Inference on A/B‐Basis Allowable Values of Weibull Distribution in Small Samples

ABSTRACT

The Weibull distribution is widely used to characterize the fracture strength of brittle materials, including ceramics, metallic alloys, and composite systems. However, determining reliable confidence intervals for Weibull parameters and percentile values under small‐sample conditions remains challenging due to the high cost and limited availability of experimental data. In engineering practice, the 95% one‐sided lower confidence bounds for the first and 10th percentiles of the Weibull distribution, commonly referred to as the A‐basis and B‐basis values, are essential for material qualification and structural design. To address this issue, several approaches are investigated in this study, including the pivot quantity method, the Bootstrap method, a nonparametric estimation approach based on minimum discrepancy estimation, the Fisher information matrix method, the traditional linear regression method, and the weighted linear regression method. Their statistical performance is systematically evaluated through Monte Carlo simulations. The results indicate that the Fisher information matrix method consistently provides the highest estimation accuracy across most parameter combinations, while the nonparametric approach exhibits competitive performance and robust behavior. Finally, the applicability of the proposed methods is demonstrated using an experimental dataset of ceramic strength, confirming their effectiveness in estimating reliable lower confidence limits under small‐sample conditions.