Several components comprising a system are to be maintained, while service resources are limited. An optimal inspection and repair policy yields minimal losses. Charges are for checking, repair, and lost time elapsed from component's failure to its detection. This paper examines a model of N identical components, possessing exponential failure distributions, operating simultaneously; only one component can be served (checked or repaired) at a time. The solution is based on Howard's method for solving sequential decision processes. Numerical computations indicate that losses by the best feasible policy that disregards the future (i.e., disregards other components of the system) are almost as low as long-run minimal ones.