Survival function

The survival function, also known as a survivor function or reliability function, is a property of any random variable that maps a set of events, usually associated with mortality or failure of some system, onto time. It captures the probability that the system will survive beyond a specified time.
The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. Another name for the survival function is the complementary cumulative distribution function.
Definition
Let T be a continuous random variable with cumulative distribution function F(t) on the interval [0,∞). Its survival function or reliability function is:
Properties
Every survival function S(t) is monotonically decreasing, i.e. for all .
The time, t = 0, represents some...