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Optimal preventive maintenance policy for a system of machines subject to random breakdowns and repairs is derived using optimal control theory. The optimal policy is shown to be `bang-bang'. The model accounts for the waiting line at the repair facility and establishes a link between machine maintenance and classical repairman problem involving machine interference. An example illustrates the procedure to obtain the optimal preventive maintenance policy. An important feature of this work is that the usual assumption of the steady-state behaviour of the queue is relaxed (by directly considering the Kolmogorov differential equations as state equations of the system) and its transient behaviour is explicitly taken into account.