Transient Analysis of ak-out-of-n:GSystem withN-Policy, Repairmen’s Multiple Vacations, and Redundant Dependency

Abstract

This paper analyzes ak-out-of-n:Grepairable system withN-policy, repairmen’s multiple synchronous vacations, and redundant dependency. When there is no failed component in the system, the repairmen leave for a vacation, the duration of which follows a phase type distribution. Upon returning from vacation, they should take another vacation if there are less thanNfailed components waiting in the system. This pattern continues until at leastNfailed components are waiting. Moreover, the redundant dependency which is a special kind of failure dependency is taken into account in the multicomponent system. Under such assumptions, the availability, the rate of occurrence of failures, and the reliability of the system are derived in transient regime by applying the quasi-birth-and-death process. Furthermore, the Runge-Kutta method is carried out to numerically discuss the time-dependent behavior of the system reliability measures. Finally, a special case of the system is presented to show the validity of our model.