Reliability Modeling for Sparsely Connected Homogeneous Multistate Consecutive-k-Out-of-n: GSystems

Abstract

Compared to binary-state system models, multistate (MS) system models are more practical and useful when describing complex systems in applications, such as communication systems, oil pipeline systems, and grid or cloud computing infrastructures. This paper models a generalized sparsely connected MS consecutive- ${k}$ -out-of- ${n}$ : ${G}$ system. The proposed model is regarded as a natural extension of the consecutive- ${k}$ -out-of- ${n}$ system. Moreover, the proposed system model could cover three special MS submodels, i.e., a decreasing MS: ${G}$ system model, an increasing MS: ${G}$ system model, and a nonmonotonic MS: ${G}$ system model. Three corresponding real-world examples are given to illustrate the applications of the model. Meanwhile, by utilizing the well-known finite Markov chain imbedding method, the explicit system reliability and state distribution for the three kinds of submodels are presented, respectively. Finally, the developed indexes and analysis method are demonstrated by numerical examples.