Reliability analysis of parallel systems with dependent components and Archimedean copulas

In this paper, preservation properties of reversed hazard rate order and a relative overall reversed hazard rate order under the structure of a parallel system with dependent components having lifetimes coupled by an Archimedean copula are established. We also study preservation properties of some related classes of lifetime distributions under the structure of that kind of parallel systems. Examples of proper Archimedean copulas are provided. The empirical estimator of the relative overall reversed hazard rate function is proposed and its consistency is explored theoretically and via simulation studies. Finally, the applicability of the studied concepts is discussed by some illustrative examples.