Cost analysis of N-policy vacation machine repair problem with optional repair

In this paper, we deal with the N-policy machine repairable system with warm spares and two repairmen under optional repair. The first repairman is always available to serve the failed units in the system while the second repairman leaves for a vacation of random length when the number of failed units is less than N. The second repairmen firstly performs essential repair to all failed units and then may provide second optional repair to some failed units which demand for it. We construct the system state governing equations and the system performance measures under transient condition which are examined by using a numerical approach based on Runge-Kutta method of the fourth order. Further, the sensitivity and cost analysis are facilitated to demonstrate the validity of the model by taking a numerical illustration. The effect of different parameters on system performance indices is demonstrated graphically.