Ordering Properties of Systems with Two Dependent Components

The study of systems with dependent components from a reliability point of view is a very important topic. However, the majority of the articles study the case of independent components. In this article, we study how the dependency influences the performance of the system. We extend some comparison results obtained in the case of independent components to the case of two dependent components. We show that the more diverse the exponential parameters of the two components, the stronger (weaker) the parallel (series) system in the stochastic ordering. We apply our general results to some common bivariate models in the reliability theory.