In this project, estimation of Reliability 0 =P(X >Y) in case of Weibull distribution will be considered. The Maximum Likelihood Estimators (MLES) and Weighted Likelihood Estimators (WLES) under Simple Random Sampling (SRS) and Ranked Set Sampling (RSS) as well as the method of moments and Method of linear regression Estimators of this parameter will be considered under SRS. The above estimators will be compared via their bias and mean square error (MSE). Also, the asymptotic distribution of the MLES and the WLEs of a will be derived and then used to construct asymptotic confidence intervals (Cls) of the parameter. Then these Cls will be compared via their expected lengths and their coverage