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We present a mathematical model of the three-unit system consisting of two active units and one reserve. For each unit, the time until the failure, the time until the preventive maintenance, the repair time and the preventive maintenance time are random variables; the first two are exponentially distributed and the last two have arbitrary probability distributions. The obtained system of equations is solved using the Laplace transform. From this it is possible to obtain the expected lifetime of the system. Under the assumption that the repair and the preventive maintenance are quick, we prove a limit theorem for the distribution of the lifetime of the system.