Dwell time on Web pages has been extensively used for various information retrieval tasks. However, some basic yet important questions have not been sufficiently addressed, eg, what distribution is appropriate to model the distribution of dwell times on a Web page, and furthermore, what the distribution tells us about the underlying browsing behaviors. In this paper, we draw an analogy between abandoning a page during Web browsing and a system failure in reliability analysis, and propose to model the dwell time using the Weibull distribution. Using this distribution provides better goodness-of-fit to real world data, and it uncovers some interesting patterns of user browsing behaviors not previously reported. For example, our analysis reveals that Web browsing in general exhibits a significant "negative aging" phenomenon, which means that some initial screening has to be passed before a page is examined in detail, giving rise to the browsing behavior that we call "screen-and-glean." In addition, we demonstrate that dwell time distributions can be reasonably predicted purely based on low-level page features, which broadens the possible applications of this study to situations where log data may be unavailable.