Learning with groups of sequential data
The data that you are showing is typical survival data. If you want to model the event depending on time and value you should look into survival models with time dependent covariates. If you want to do this without any assumptions on the distribution you can start with a Kaplan Meier estimate as explained here. If you want to use parametric models you can look at Weibull or Gamma regression. 

If you are new to this topic I can highly recommend to browse the examples of the packages in the CRAN Survival Task View.