This study introduces and investigates the truncated unit exponentiated Ailamujia (TUEA) distribution within the framework of a progressive Type–Ⅱ censoring scheme. By incorporating truncation on the unit interval, the proposed model extends the unit exponentiated Ailamujia distribution, significantly enhancing its flexibility for modeling bounded lifetime data. We derive the fundamental mathematical properties of the TUEA model, including the probability density function, the cumulative distribution function, reliability measures, and hazard rate functions. Statistical inference for the model parameters is developed within both frequentist and Bayesian frameworks using progressive Type–Ⅱ censored data. The maximum likelihood estimates are computed through the Newton–Raphson iterative algorithm, whereas Bayesian inference is carried out under symmetric squared error and asymmetric LINEX loss functions. Point estimates and highest posterior density credible intervals are obtained via Markov chain Monte Carlo (MCMC) sampling procedures. In addition, a comprehensive Monte Carlo simulation study is conducted to investigate the finite sample performance of the new estimators in terms of bias, mean square error, and confidence interval coverage probability. In addition, the practical usefulness of the TUEA distribution is shown via an analysis of a real-life data sets, where the new model exhibits a better fit than competing models.

This study introduces a novel and flexible distribution called the truncated exponentiated Ailamujia (TEA) distribution, designed for modeling bounded lifetime data, particularly in engineering applications. The TEA distribution enhances the flexibility of the classic Ailamujia model by incorporating two shape parameters, allowing it to capture a wide range of hazard rate behaviors, including increasing, decreasing, and bathtub shapes. We investigated the mathematical properties of the TEA distribution, including its probability density function, moments, entropy measures, and order statistics. To estimate the model parameters, several classical and modern techniques are developed and compared, including maximum likelihood estimation (MLE), least squares estimation (LSE), weighted LSE, Cramér-von Mises estimation, maximum product spacing estimation, Anderson-Darling and right-tail Anderson-Darling estimation, Percentile estimation, and Bayesian estimation via the Markov chain Monte Carlo (MCMC) method. The effectiveness and flexibility of the proposed model were validated through extensive Monte Carlo simulations and real-life engineering datasets. The results demonstrate that the TEA distribution consistently provides a better fit compared to several well-known competing models. These findings highlight the practical value of the TEA model for engineers and statisticians working with bounded data of reliability type.