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

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.

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Binary Decision Diagrams and Extensions for System Reliability Analysis

10.1002/9781119178026 ◽

2015 ◽

Cited By ~ 40

Author(s):

Liudong Xing ◽

Suprasad V. Amari

Keyword(s):

Reliability Analysis ◽

System Reliability ◽

Binary Decision Diagrams ◽

Decision Diagrams ◽

Binary Decision ◽

System Reliability Analysis

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Complementary Intersection Method for System Reliability Analysis

Journal of Mechanical Design ◽

10.1115/1.3086794 ◽

2009 ◽

Vol 131 (4) ◽

Cited By ~ 51

Author(s):

Byeng D. Youn ◽

Pingfeng Wang

Keyword(s):

Reliability Analysis ◽

System Reliability ◽

High Efficiency ◽

Second Order ◽

Approximation Formula ◽

Joint Failure ◽

System Reliability Analysis ◽

Reliability Method ◽

Reliability Methods ◽

Intersection Method

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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