In this paper, the propose is to use the xtreme value distribution as the rate of occurrence of the non-homogenous Poisson process, in order to improve the rate of occurrence of the non-homogenous process, which has been called the Extreme value Process. To estimate the parameters of this process, it is proposed to use the Maximum Likelihood method, Method of Moment and a smart method represented by the Artificial Bee Colony:(ABC) algorithm to reach an estimator for this process which represents the best data representation. The results of the three methods are compared through a simulation of the model, and it is concluded that the estimator of (ABC) is better than the estimator of the maximum likelihood method and method of moment in estimating the time rate of occurrence of the proposed Extreme value process. The research also includes a realistic application that deals with the operating periods of two successive stops for the raw materials factory from the General Company for Northern Cement / Badush Cement Factories (new) during the period from 1/4/2018 to 31/1/2019, in order to reach the time rate of factory stops.
