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Research Papers

Complementary Intersection Method for System Reliability Analysis

[+] Author and Article Information
Byeng D. Youn

 University of Maryland, College Park, MD 20742bdyoun@umd.edu

Pingfeng Wang

 University of Maryland, College Park, MD 20742pfwang@umd.edu

J. Mech. Des 131(4), 041004 (Mar 20, 2009) (15 pages) doi:10.1115/1.3086794 History: Received March 18, 2008; Revised January 07, 2009; Published March 20, 2009

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)–order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability methods for evaluating the probabilities of the second–order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Definition of the CI event E12

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Figure 2

Mean value point d∗ and contours of two limit state functions

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Figure 3

Flowchart of the CIM for system reliability analysis

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Figure 4

Three performances in a series system and ten design points

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Figure 5

Accuracy of system reliability analysis at ten design points

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Figure 6

Absolute errors in system reliability (%) for the mathematical example

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Figure 7

Accuracy of system reliability analysis at eight design points for the VSI example

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Figure 8

Absolute errors in system reliability (%) for the VSI example

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Figure 9

Sea vessel end connections

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Figure 10

Sea vessel model

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Figure 11

Longitudinal end connections

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Figure 12

Definition of system components

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