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.

Let T be a continuous random variable with cumulative distribution function F(t) on the interval [0,∞). Its survival function or reliability function is:

Every survival function R(t) is monotonically decreasing, i.e. Failed to parse (Missing texvc executable; please see math/README to configure.): R(u) \le R(t)

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The time, t = 0, represents some origin, typically the beginning of a study or the start of operation of some system. R(0) is commonly unity but can be less to represent the probability that the system fails immediately upon operation.