Liudong Gu, Guanjun Wang, Yifan Zhou, Fengjun Duan
The reliability of a performance sharing system (PSS) is significantly influenced by its topological structure. Ring-structured PSSs, despite their widespread application in practical systems, have not been studied due to the complexity introduced by the unique interconnected structure. This article investigates the reliability evaluation of a multistate ring-structured PSS, where several production units are connected in sequence, forming a ring. Since the system fails if any demand remains unsupplied, performance sharing mechanism enables the performance of a unit to be shared by adjacent units to enhance system reliability. Two auxiliary variables are introduced to represent the performance and transmission states of each unit. The system is analyzed recursively to determine and update the system state. Based on the analysis procedure, a system reliability evaluation algorithm is developed using the multivariable universal generating function. Two numerical examples are provided to illustrate and validate the proposed methods and models. Several sensitivity analysis experiments are conducted to verify the effectiveness of the performance sharing mechanism in ring-structured PSSs and identify the bottleneck units that affect system reliability.