I want to model probability of an event, which is typically modelled by survival methods. However, the predicted survival function is always non-increasing. My case is however opposite: The probability of survival increases in time, i.e. a subject which already survived some time has higher probability to survive than the subject which is younger. Does it make sense to use survival analysis for this, or are there any other approaches dealing with right censored data ?
The terminology of survival and hazard functions can be confusing.*
What you describe is a decreasing hazard of an event over time. The hazard is the instantaneous risk of an event given that you have already survived up to that time. A survival model can readily deal with a decreasing hazard over time. For example, for some parameter values a Weibull distribution has a continuously decreasing hazard over time.
The survival function itself, for an event that happens only once per individual, represents the total fraction of the initial group still without the event at any particular time after the start. That necessarily is non-increasing with time.
*Earlier today, for example, I temporarily mixed up cumulative hazard with cumulative event probability, until I caught myself. Loose common-language use of such words means that special care and vigilance are needed in their technical use.