Redundancy mechanisms to systems with statistically dependent component and redundancy lifetimes

This study deals with redundancy mechanisms of coherent systems with statistically dependent component and redundancy lifetimes. We derive the distortion function of coherent system with a redundancy mechanism at component level, and then we present the usual stochastic order and hazard rate order on redundant system lifetimes. The main results not only enrich the framework of research in this line but also supplement some corresponding results in recent references. Several examples are presented to illustrate the results as well.