Abstract This paper develops a rigorous and unified preservation framework for hazard rate and relative average hazard rate stochastic orders in series and parallel systems with dependent component lifetimes. While preservation of hazard-rate-based orders is well understood under independence, their behavior under dependence, particularly for the relative average hazard rate order, remains largely unexplored due to the intrinsic complexity introduced by dependence structures. To address this gap, dependence is modeled via Archimedean copulas, which allow for a flexible and analytically tractable representation of positive dependence beyond classical assumptions. We derive explicit sufficient conditions under which hazard rate and relative average hazard rate orders are preserved from component lifetimes to system lifetimes, revealing a clear separation between the roles of marginal distributions and copula generators. This analysis demonstrates that generator properties fundamentally govern the transmission of stochastic orderings in dependent environments, a phenomenon absent in independent system models and not captured by existing preservation results. Several illustrative examples based on commonly used Archimedean copulas are provided to demonstrate the sharpness and applicability of the proposed conditions. The results substantially advance preservation theory in reliability analysis by incorporating dependence effects and, to the best of our knowledge, offering the first comprehensive treatment of relative average hazard rate order preservation in dependent series and parallel systems. These findings provide both theoretical insight and practical guidance for reliability modeling and risk assessment in complex dependent systems.
Manshi et al. (Tue,) studied this question.