The Hierarchical Weighted Multi-State $k$ -out-of- $n$ System Model and Its Application for Infrastru

A multi-state system (MSS) model is a more flexible tool for representing engineering systems than the conventional binary system model, which has been widely studied in recent research. The multi-state weighted k-out-of-n system model is the generalization of the multi-state k-out-of-n system model, where the component i in state j carries a certain utility. In this paper, we propose a multi-state system structure called hierarchical weighted multi-state k-out-of-n systems. In such a system, the structure of the system can be decomposed into different hierarchical levels, and a subsystem at each level can be represented using a multi-state weighted k-out-of-n structure. The proposed system structure can find applications in many real life systems, and a municipal infrastructure is a typical example of such a structure. The definition of the hierarchical multi-state weighted k-out-of-n system model is proposed in this paper. Universal generating functions (UGF) are used to evaluate reliabilities of the defined systems. Moreover, to reduce computational complexity, recursive algorithms are developed to obtain lower, and upper bounds of the defined system reliabilities.