  In this manuscript, we studied the stochastic ordering behavior of series as
well as parallel systems lifetimes comprising dependent and heterogeneous
components, experiencing random shocks, and exhibiting distinct dependency
structures. We establish certain conditions for the lifetime of individual
components, the dependency among components defined by Archimedean copulas, and
the impact of random shocks on the overall system lifetime to reach the
conclusion. We consider components whose survival functions are either
increasing log-concave or decreasing log-convex functions of the parameters
involved and systems exhibit different dependency structures. These conditions
make it possible to compare the lifetimes of two systems using the usual
stochastic order framework. Additionally, we provide examples and graphical
representations to elucidate our theoretical findings.
