Tile-based virtual reality (VR) video consists of high-resolution tiles that are displayed in accordance with the users' viewing directions and a low-resolution tile that is the entire VR video and displayed when users change their viewing directions. Whether users perceive quality degradation when watching tile-based VR video depends on high-resolution tile size, the quality of high- and low-resolution tiles, and network condition. The display time of low-resolution tile (hereafter delay) affects users' perceived quality because longer delay makes users watch the low-resolution tiles longer. Since these degradations of low-resolution tiles markedly affect users' perceived quality, these points have to be considered in the quality-estimation model. Therefore, we propose a bitstream-quality-estimation model for tile-based VR video streaming services and investigate the effect of bitstream parameters and delay on tile-based VR video quality. Subjective experiments on several videos of different qualities and a comparison between other video quality-estimation models were conducted. In this paper, we prove that the proposed model can improve the quality-estimation accuracy by using the high- and low-resolution tiles' quantization parameters, resolution, framerate, and delay. Subjective experimental results show that the proposed model can estimate the quality of tile-based VR video more accurately than other video quality-estimation models.