Some new ordering results on residual life and inactivity time of series systems with two components having statistically dependent lifetimes

This study considers two components with statistically dependent lifetimes, and compares the residual lifetime of the series system of them and the lifetime of the series of used components with residual lifetimes. Sufficient and necessary conditions about the usual stochastic order and hazard rate order are developed. The findings reveal that the dependence structure is critical in determining whether the used system is more reliable. The inactivity time is also investigated. Numerical examples are also presented to illustrate the findings.