This paperdeals with the newly developed distribution which called Transmuted Arcsine Distribution (TAS) for Salma and Arwa (2018). Classical estimation methods such as Maximum Likelihood (ML), Least Squares (LS) and the Moments Method (MOM) are used to estimate the unknown parameter and the reliability function. Moreover, the comparing between the classical methods are presented in terms of estimated quality using MSE of the estimator and MSE of the reliability function. Finally, three real data sets are analyzed to illustratesthe proposed methods.