Survivor function
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The 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 survivor function is used in a broader range of applications, including human mortality.
Definition
Definition. Let X be a continuous random variable with cumulative distribution function F(t) on the interval [0,∞). Its survivor-, or reliability-function is:
<math>R(t) = P\{T\geq t\} = \int_t^{\infty} f(u)du = 1-F(t).<math>
Properties
Every survivor function R(t) is monotone decreasing, i.e. <math>R(u) < R(t)<math> for <math>u > t<math>
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.
Again, limt→∞R(t) is commonly zero but can be greater to represent a system in which eternal life is possible.
Related concepts
See also: