We propose a fast and reliable 3D object detection method that can be applied for complicated scenes consisting of randomly stacked objects. The proposed method uses '3D vector pair' that has a common start point and different end points and it has surface normal distribution as the feature descriptor. By considering the observability of vector pairs, the proposed method has been achieved high recognition performance. Observability factor of the vector pair is calculated by simulating the visible state of the vector pair from various viewpoints. By integrating the observability factor and the distinctiveness factor proposed in our previous work, vector pairs that have effectiveness for matching are extracted and these are used for object pose estimation. Experiments have confirmed that the proposed method increases the recognition success rate from 45.8% to 93.1%, in comparison with the state-of-the-arts method. The processing time of the proposed method is fast enough for the robotic bin-picking.