In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988. It is defined as

The geometric process. Given a sequence of non-negative random variables :${\displaystyle \{X_{k},k=1,2,\dots \}}$, if they are independent and the cdf of ${\displaystyle X_{k}}$ is given by ${\displaystyle F(a^{k-1}x)}$ for ${\displaystyle k=1,2,\dots }$, where ${\displaystyle a}$ is a positive constant, then ${\displaystyle \{X_{k},k=1,2,\ldots \}}$ is called a geometric process (GP).

The GP has been widely applied in reliability engineering

Below are some of its extensions.