Evaluating the lifetime performance index of Burr III products using generalized order statistics with modeling to radiotherapy data

Abstract

In reliability analysis and quality control, evaluating the lifetime performance index ($C_L$) of products is critical for ensuring quality standards and optimal performance. This study introduces a comprehensive framework for assessing the lifetime performance index $C_L$ of products following a Burr III distribution. The analysis utilizes generalized order statistics (GOS), with a particular emphasis on two key censoring schemes, namely, the progressive Type-II censoring (PTIIC) and progressive first-failure censoring (PFFC). We develop maximum likelihood estimators and Bayesian estimators, under both informative and non-informative priors, leveraging symmetric squared error and asymmetric loss functions. Simulation studies are conducted to examine the bias, root mean squared error, and other performance metrics across various censoring schemes. Additionally, the practical applicability of the proposed methods is demonstrated through real-world radiotherapy data analysis.

The results reveal that incorporating informative priors significantly improves estimation accuracy in the used samples under PTIIC and PFFC schemes. Furthermore, the proposed methodology enhances the precision of lifetime performance index estimation, especially for products with high reliability demands. This work offers practitioners in the fields of reliability engineering and quality control valuable insights through the provision of robust estimation frameworks for censored reliability data. Our findings is added to the literature by proving the efficacy of Burr III modeling with GOS and its advanced censoring schemes, laying the groundwork for future researchers in statistical inference for reliability analysis.