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.

In this paper, we consider four different kinds of multistate consecutive-k systems, namely a multistate linear m-consecutive-k-out-of-n: G system, a multistate linear consecutive-k-out-of-n: G system with sparse d, a multistate linear m-consecutive-k-out-of-n: G system with sparse d, and a multistate linear <; n, f, k >: G system. The reliability formulas for these systems are derived by using the finite Markov chain imbedding approach. Unlike some previous research, the vectors m, k, d, and f do not need to be monotonic in this paper. Some illustrative examples are also presented to show how the reliabilities of the four multistate consecutive-k systems are calculated.