<p>This paper investigates series and parallel systems consisting of <i>k</i> subsystems with dependent and heterogeneous components. The components of the systems follow from the accelerated lifetime and the proportional reversed hazard models. We suppose that the independent subsystems have different Archimedean copulas for their dependence which is modeled by Archimedean copulas. We establish sufficient conditions for stochastic comparisons of two series (or parallel) systems under three scenarios. First, we compare two systems where the vector of accelerated lifetime or proportional reversed hazard parameters of the first system majorizes that of the second. Second, we compare systems based on the vector of the number of components in each subsystem, where the first system’s vector majorizes the second. Third, we consider cases where both the number of components in each subsystem and the number of subsystems differ between the two systems. Finally, we provide numerical examples to illustrate our theoretical findings.</p>

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Ordering Results for Series and Parallel Systems with Dependent and Heterogeneous Components Under Archimedean Copula Dependence

  • Omid Shojaee,
  • Manoochehr Babanezhad

摘要

This paper investigates series and parallel systems consisting of k subsystems with dependent and heterogeneous components. The components of the systems follow from the accelerated lifetime and the proportional reversed hazard models. We suppose that the independent subsystems have different Archimedean copulas for their dependence which is modeled by Archimedean copulas. We establish sufficient conditions for stochastic comparisons of two series (or parallel) systems under three scenarios. First, we compare two systems where the vector of accelerated lifetime or proportional reversed hazard parameters of the first system majorizes that of the second. Second, we compare systems based on the vector of the number of components in each subsystem, where the first system’s vector majorizes the second. Third, we consider cases where both the number of components in each subsystem and the number of subsystems differ between the two systems. Finally, we provide numerical examples to illustrate our theoretical findings.