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Research Papers

Time-Dependent System Reliability Analysis for Bivariate Responses

[+] Author and Article Information
Zhen Hu

Department of Industrial and
Manufacturing Systems Engineering,
University of Michigan-Dearborn,
2340 Heinz Prechter Engineering
Complex (HPEC),
Dearborn, MI 48128
e-mail: zhennhu@umich.edu

Zhifu Zhu

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
400 West 13th Street, Toomey Hall 290D,
Rolla, MO 65409
e-mail: zzgc5@mst.edu

Xiaoping Du

Professor
Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
400 West 13th Street, Toomey Hall 290D,
Rolla, MO 65409
e-mail: dux@mst.edu

1Corresponding author.

Manuscript received January 28, 2016; final manuscript received October 18, 2017; published online December 20, 2017. Assoc. Editor: Sankaran Mahadevan.

ASME J. Risk Uncertainty Part B 4(3), 031002 (Dec 20, 2017) (14 pages) Paper No: RISK-16-1020; doi: 10.1115/1.4038318 History: Received January 28, 2016; Revised October 18, 2017

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.

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Figures

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Fig. 1

Upcrossing events of a stochastic process

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Fig. 2

Outcrossing events of a system with bivariate responses

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Fig. 3

Flowchart of time-dependent system reliability analysis

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Fig. 5

v12+−(t) over time interval [0, 20] years

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Fig. 6

v12−+(t) over time interval [0, 20] years

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Fig. 7

v1 ∪ 2+(t) over time interval [0, 20] years

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Fig. 8

pf, 1∪2(t0, ts) over time interval [0, 20] years

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Fig. 9

pf, s(t0, ts) time interval [0, 20] years

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Fig. 10

A function generator mechanism system

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Fig. 11

v12+−(θ) over [45 deg, 105 deg]

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Fig. 12

v12−+(θ) over [45 deg, 105 deg]

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Fig. 13

v1 ∪ 2+(θ) over [45 deg, 105 deg]

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Fig. 14

Time-dependent system probability of failure over [45 deg, 105 deg]

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Fig. 21

Time-dependent system probability of failure over [0,12] months

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Fig. 20

v1 ∪ 2+(θ) over [0, 12] months

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Fig. 19

v12−+(θ) over [0, 12] months

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Fig. 18

v12+−(θ) over [0, 12] months

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Fig. 17

Stress response of the turbine blade

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Fig. 16

Flowchart of the stress analysis for the turbine blade

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Fig. 15

Geometry configuration of the turbine blade: (a) side view, (b) front view, and (c) top view

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