Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, a product may fail due to time-dependent operating conditions and material properties, and component degradation. The reliability degradation with time may significantly increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. In this work, we consider the first-passage reliability, which accounts for the first time failure of non-repairable systems. Methods are available that provide an upper bound to the true reliability, but they may overestimate the true value considerably. This paper proposes a methodology to calculate the cumulative probability of failure (probability of first passage or upcrossing) of a dynamic system with random properties, driven by an ergodic input random process. Time series modeling is used to characterize the input random process based on data from a “short” time period (e.g. seconds) from only one sample function of the random process. Sample functions of the output random process are calculated for the same “short” time because it is usually impractical to perform the calculation for a “long” duration (e.g. hours). The proposed methodology calculates the time-dependent reliability, at a “long” time using an accurate “extrapolation” procedure of the failure rate. A representative example of a quarter car model subjected to a stochastic road excitation demonstrates the improved accuracy of the proposed method compared with available methods.

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