This research aims to estimate the reliability function of the Rayleigh distribution Under Type-II-Censored Data, which represents. The time of the machine's operation until the failure, and three methods were chosen to estimate the reliability function, which are, the maximum likelihood method, the momentary method, and the least squares method. As the values of the reliability function were calculated for real data related to the machines of theof the machines of Baghdad Pepsi Cola Company, and the comparison was made between the methods of estimating reliability by choosing the largest arithmetic mean for the reliability of the machines, and the greatest possibility appeared the best method, and the researcher concluded that the average times working until holidays is (4) months with a reliability of 87%.