Weibull distribution is widely used in the modeling of mechanical properties such as tensile strength of ceramic and composite materials. The 95% one-sided confidence lower bounds on the 1st and 10th Weibull percentiles, namely A-basis and B-basis material properties, are important in reliability studies for understanding early failures and reducing risks. These lower bounds are generally estimated by small samples due to the high costs of the experiments, hence the precision of estimation remain low. Therefore, in the literature, many exact and approximate interval estimation methods for Weibull percentiles have been proposed for achieving better performance. In this study, a comprehensive comparison of the exact methods with Monte-Carlo simulations has been made. In addition, some methods developed for Weibull parameters are also included in this comparison since they can be used for exact lower bound estimation but have never used for this purpose in the literature. In the study, the lower bounds have been estimated by the maximum likelihood method, the Menon method and 25 different models of weighted/ unweighted least squares methods (such as improved estimators, interchanged axes), and average false coverage probabilities are used for the comparison criterion. According to the simulation results, the maximum likelihood and the weighted least squares method with Faucher & Tyson weight factors have very similar performances for sample sizes less than 8; and the maximum likelihood method has always shown the best performance for sample sizes greater than or equal to 20. However, it is emphasized that linear regression methods are more practical in terms of ease of calculation when performance differences are negligible.