In survival analysis, the survival function plays a central role. This can be defined as the probability that an individual survives beyond time t. While t can range from 0 to infinity (∞), the survival function is restricted to vary between 0 and 1.
Moreover, the probability of survival at t=0 is 1, whereas the probability of survival goes to 0 when t=∞. In theory, the survival function is smooth, but we usually observe events on a discrete time scale (e.g. years, months, days).