Advanced Analysis of the Newly Unit-Lindley Model Under Improved Censoring: Applications to Biomedical and Engineering Systems

In modern reliability and survival analysis, modeling bounded-lifetime data under complex sampling mechanisms remains a challenging yet practically significant problem, particularly in biomedical and engineering applications where experimental time and cost constraints are critical. This study develops a comprehensive inferential framework for the unit-Lindley (ULind) distribution under the improved adaptive progressive Type-II censoring (I-AP-CT2) strategy, a flexible design that ensures bounded test duration while accommodating progressive removal of experimental units. The proposed approach integrates both classical and Bayesian paradigms to enable robust estimation of the model parameter, reliability function, and hazard rate function. Maximum likelihood estimators are derived, and their asymptotic properties are established, with interval estimation constructed via normal approximation and log-transformed techniques. To address analytical intractability, a Bayesian framework via MCMC-based is formulated with a gamma prior, yielding credible and highest posterior density intervals. An extensive Monte Carlo simulation study is conducted to evaluate estimator performance under diverse censoring scenarios, demonstrating that Bayesian procedures consistently outperform their frequentist counterparts in terms of accuracy, stability, and interval efficiency. The practical relevance of the proposed methodology is illustrated through two real-world applications involving kidney dialysis survival data and petroleum engineering reliability data, representing critical domains where accurate modeling of failure behavior directly impacts clinical decision-making and industrial risk management. The findings highlight the flexibility of the ULind model in capturing complex hazard rate shapes and confirm the effectiveness of the I-AP-CT2 mechanism as a realistic and efficient experimental design.