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Joint importance measures in network system

Many real world systems (electric power, transportation, telecommunication, etc) are multistate systems composed of multistate components in which system reliability can be computed in terms reliabilities of its components. Such systems may be regarded as flow networks whose arcs (components) have independent, discrete, and multi-valued random capacities. An arc can, at different conditions, be characterized by different performance levels, causing network system to work with different levels of output performance. The criticality of such arcs must be measured with reference to their performance level and reliability, and its contribution to the overall system output performance measure(OPM). In this paper, we introduce a generalized concept of importance measures and joint importance measures for the flow network made up of multistate arcs with respect to output performance measures (expected performance, reliability and availability). An approach based on the universal generating function (UGF) for the evaluation of the proposed joint importance measures is introduced. An illustrative example is given.