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The idea of writing a monograph on the WEIBULL distribution first came to me in the late 1960s when-at the Technical University of Berlin (West). This study focus to Finding the unknown parameters estimators for Weibull distribution by using the classical method (Maximum Likelihood Estimator), the Bayesian method (Bayesian Shrinkage Estimator), and the robust method (M- and Median/MAD Estimator). Because this data do not have a problem, the researcher has generalized this case by studying the simulation to include the natural data and the data that contain the outliers (contaminated data). After comparing the numerical results by using the mean squares error measure to find out the more efficient statistical methods in the estimation, the results of the study have shown that the robust method is the best statistical method to address the extremism in the data where it is used in the contaminated and natural data thesis on strategies of maintenance and replacement. And I had givenanalytical work to to students and to practitioners.