Abstract
Motivated by practical applications (e.g. flow transfer systems, electromagnetic accelerating systems and defense systems), in this paper, we consider combined gap constraints in modelling and analysing linear multistate consecutively connected systems (LMCCS). The system has linearly ordered nodes. To provide certain connectivity among these nodes required by the system functionality, some of them host statistically independent multistate connection elements (MCEs). Each MCE is used to provide a connection between its host and a random number of next nodes according to a known probability mass function. The system fails if it contains at least m nodes not connected with any previous node or at least n ≤ m consecutive nodes not connected with any previous node. In other words, the system functions as long as the number of single-node gaps is less than m and the size of any consecutive gap is smaller than n. Such systems with the combined gap constraints are referred to as m/nCCS. An algorithm based on universal generating functions is proposed for the reliability evaluation of m/nCCS and its computational complexity is analysed. Based on the suggested reliability evaluation algorithm, importance analysis is also performed for m/nCCS, which can assist in identifying the most influential elements or weakness of the system design. Illustrative examples are provided.