Time-Dependent Reliability Estimation for Dynamic Systems Using a Random Process Approach

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. This paper proposes a methodology to calculate the cumulative probability of failure (probability of first passage or upcrossing) of a dynamic system, 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, assuming that it is impractical to perform the calculation for a “long” duration (e.g. hours). Our proposed methodology calculates the cumulative probability of failure or equivalently, 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 on a stochastic road demonstrates the improved accuracy of the proposed method compared with available methods.