In practical situations, systems often suffer shocks from external stressing environments, stressing the system at random. These random shocks may have non-ignorable effects on the system's reliability. In this paper, we provide sufficient (and necessary) conditions on components' lifetimes and their surviving probabilities from random shocks for comparing the lifetimes of two fail-safe systems by means of the usual stochastic, hazard rate, and likelihood ratio orderings. Numerical examples are presented to highlight these theoretical results as well.
