A Small‐Sample Reliability Estimation Method Based on Bootstrap Resampling With B‐Spline Empirical Distribution and K‐Medoids Clustering

ABSTRACT Reliability analysis with small samples is constrained by limited data representativeness and sensitivity to boundary effects and extreme observations. Traditional Bootstrap methods introduce discontinuities in empirical distribution construction and tend to incorporate extreme values during resampling, leading to biased distribution representation and unstable parameter estimation. To address these issues, an improved Bootstrap framework is developed by integrating B‐spline‐based empirical distribution construction with K‐medoids clustering. B‐spline functions are employed to generate smooth and continuous empirical distributions that improve boundary behavior, while K‐medoids clustering is introduced to preprocess resampled data and reduce the influence of outliers. Simulation studies are conducted based on small‐sample Weibull‐distributed failure data, where performance is evaluated through comparisons with the conventional Bootstrap method and the maximum likelihood estimation approach. The effects of resampling size and cluster number on estimation stability are further systematically examined. Results demonstrate that the proposed method enhances both stability and accuracy of parameter estimation under small‐sample conditions, providing a feasible solution for reliability analysis with limited data.