An Improved Sample-Aggregation Method for Weibull Estimation of Bushing Maximum Friction Torque Under Small-Sample Conditions

This study addresses the instability of statistical modeling for small-sample maximum friction torque data under multiple temperature conditions. Within the Weibull distribution framework, a sample-aggregation method is proposed, and a unified modeling scheme separating central tendency from dispersion structure is established. This approach enables equivalent aggregation of data across different temperature levels while preserving structural consistency, thereby improving parameter estimation stability and statistical efficiency. To overcome the tendency of single-criterion optimization to fall into local optima under small-sample conditions, a secondary identification criterion combining residual minimization with a Levene-based statistical consistency test is introduced, and a dual-level search strategy is used to obtain a more robust global optimal solution. The parameter estimation results indicate that direct estimation based on small samples produces unstable parameters, with the coefficient of variation of the shape parameter reaching approximately 7.4%. In contrast, the sample-aggregation method shows that the scale parameter increases with temperature, while the location parameter first decreases and then increases due to the combined influence of central tendency and dispersion. The parameters obtained by the aggregation method exhibit more stable and regular variation trends with temperature. The results demonstrate that the proposed method significantly improves parameter stability and statistical efficiency for small-sample maximum friction torque data and provides a practical statistical modeling approach for multi-condition small-sample engineering data.