Reliability of phase mission linear consecutively-connected systems with constrained number of gaps

Linear Consecutively-Connected System (LCCS) consists of a set of linearly ordered nodes. Some nodes contain statistically independently Connection Element (CEs) except the last one. Each CE can provide a connection between the node it belongs and the next nodes along the nodes sequence. In many situations such as flow transmission and communication networks, a system has to perform a different transmission task during multiple phases of mission. In each phase, the transmission system can be modeled as a LCCS. The phase mission linear consecutively-connected system is denoted PH-LCCS. In traditional PH-LCCS models, the disconnection of any node in a phase mission causes the failure of the phase mission. While the bypass transportation systems are developed, each phase mission in the PH-LCCS system allow a limited number of disconnected nodes referred as gaps. The paper generalizes the traditional PH-LCCS model with a limited number of gaps in each phase mission. In the generalized PH-LCCS model, a phase mission fails if the number of gaps in the phase mission is equal or greater than a specific limitation. The failure of any phase mission causes the failure of the entire system. The generalized PH-LCCS model is evaluated by a recursive algorithm. The proposed algorithm takes into account the number of gaps, phase mission and the path configuration. The proposed model is illustrated by an example.