Repairable consecutive-k-out-of-n:F system with fuzzy states

In this paper, we study a repairable consecutive-k-out-of-n:F system with fuzzy states. The maintenance of the system is carried out by r repairmen or repair facilities. The system is 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 same 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. When the system displays a gradual degradation of its performance, its reliability is then analyzed in terms of fuzzy failure and success states. The difference between fuzzy reliability theory and the conventional reliability theory is highlighted.