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Information About

Survival Function





DEFINITION


Let ''X'' be a continuous random variable with Cumulative Distribution Function ''F''(''t'') on the interval [0,∞). Its ''survival-'', or ''reliability-function'' is:

:R(t) = P\{T\geq t\} = \int_t^{\infty} f(u)\,du = 1-F(t).


PROPERTIES


Every survival function ''R''(''t'') is Monotone Decreasing , i.e. R(u) < R(t) for u > t

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, lim''t''→∞''R''(''t'') is commonly zero but can be greater to represent a system in which Eternal Life is possible.


SEE ALSO