Reliability Assessment and Lifetime Performance Index for the Two‐Parameter Chris–Jerry Distribution Under Progressive Type‐II Censoring

The evaluation of lifetime performance is an important issue in industrial quality control and biomedical applications. This study proposes a comprehensive statistical framework for estimating the lifetime performance index () based on the Two‐Parameter Chris–Jerry (TPCJ) distribution under the Progressive Type‐II Censoring (P‐II‐C) scheme. Both classical and Bayesian estimation (BE) methods are considered. Maximum likelihood estimation (MLE) is used to obtain point and interval estimates of the model parameters and the performance index, while BE is implemented using the Markov chain Monte Carlo (MCMC) method. In addition, statistical hypothesis testing procedures are developed to assess whether the lifetime performance index satisfies a predetermined target value. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators under different censoring schemes. The results indicate that the Bayesian approach generally provides more accurate and stable estimates than the classical method. To illustrate the applicability of the proposed methodology, an infant mortality dataset is analyzed. The findings demonstrate that the TPCJ distribution provides a flexible and effective model for lifetime performance assessment compared with several competing distributions.