Mathematical Modeling and Performance Analysis of Machine Repairable System with Hot Spares

In the present article, a machine repairable system with hot standby and two repairmen is considered. The partial server vacation policy is applied for both the repairmen. The first repairman never takes vacations and always available to serve the failed units. If the numbers of failed units are less than N, then the second repairman can take leave for period of random length. This repairman returns back if there are N or more failed units/machines accumulated in the system, Otherwise, this repairman goes for further vacations. The time period of vacations is distributed exponentially. With the help of transition diagram, steady-state probabilities equations are developed using Markov process theory. These equations are solved recursively. The derivations of some queuing and reliability measures are also developed. A cost model is developed to determine the optimum value of N while the system availability is maintained at a certain level. Sensitivity analysis of the system is investigated and reliability characteristics of the system are analyzed.