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In order to help avoid or mitigate rear-end collisions a Pre-Collision System (PCS) was developed. The purpose of this study is to clarify the Time-to-Collision (TTC) distribution when approaching a lead vehicle under normal driving condition. To enhance the effectiveness of PCS, warnings and/or automatic brake activation should happen as early as possible, however, if too early there is a high possibility of false warnings or activations, which is not desirable. If the distribution of distance to a lead vehicle under normal driving conditions is quantified, an approach limit can be estimated. In this study, we try to clarify a TTC distribution that is approximated by a log-normal distribution. Then, we investigate the Enhanced Time-to-Collision (ETTC) that is the secondary predictive value of TTC. And, we clarify the log-normal distribution of ETTC is a more stable approximator of normal driving than a log-normal distribution of TTC.