On Cross-Group Record Sampling: Inference and Future Observations of Weibull Distribution

Abstract It is known that the records are rarely occurred and only a limited number of records being observed from large number of data. To overcome this problem, group-based record sampling involves considering Weibull record data from different groups or categories based on relevant features can be implemented. Both the maximum likelihood and a hierarchical Bayesian approaches are used to estimate the common shape parameter, the main scale parameter based on calibrated through differences across test facilities, and reliability measures such as the reliability function, hazard rate, and median time to failure. A Gibbs sampler with Metropolis–Hastings steps is employed to obtain posterior and predictive distributions, allowing for sample-based parameter estimation and prediction of future records from the observed data. The performance of the proposed approach is assessed through numerical simulations and real data analyses. The results show that cross-group record sampling yields more accurate and reliable inference than traditional single-group record analysis, with the Bayesian approach offering strong and often superior performance compared to the frequentist method.