Time-Dependent Reliability Analysis for Bivariate Responses
Time-dependent system reliability is measured by the probability that the responses of a system do not exceed prescribed failure thresholds over a period of time. In this work, an efficient time-dependent reliability analysis method is developed for bivariate responses that are general functions of random variables and stochastic processes. The proposed method is based on single and joint upcrossing rates, which are calculated by the First Order Reliability Method (FORM). The method can efficiently produce accurate upcrossing rates for the systems with two responses. The upcrossing rates can then be used for system reliability predictions with two responses. As the general system reliability may be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis for general systems with more than two responses. Two examples, including a parallel system and a series system, are presented.