Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. The reliability usually degrades with time increasing 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. In this article, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available which provide an upper bound to the true reliability which may overestimate the true value considerably. The traditional Monte-Carlo simulation is 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. A detailed example demonstrates the accuracy and efficiency of the proposed importance sampling method over the traditional Monte Carlo simulation.

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