Often, reliability systems suffer shocks from external stress factors, stressing the system at random. These random shocks may have non-ignorable effects on the reliability of the system. In this paper, we provide sufficient and necessary conditions on components’ lifetimes and their survival probabilities from random shocks for comparing the lifetimes of two fail-safe systems in two cases: (i) when components are independent, and then (ii) when components are dependent. We then apply the results for some distribution-free random variables with possibly different parameters to illustrate the established results.
