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.

Meeting Name

ASME 2015 International Mechanical Engineering Congress and Exposition (2015: Nov. 13-19, Houston, TX)


Mechanical and Aerospace Engineering

Keywords and Phrases

Random processes; Reliability; Risk analysis; Risk assessment; Safety engineering; Stochastic systems; Structural analysis; Bivariate response; Failure thresholds; First order reliability methods; General functions; General systems; System reliability; Time dependent reliability analysis; Time-dependent systems; Reliability analysis

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2015 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Nov 2015