Randomly distributed wireless sensors used to monitor and detect a moving object were investigated, and performance measures such as the expected time/space detection ratio were theoretically analyzed. In particular, the insensitivities (robustness) of the performance measures to the conditions of the distributed wireless sensors and the target object were analyzed. Robust explicit equations for these performance measures were derived, and these equations can be used to calculate them without knowing the sensing area shape or the target object trajectory. These equations were applied to the following two applications. (1) They were used to estimate the impact of active/sleeping state schedule algorithms of sensors on the expected ratio of the time that the sensors detect the target object during its movement. The results were used to identify the active state schedule that increases the expected time ratio. (2) They were also applied to a sensor density design method that uses a test object. This method can be used to ensure that the expected time ratio that at least one sensor can detect the target satisfies the target value without knowing the sensing area size or the movement of the target object.