A Bayesian–Weibull Model for Limited‐Sample Flexural Strength Estimation of Porcelain Insulators Incorporating Size Effect

ABSTRACT Porcelain insulators in substations are subjected to wind and seismic actions, and flexural strength is therefore a key parameter in their mechanical assessment. However, porcelain insulators cover a wide range of structural sizes and configurations, whereas strength evaluation is often based on limited tests on only a few specimen types. This study develops a Bayesian Weibull model for flexural‐strength estimation of porcelain insulators under limited‐sample conditions while accounting for size effect. Three‐point bending tests were conducted on 20 small‐sized porcelain rod insulators, and bending tests were performed on eight porcelain hollow insulators. The rod‐insulator data were used to characterize the probabilistic distribution of flexural strength, and the hollow‐insulator data were further used to calibrate the size‐effect relation within the proposed framework. Specifically, the baseline Bayesian–Weibull model yielded a mean absolute percentage error (MAPE) of 3.48% for the small rod insulators. Crucially, the upgraded size‐effect model incorporated specimen‐specific propagated measurement uncertainties, utilizing the small rod geometry strictly as a mathematical reference volume. All eight hollow‐insulator observations fell within their corresponding 95% full‐data posterior predictive intervals, while eight‐fold specimen‐level leave‐one‐out cross‐validation (LOOCV) yielded a MAPE of 5.08%. These results provide a preliminary internal assessment of the predictive performance of the proposed model within the tested insulator groups. Within the scope of the present tests, the proposed model provides a probabilistic basis for flexural‐strength estimation of porcelain insulators under data‐limited conditions, while further independent tests are required to assess its applicability to additional geometries and manufacturing groups.