Complementary Intersection Method (CIM) for system reliability analysis

Document Type

Conference Proceeding

Publication Date

4-16-2007

Department

Department of Mechanical Engineering-Engineering Mechanics

Abstract

Researchers desire to evaluate system reliability uniquely and efficiently. Despite its strong technical demand, little progress has been made on system reliability analysis in the last two decades. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the second order bound method gives fairly accurate prediction for system reliability assuming that the probabilities of second-order joint events are accurately obtained. Two primary challenges in system reliability analysis are evaluation of the probabilities of second-order joint events and no unique system reliability for design optimization. Firstly, the greatest technical demand is found in an accurate and efficient method to numerically evaluate the probability of a second-order joint event. Secondly, the system reliability must be uniquely defined for system Reliability-Based Design Optimization (RBDO), so that its sensitivity can be derived from the uniquely defined system reliability. This paper proposes the Complementary Interaction Method (CIM) to evaluate the probability of any second-order joint event numerically and to uniquely define the corresponding system reliability. First, the CIM defines a probability event over a complementary intersection, Eij= {X|G i* Gj≤ 0} where Gi≤ 0 and G j≤ 0 are two component's failure modes. Based on its definition, the CI-matrix is defined, which contains all information for system reliability evaluations. Second, an accurate and unique formula for system reliability assessment is proposed. In this article, three different reliability methods will be used to evaluate the defined CI-matrix numerically: First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM), and the eigenvector Dimension Reduction (eDR) method. Two examples will be used to demonstrate that the CIM with the eDR method outperforms other methods on both efficiency and accuracy for system reliability analysis.

Publisher's Statement

Copyright © 2007 SAE International. Publisher’s version of record: https://doi.org/10.4271/2007-01-0558

Publication Title

SAE Technical Papers

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