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Research Papers

A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis

[+] Author and Article Information
Pingfeng Wang

Mem. ASME, Department of Industrial and Manufacturing Engineering,  Wichita State University, Wichita, KS 67226 e-mail: pingfeng.wang@wichita.edu

Chao Hu

Department of Mechanical Engineering,  University of Maryland at College Park, College Park, MD 20742 e-mail: huchaost@umd.edu

Byeng D. Youn1

Mem. ASME, School of Mechanical and Aerospace Engineering,  Seoul National University, Seoul 151-742, South Korea e-mail: bdyoun@snu.ac.kr

1

Corresponding author.

J. Mech. Des 133(7), 071003 (Jul 08, 2011) (13 pages) doi:10.1115/1.4004198 History: Received February 28, 2011; Revised May 03, 2011; Published July 07, 2011; Online July 08, 2011

This paper presents a Generalized Complementary Intersection Method (GCIM) that can predict system reliability for series, parallel, and mixed systems. The GCIM is an extension of the original study, referred to as the Complementary Intersection Method (CIM). The CIM was developed to assess system reliability for series systems. The contribution of this paper is to generalize the original CIM so that it can be used for system reliability analysis regardless of system structures (series, parallel, and mixed system). First, we derive a closed-form system reliability formula for a parallel system through its transformation into a series system using De Morgan’s law. Second, a unified system reliability analysis framework is proposed for mixed systems by defining a new System Structure matrix (SS-matrix) and employing the Binary Decision Diagram (BDD) technique. The SS-matrix is used to present any system structure in a comprehensive matrix form. Then the BDD technique together with the SS-matrix automates the process to identify system’s mutually exclusive path sets, of which each path set is a series system. As a result, system reliability with any system structure can be decomposed into the probabilities of the mutually exclusive path sets. Five engineering examples are used to demonstrate that the proposed GCIM can assess system reliability regardless of the system structures.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Example to show the conversion of a system block diagram to SS-matrix

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Figure 2

BDD diagram and the mutually exclusive path sets

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Figure 3

GCIM framework for system reliability analysis

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Figure 4

Results of system reliability analysis at eight different reliability levels

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Figure 5

Ten brittle bar parallel system: (a) system structure model; (b) brittle material behavior in a parallel system

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Figure 6

Results of system reliability analysis at ten different reliability levels

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Figure 7

System block diagram and SS-matrix for example 3

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Figure 8

BDD diagram for example 3

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Figure 9

A cantilever beam-bar system

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Figure 10

System block diagram and SS-matrix for the cantilever beam-bar example

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Figure 11

BDD diagram for the cantilever beam-bar example

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Figure 12

A power transformer finite element model (without covering wall)

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Figure 13

Winding support bolt joint: (a) side view, (b) bottom view

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Figure 14

3-out-of-4 system with support joints

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Figure 15

CI-matrix for the power transformer example

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Figure 16

System reliability block diagram for the power transformer example

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Figure 17

BDD diagram for the power transformer example

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Figure 18

Pseudocode for constructing BDD and computing mutually exclusive path set

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Figure 19

BBD and mutually exclusive path set example using the pseudocode

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