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

There are many linear consecutive connected systems with multi-phase missions, such as the modem water diversion system. In each phase, they can be treated as a linear consecutively-connected system (LCCS), and the whole system with multi-phase missions can be modelled as the phase mission linear consecutive connected system (PM-LCCS). With the development of bypass transportation system, every phase allows a limited number of consecutive disconnections betw een nodes which can also be referred as gaps. We generalized the traditional PM-LCCS model with the M consecutive gaps in each phase mission. In the proposed model, if the number of consecutive gaps in a phase mission exceeds the limitation M, the phase mission will fail; and the failure of any phase can cause the failure of the whole system A recursive algorithm is adopted to analyze the system reliability. At last, the proposed model is implemented by an illustrative example.