Reliability assessment of two production lines using joint progressively type-II censored XLindley samples

ssessing the reliability of two production lines, whether individually or simultaneously, is of significant importance for improving manufacturing processes and guaranteeing superior product quality. This paper examines the reliability assessment of two production lines utilizing joint progressively Type-II censored samples derived from the XLindley distribution. In addition to estimating the unknown parameters, the reliability functions for each production line, as well as for both production lines simultaneously, are analyzed. Both classical likelihood-based and Bayesian methodologies are employed for estimation purposes. The maximum likelihood method is applied to obtain point estimates for the unknown parameters and reliability functions, while Bayesian analysis is performed under the squared error loss function, employing the Markov Chain Monte Carlo technique to generate samples from the posterior distribution. The approximate confidence intervals, percentile bootstrap confidence intervals, and the highest posterior density credible intervals for the unknown parameters and various reliability functions are discussed. The problem of selecting the optimal censoring plan is also considered. A comprehensive simulation study is conducted to assess the performance of the proposed methods, comparing the accuracy and efficiency of the estimates across different censoring schemes. Furthermore, the applicability of the proposed methodology is demonstrated through the analysis of two real-world data sets, underscoring its practical utility within the field of reliability. Finally, three criteria, namely A-optimality, D-optimality, and F-optimality, are considered to determine the optimal censoring plan.