fail-safe systems having dependent components with Archimedean copula and exponentiated location-scale distributions

Abstract

In this paper, we study stochastic comparisons of two fail-safe systems with dependent components having an Archimedean copula for the joint survival function and general exponentiated location-scale lifetime distributions. We first present sufficient conditions for the usual stochastic order between fail-safe systems when the components have different exponentiated location-scale distributions but with the same Archimedean copula. Next, the hazard rate ordering of fail-safe systems is discussed when the components in the two systems are independent and follow multiple-outlier exponentiated location-scale models. Several examples are then presented to illustrate the theoretical results established here.

Keywords:

• Hazard rate order
• usual stochastic order
• fail-safe systems
• Archimedean copulas
• exponentiated location-scale distribution

Acknowledgements

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

Disclosure statement

No potential conflict of interest was reported by the author(s).