On the Time-Dependent Reliability of Non-Monotonic, Non-Repairable Systems

The system response of many engineering systems depends on time. A random process approach is therefore, needed to quantify variation or uncertainty. The system input may consist of a combination of random variables and random processes. In this case, a time-dependent reliability analysis must be performed to calculate the probability of failure within a specified time interval. This is known as cumulative probability of failure which is in general, different from the instantaneous probability of failure. Failure occurs if the limit state function becomes negative at least at one instance within a specified time interval. Time-dependent reliability problems appear if for example, the material properties deteriorate in time or if random loading is involved which is modeled by a random process. Existing methods to calculate the cumulative probability of failure provide an upper bound which may grossly overestimate the true value. This paper presents a methodology to accurately estimate the cumulative probability of failure for non-monotonic in time systems in the presence of an input random process using an equivalent time-invariant "composite" limit state. Dynamics or vibration systems are commonly non-monotonic in time. Input stationary or non-stationary random processes are represented using autoregressive moving average modeling. Multiple examples demonstrate the accuracy of the proposed method and compare it with existing methodologies.