Reliability evaluation of linear multi-state consecutively-connected systems constrained by m consecutive and n total gaps

•A new model of multi-state consecutively-connected system (LMCCS-MN) is proposed.•The non-uniform distributed nodes are involved in the proposed LMCCS-MN model.•An algorithm for system reliability evaluation is provided by the UGF method.•The computational complexity of the proposed algorithm is discussed in detail.•Optimal element allocation problem is formulated and solved.

This paper extends the linear multi-state consecutively-connected system (LMCCS) to the case of LMCCS-MN, where MN denotes the dual constraints of m consecutive gaps and n total gaps. All the nodes are distributed along a line and form a sequence. The distances between the adjacent nodes are usually non-uniform. The nodes except the last one can contain statistically independent multi-state connection elements (MCEs). Each MCE can provide a connection between the node at which it is located and the next nodes along the sequence. The LMCCS-MN fails if it meets either of the two constraints. The universal generating function technique is adopted to evaluate the system reliability. The optimal allocations of LMCCS-MN with two different types of failures are solved by genetic algorithm. Finally, two examples are given for the demonstration of the proposed model.