Small-Sample MTBF Reliability Modelling of Wind Turbine Main Bearings Based on Three-Way Expansion Bootstrapping

Wind turbine main bearings are critical components in the drivetrain and are characterised by long service life, low failure rates, and limited failure-interval samples, which increases uncertainty in reliability assessment and maintenance decision-making. To improve the utilisation of limited failure-interval information in small-sample reliability modelling, this study develops a unified three-way expansion Bootstrap strategy combined with a three-parameter Weibull distribution. The principal methodological contribution lies in integrating intra-interval supplementary sampling, left-boundary expansion, and right-boundary expansion within the same sample-generation framework, thereby enabling the main distributional information and boundary information contained in the available failure-interval samples to be utilised jointly. Based on 36 equivalent failure-interval samples obtained from Romax fatigue-life simulations under different operating conditions, the proposed method is compared with traditional Bootstrap and two-way expansion Bootstrap methods. The results of the two-sample K-S test indicated that no statistically significant distributional difference was detected between the expanded samples and the original sample. Using the three-parameter Weibull fitting results obtained from the original 36-sample dataset as the reference, the proposed three-way expansion method yields the smallest relative deviation of the scale parameter η among the three expansion strategies, at 2.69%. The MTBF relative deviations of the traditional Bootstrap, two-way expansion Bootstrap, and three-way expansion Bootstrap methods were 4.81%, 7.36%, and 7.76%, respectively. Repeated simulation results further show that the three-way expansion method provides substantially lower MTBF variability than the traditional Bootstrap method, although the two-way expansion method yielded the smallest MTBF standard deviation. The results demonstrate the methodological potential of the proposed strategy for small-sample MTBF modelling of wind turbine main bearings under the investigated simulation conditions.