Reliability evaluation of multi-state (k1,k2,…,km)-out-of-(n1,n2,…,nm) system with common bus performance sharing

Abstract

The reliability of multi-state $(k_1,k_2,\dots ,k_m)$-out-of-$(n_1,n_2,\dots ,n_m)$ system with performance sharing is investigated in this paper. The system consists of $m$ types of components, comprising a total of $n$ components, where each type $i$ contains $n_i$ components. The system work normally only if at least $k_i$ components performance in each type $i$ satisfy the random demands. Two stages of performance transmission are considered in the paper. In the first stage, surplus performance (SP) of components within the same type is transmitted to performance deficiency (PD) components via the common bus without any performance loss. In the second stage, after performance sharing within the same type is complete, the SP between different types can be transmitted to other types with PD through other common bus. At the same time, the loss of performance transmit between different types is considered. The reliability of the $(k_1,k_2,\dots ,k_m)$-out-of-$(n_1,n_2,\dots ,n_m)$ system is assessed using the universal generating function (UGF) approach. Finally, numerical analysis and collaborative computer system as example are conducted to demonstrate the effectiveness of the proposed model and method.