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In many life tests, the initial censoring of items results in withdrawing a portion of the survivors while some remain on test until failure or until a subsequent stage of censoring. If the censoring is progressive through several stages, the resulting sample consists of censored items intermingled with failed ones. The maximum likelihood estimator (MLE) and a least squares median ranks estimator (LSMRE) apply in this situation. Using Monte Carlo methods, the statistical properties of these estimators for the parameters and percentiles of the 2-parameter Weibull distribution are determined. The results are: 1. The MLE performs well in estimating the parameters and percentiles for complete samples of moderate to large size (25 and 100). For small sample size (10) and/or censored samples it performs relatively well in estimating the scale parameter and the upper percentiles of this distribution. 2. The LSMRE was generally less reliable than the MLE in estimating the scale parameter and the upper percentiles of the distribution. It performed relatively well when estimating the shape parameter and the lower percentiles.