Ghobad Saadatkia

‎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 parallel‎ ‎systems by means of usual stochastic and reversed hazard rate orders‎, ‎when the matrix of parameters changes to another matrix in a mathematical sense‎. ‎The results‎ developed in this paper generalize some known results in the literature‎.