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This paper deals with a one-unit system that the system's failure can be detected only by inspection. This inspection takes a non-negligible random time. Consequently the system is down during the inspection whether it is operable or not. When the system's failure is detected by i-th inspection (i = 1,2, ... , n+l), the system is repaired. When the system is operable at the time of the (n+ 1)-st inspection, preventive maintenance is performed. It is assumed that a system is as good as new after repair or preventive maintenance is performed and i~ put in operation immediately. Under this inspection policy, the Laplace transform of the point-wise availability and the stationary avail­ ability of the system are derived by using the method of supplementary variables. We discuss the optimum inspection policy maximizing the stationary availability. It is to determine an optimal number of times of inspection and optimal inspection peIiods. It is shown that there exists an optimum inspection policy under some conditions on the failure distribution and the mean maintenance time.