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This book considers the estimation problem for the unknown parameters of the exponentiated Weibull family in the progressively Type I interval censored and progressive Type II censored with fixed and random removals, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the unknown parameters and the asymptotic variance covariance matrix of estimates are obtained. Results for exponential and Weibull failure distributions by presented in the literatures can be obtained as a special cases. The time required to complete the test under these types is studied. An illustrative example is presented using "MATHCAD" package.