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In this study, a new IE (Inclusion-Exclusion Principle) involving some intuitive properties that characterize the structure of the intersections of d-minimal paths (d-MP)/d-minimal cuts (d-MC), and the relationships between d-MP/d-MC is developed to improve the IE for calculating the exact multi-state network (MSN) reliability. The proposed IE (called the Greedy-B&B-IE) developed first a greedy procedure for reordering d-MP/d-MC to speed up the procedure in detecting & deleting dominated terms. Then, a Branch-and-Bound (B&B)-based technique is proposed to implement the IE to reduce the number of intersections, and decrease the number of multiplications required for calculating the probability value of each term.
Date of Publication: March 2008