In the mathematical theory of probability, a generalized renewal process (GRP) or G-renewal process is a stochastic point process used to model failure/repair behavior of repairable systems in reliability engineering. Poisson point process is a particular case of GRP.

The G-renewal process is introduced by Kijima and Sumita through the notion of the virtual age.

Kaminskiy and Krivtsov extended the Kijima models by allowing q > 1, so that the repair damages (ages) the system to a higher degree than it was just before the respective failure.

Mathematically, the G-renewal process is quantified through the solution of the G-renewal equation:

A closed-form solution to the G-renewal equation is not possible. Also, numerical approximations are difficult to obtain due to the recurrent infinite series. A Monte Carlo based approach to solving the G-renewal Equation was developed by Kaminiskiy and Krivtsov.

The G–renewal process gained its practical popularity in reliability engineering only after methods for estimating its parameters had become available.

The nonlinear LSQ estimation of the G–renewal process was first offered by Kaminskiy & Krivtsov. A random inter-arrival time from a parameterized G-Renewal process is given by:

The Monte Carlo solution was subsequently improved and implemented as a web resource.