This paper addresses the reliability analysis problem for a k-out-of-(n+1): G multi-state system (MSS) with performance sharing mechanism. This MSS consists of two categories of units connected into a star topology configuration. The first category of unit is a main unit of the system which occupies the central location of the star configuration, and the second category of units are reserve units distributed at the terminal locations. All reserve units are connected to the main unit in a point-to-point manner through the intermediate transmitters with limited performance transmission capacities. Both the performance and the demand of each unit are random variables. The surplus performance of any reserve unit can be transmitted to the main unit through the transmitter between them, and then the excess performance of the main unit can be further transmitted to other reserve units which are experiencing performance deficiency. The system is reliable if and only if the demands of the main unit and at least k-1 reserve units are satisfied after performance redistribution. An algorithm based on the universal generating function (UGF) technique is developed to calculate the reliability of the proposed MSS with performance sharing. An analytical and a numerical example are presented to illustrate the advantages and applications of the proposed method.
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