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.