A New Exponential-Type Model Under Unified Progressive Hybrid Censoring: Computational Inference and Its Applications

A new odd exponential-type (NOT-Exp) distribution provides a flexible and analytically tractable framework for modeling lifetime data exhibiting non-constant hazard behaviors, including increasing, decreasing, bathtub-shaped, and unimodal forms, which are commonly observed in real-world reliability and survival studies. In this work, a comprehensive inferential methodology is developed for the NOT-Exp model under a unified progressive Type-II hybrid censoring, allowing several traditional censoring designs to be treated as special cases within a single unified structure. The main advantages of the proposed model lie in its ability to capture complex risk dynamics while maintaining mathematical simplicity, making it particularly suitable for censored lifetime data. Classical inference is conducted via maximum likelihood estimation, along with two asymptotic confidence interval constructions based on normal and log-normal approximations for both model parameters and reliability characteristics. In addition, a Bayesian estimation framework is introduced using independent gamma priors and Markov chain Monte Carlo techniques to obtain posterior estimates, credible intervals, and highest posterior density regions. Extensive simulations demonstrate the accuracy, stability, and robustness of the proposed estimators under varying sample sizes, censoring intensities, and prior specifications. Applications to airborne toxicological variation data and bank customer waiting times highlight the practical importance of the methodology, where the NOT-Exp model consistently outperforms twelve competing lifetime distributions according to standard goodness-of-fit criteria. These results confirm that the suggested design gives a strong and versatile tool for analyzing complex censored lifetime data across environmental and service-system applications.