Reliability analysis for a k-out-of-n:G system with redundant dependency and repairmen having multiple vacations

This paper studies a k-out-of-n:G repairable system with n identical machines and R repairmen. In this multi-machine system, both the redundant dependency and the multiple vacations policy for repairmen are taken into account. All vacations of the R repairmen are independent and identically distributed, and they are also independent with the other processes. By using the discrete transforms method and the Runge-Kutta method, the machine repair problem is analyzed theoretically and numerically. The influences of the redundant dependency and the repair capacity on the reliability of the system are obtained. Moreover, through some special cases, the insight on the effect of repair capacity and redundant dependency class on the reliability of the system is provided.