A Comparison Between The Geometric Stochastic Process and a Related Process with an Application

In this research, we compared the geometric stochastic process with a related process ( -series stochastic process), in order to reach to the best process used to analyze monotone trend data, by using the modified moments and the maximum likelihood methods to estimate the parameters of the geometric stochastic process and -series stochastic process, on the assumption that the probability distribution for the first stop is lognormal. The comparison between these two processes, depending on the criteria proposed in the search. Keyword: geometric process, modified moment, Series Process, maximum likelihood, Cement factory.We also studied the successive inter arrival between failures of the General Company of Northern Cement and test whether the data follow processes or not, as well as estimating the parameters of the processes and compared them.