Reliability Analysis of Gnedenko System with Multiple Working Vacations

Abstract This study introduces a new Gnedenko repairable system consisting of N working units and 1 warm standby unit, with the repairman taking multiple working vacations (MWVs). Assume that the failure time of the unit and the vacation time of the repairer follow an exponential distribution, and that the repair time of the equipment satisfies the random distribution. Application of the supplementary variable method (SVM) and Markov process theory, the system is modelled, and the Laplace transform (LT) method and Tauber theorem are used to obtain the LT of transient reliability indices such as transient availability, transient failure frequency, and reliability, as well as the expressions for steady-state (SS) indices such as SS availability, SS failure frequency, and mean time to first failure (MTTFF).