I have a dataset of individuals. Each individual has the same start time at which we begin observing them. There is also an end time for all individuals. Some individuals fail before they reach the end time and some individuals never fail and reach the end time (i.e. they succeed). This is a survival analysis problem in that I am trying to model a time to event (failure). Where my confusion comes in is with the individuals who succeed. I obviously cannot treat these individuals as observed failures, but I also cannot treat them as censored. This is because censorship implies that they were not observed to fail but they will fail at some point in the future (we just don't know when). This is not true in my case because if an individual does not fail up to the end time, it will never fail. So how do I deal with these individuals who never fail? Is this still a survival analysis problem?
Here is an example.
Say a group of athletes all begin training for the next olympic games. Some of them will end up getting injured from training and will not be able to compete. But if an athlete does not get injured until the date of the olympic games, then he/she would be able to compete (i.e. succeed). So these athletes that don't get injured and are able to compete are not censored, because whether they get injured after the olympics is irrelevant. All we care about is whether they get injured up to the date of the olympics