Repairable consecutive-k-out-of-n: G systems with r repairmen

In this paper, we study repairable consecutive-k-out-of-n: G systems with r repairmen. The systems are either circular or linear. It is assumed that the working time, and the repair time of each component in the system are both exponentially distributed; and every component after repair is 'as good as new'. Each component is classified as either a key component, or an ordinary one according to its priority role to the system's repair. By using the definition of generalized transition probability, the state transition probabilities of the system are derived. Some important indices related to repairmen are obtained, and some reliability indices are derived by using the Laplace transform technique. Numerical examples are then studied in detail to demonstrate the theoretical results developed in the paper. The proposed method, and its numerical illustrations for the examples verify the validity & generality of the studied system.