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This paper contains results on the development of accurate methods for the mean value estimation for a stochastic process with statistically dependent outcomes. Firstly, the regenerative method is explained, and then. a new method, based on the expression for the sample size as a function of the accuracy of estimation, is developed and explained. In contrast to the regenerative method, which estimates the confidence interval for the defined confidence level and a constant sample size, the proposed method and techniques estimate the mean value with the pre-specified accuracy and with a variable sample size.