Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time-dependent operating conditions and material properties, component degradation, etc. The reliability degradation with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time interval. In this work, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available in the literature, which provide an upper bound to the true reliability which may overestimate the true value considerably. Monte-Carlo simulations are accurate but computationally expensive. A computationally efficient importance sampling technique is presented to calculate the cumulative probability of failure for random dynamic systems excited by a stationary input random process. Time series modeling is used to characterize the input random process from only one sample function of the random process. Examples are presented to demonstrate the accuracy and efficiency of the proposed importance sampling method over the traditional Monte Carlo simulation.