While web-based surveys are a convenient research tool, the ease of dropping out in the online setting has become a growing issue in ensuring data quality. One theory is that dropout, or attrition, occurs in phases that can be generalized to phases of high dropout and phases of stable use. In order to detect these phases, survey dropout is considered as a time-to-event outcome and tests within change-point hazard models are introduced. Here, we apply the multiple change-point exponential model and extend the single change-point Weibull model to account for multiple change-points. We also introduce a likelihood ratio test to aid in determining the number of distinct phases, using Monte Carlo simulations of the null hypothesis of no attrition phases or change-points against the alternative hypothesis that distinct attrition phases exist (at least one change-point). The performances of these change-point hazard models are compared using both a simulation study and also with application to survey data on patient cancer screening preferences, as well as compared to previous work with discrete models.