The failure rate of dynamic systems with random parameters is time-varying even for linear systems excited by a stationary random input. In this paper, we propose a simulation-based method to estimate this time-varying failure rate. The input and output stochastic processes are discretized using a small time step to calculate the trajectories of the output stochastic process accurately through simulation. The planning horizon (time of interest) is then partitioned into a series of longer correlated time intervals and the Saddlepoint approximation (SPA) is employed to estimate the distribution of maximum response and thus obtain the probability of failure in each time interval. Using the same simulated trajectories with SPA, a time-dependent copula is built to provide the correlation between the response in each time interval and the response up to that time interval. The time-varying failure rate is finally estimated at each discrete time, using the probability of failure in each time interval and the correlation information from the estimated copula. The effectiveness of the proposed method is illustrated with a vehicle vibration example.

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