Performance analysis for F-policy machine repair problem with unreliable server balking, working breakdown and retention

In this paper we study the controlled arrival of machine repair problem with balking, working breakdowns, reneging, and retention of failed machines. Failure times and service times of operating machines are assumed to follow the exponential distribution. When the service station works in normal mode, it is subject to breakdowns while a breakdown occurs, the service station requires repair by the repairing facility. The service station's breakdown and repair times are also presumptively exponentially distributed. Additionally, it is assumed that during a breakdown period of the service station, the service station may allow to provide service to the failed machines with slower service rate. The Runge-Kutta method (4, 5) has been employed to obtain the transient behaviour of the machine repair model. Several system governing performance measures are calculated. A cost function is constructed and also the sensitivity analysis is performed to explore the effect of different parameters.