A Sampling Approach to Extreme Value Distribution for Time Dependent Reliability Analysis

Abstract

Maintaining high accuracy and efficiency is a challenging issue in timedependent reliability analysis. In this work, an accurate and efficient method is proposed for limitstate functions with the following features: The limitstate function is implicit with respect to time. There is only one stochastic process in the input to the limitsate function. The stochastic process could be either a general strength or a general stress variable so that the limitstate function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. Consequently the timedependent reliability analysis is converted into its timeinvariant counterpart. The commonly used timeinvariant reliability method, the first order reliability method, is then applied to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of timedependent reliability analysis.