Complementary Intersection Method (CIM) for System Reliability Analysis

Abstract

Researchers desire to evaluate system reliability uniquely and efficiently. Despite years of research, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the probabilities of the second or higher-order joint safety (or failure) events are assumed to be known exactly although there is no numerical method to evaluate them effectively. Two primary challenges in system reliability analysis are how to evaluate the probabilities of the secondor higher-order joint safety events and how to uniquely obtain the system reliability so that the system reliability can be used for Reliability-Based Design Optimization (RBDO). This paper proposes the Complementary Interaction Method (CIM) to define system reliability in terms of the probabilities of the component events, Ei = {X |Gi ≤ 0}, and the complementary interaction events, Eij = {X |Gi⋅Gj ≤ 0}. For large-scale systems, the probabilities of the component and complementary interaction events can be conveniently written in the CI-matrix. In this paper, three different reliability methods will be used to construct the CI-matrix numerically: First-Order Reliability Method (FORM), SecondOrder Reliability Method (SORM), and the Eigenvector Dimension Reduction (EDR) method. Two 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.