Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs |
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| Authors: | Yi-Kuei Lin |
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| Affiliation: | 1. Department of Business Administration, Feng Chia University, Taichung 407, Taiwan;3. Department of Industrial Engineering and Management, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan;4. Department of Business Administration, Asia University, Taichung 413, Taiwan;5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan;6. Department of Business Administration, Chaoyang University of Technology, Taichung 413, Taiwan;1. Department of Industrial Engineering and Management, National Quemoy University, Kinmen County 892, Taiwan;2. Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 300, Taiwan;3. Department of Business Administration, Asia University, Taichung 413, Taiwan;4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan;5. Department of Business Administration, Chaoyang University of Technology, Taichung 413, Taiwan;6. Department of Distribution Management, National Chin-Yi University of Technology, Taichung, Taiwan |
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| Abstract: | This paper deals with a stochastic-flow network in which each node and arc has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system reliability that the maximum flow of the network is not less than a demand (d+1). A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for d, and then the system reliability can be calculated in terms of such points. The upper boundary point for d is a maximal vector, which represents the capacity of each component (arc or node), such that the maximum flow of the network is d. A computer example is shown to illustrate the solution procedure. |
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| Keywords: | Node failure Minimal cut Upper boundary point for d Stochastic-flow network System reliability |
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