Consider a system which has n independent components whose time dependent strengths YtY t Y t 1 ( ), , , 2 ( ) … n ( ) are independent identically distributed random processes. Let random processes XtX t X t 1 ( ), , , 2 ( ) … m ( ) denote the common multiple stresses experienced by the components at time t . The reliabilities of the components in the system can chance as a result of their deterioration or in consequence of variable stresses over time. Degradation in components reliabilities in the system can lead to the degradation of the entire system reliability. In this paper, we propose a new method for determining the time dependent component reliability of the system under stress-strength setup. The proposed method provides a simple way for evaluating the reliability of the system at a certain time period. Computational results are also presented for the reliability of coherent system and consecutive k -out-of- n system.