Robust Estimation of the Scale Parameter for Rayleigh Distribution under Type-I Hybrid Censoring

Aims: This study aims to develop robust estimation techniques for the scale parameter of the Rayleigh distribution under Type-I hybrid censoring, addressing a gap in the existing reliability and survival literature.

Study Design: A simulation-based study was conducted to compare the performance of maximum likelihood estimators (MLEs) and Bayesian estimators for the scale parameter.

Methodology: We derived likelihood functions and estimators for both MLE and Bayesian approaches. A comprehensive Monte Carlo simulation study was employed to evaluate the performance of these estimators, focusing on root mean squared errors (RMSEs) under various conditions.

Results: The results indicated that RMSEs decreased with increasing sample sizes and higher censoring parameters. Bayesian estimators consistently outperformed MLEs, particularly with well-chosen priors, demonstrating lower RMSEs across all scenarios.

Conclusion: The findings highlight the robustness and superiority of Bayesian methods in accurately estimating parameters under Type-I hybrid censoring, providing valuable insights for enhancing reliability and maintenance strategies in engineering systems. Future research may extend these methodologies to other distributions and real-world applications.