This paper derives the limiting availability of the standby unit by considering three types of failures. Assuming the standby unit can fail during the standby period (type Ⅰ failure), the periodic test is employed to check the unit condition. Although the periodic test is capable of detecting failures during the standby period, it can cause test-induced failures for the standby unit at the start of the test (type Ⅱ failure). Also the aging process of the standby unit during the test period needs to be taken into account (type Ⅲ failure), which is not treated in the existing studies. To identify relationships between the optimal periodic test interval an various failure characteristics of the standby unit. several experiment are performed assuming Weibull distribution as an operating time distribution of the standby unit. The result of this paper can be applied to determine an appropriate test interval for the standby unit in priority redundant system to enure higher reliability characteristics.