City University of Hong Kong
A multi-state network under consideration consists of a source node, a sink node, and some independent failure prone components in between. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multi-state networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches to generate all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the component state vector not smaller than at least one of the d-MPs. A more efficient method for this union of events probability evaluation is needed.
In this presentation, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Product (SDP) principle, and named it Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is, based on the SDP principle and a specially defined "maximum" operator, that the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L-1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing with Aven's algorithm (1985) which has been recognized as efficient. It is found that RSDP is more efficient than Aven's algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multi-state network reliability given all d-MPs.
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Event: |
MEEM Seminar 0809_006 |
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Date: |
24 July 2008 (Thursday) |
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Time: |
3:30 pm (Tea reception at 3:00 pm) |
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Venue: |
Room B5307 |
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Speaker: |
Professor Ming J Zuo |
Professor Ming J Zuo received the Bachelor of Science degree in Agricultural Engineering in 1982 from Shandong Institute of Technology, China, and the Master of Science degree in 1986 and the Ph.D. degree in 1989 both in Industrial Engineering from Iowa State University, Ames, Iowa, U.S.A. He is currently Professor in the Department of Mechanical Engineering at the University of Alberta, Canada. His research interests include system reliability analysis, maintenance planning and optimization, signal processing, and fault diagnosis. He is Associate Editor of IEEE Transactions on Reliability, Area Editor of the International Journal of Performability Engineering, and Editorial Board Member of IIE Transactions and International Journal of Quality, Reliability and Safety Engineering. He is a senior member of IEEE and IIE. He received the 2006 and the 2008 IIE Golomski Awards and the Best Paper Award at the 2005 IIE Industrial Engineering Research Conference.
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