Time-Dependent System Reliability Analysis for Bivariate Responses


Time-dependent system reliability is computed as the probability that the responses of a system do not exceed prescribed failure thresholds over a time duration of interest. In this work, an efficient time-dependent reliability analysis method is proposed for systems with bivariate responses which are general functions of random variables and stochastic processes. Analytical expressions are derived first for the single and joint upcrossing rates based on the first-order reliability method (FORM). Time-dependent system failure probability is then estimated with the computed single and joint upcrossing rates. The method can efficiently and accurately estimate different types of upcrossing rates for the systems with bivariate responses when FORM is applicable. In addition, the developed method is applicable to general problems with random variables, stationary, and nonstationary stochastic processes. As the general system reliability can be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis of general systems with more than two responses. Three examples, including a parallel system, a series system, and a hydrokinetic turbine blade application, are used to demonstrate the effectiveness of the proposed method.


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Intelligent Systems Center

Keywords and Phrases

Random processes; Random variables; Reliability; Stochastic systems; Structural analysis; Systems engineering; Turbomachine blades, Analytical expressions; First order reliability methods; Hydrokinetic turbines; Non-stationary stochastic process; System reliability; Time dependent reliability; Time-dependent systems; Up crossings, Reliability analysis

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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© 2018 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Sep 2018