The reliability of systems with stair-type consecutive minimal cuts

This paper considers the component system with stair-type consecutive minimal cuts. The system consists of n components and the set of minimal cuts can be linearly ordered. The proposed system generalizes the typical consecutive-k-out-of-n: F systems. By using integer linear programming, this paper shows that such a system can be converted into the consecutive-k-out-of-n: F systems with the insertion of artificial ‘broken-down’ components. Then the system reliability can be obtained by the product form of component reliability matrices and the limit behavior of system could be easily analyzed.