The Weibull distribution is one of the most widely used distributions in reliability analysis. The ability to accurately estimate the parameters of Weibull distributed data can be very useful, and particularly important when dealing with small data sets and high degrees of censoring. This project aims to compare the performance of the maximum likelihood (ML) method and a generalised least squares (GLS) method in estimating the parameters of small, censored Weibull distributed data. The study involves a simulation of type II censored Weibull data to estimate the log-Weibull parameters and predict the quantiles of the next failure. Simulations were performed across a broad range of sample sizes and number of observed failures. We evaluated the efficiency and accuracy of both estimation methods. The simulation results demonstrated that the unbiased versions of the ML estimators consistently outperform the GLS estimators in terms of efficiency. The root mean squared error (RMSE) of the ML estimator were lower, indicating a higher accuracy in parameter estimation.