N -policy for a machine repair system with spares and reneging

Abstract This paper deals with the reliability characteristics of a machine repairable system with M -operating and S warm standby units. The units are assumed to fail in Poisson fashion. There is a provision of a removable repairman which repairs failed units according to exponential distribution. Due to impatience, the failed units may renege when repairman is busy. When N or more units are failed, the removable repairman turns on and starts the repair work. The repairman turns off when the system is empty. We use Laplace transforms technique to derive the explicit expressions of the reliability function and the mean time to system failure. Numerical results to highlight the effects of various system parameters to the reliability indices on the system have been provided.