AbstractWe consider a model withM+Nidentical machines. As many asNof these can be working at any given time and the others act as standby spares. Working machines fail at exponential rate λ, spares fail at exponential rale γ, and failed machines are repaired at exponential rate μ. The control variables are λ. μ, and the number of removable repairman,S, to be operated at any given time. Using the criterion of total expected discounted cost, we show that λ,S, and μ are monotonic functions of the number of failed machinesM,N, the discount factor, and for the finite time horizon model, the amount of time rem