Reliability analysis is critical in various scientific fields, necessitating robust lifetime models that effectively capture real-world failure mechanisms. This work explores a novel extension of the classical ToppLeone (TL) lifespan model, called the generalized-TL (GTL) distribution, when datasets are gathered from adaptive progressive Type-II censoring. This model is highly superior for analyzing complex lifetime data with diverse hazard rate structures, including decreasing, increasing, and bathtub-shaped patterns. Employing both likelihood and Bayes estimation approaches, this work attempts to infer the unknown parameters and the reliability and failure rate functions of the GTL model. The Bayesian inference is created using the squared-error loss and independent gamma assumptions. Asymptotic and credible intervals are also established for each unknown quantity. Since the posterior density is complicated, the Markov chain using the Monte Carlo approach is utilized to get information from the whole marginal posterior densities and thus assess the acquired Bayesian point and interval estimations. Using four optimality criteria, the optimum censoring is given among competing progressive techniques. The effectiveness of the offered estimations is tested against numerous parameters using comprehensive Monte Carlo comparisons. Lastly, the practical utility of the GTL model is demonstrated through two applications using different real-world datasets collected from veterinary medicine and engineering reliability studies. Our findings state that the Bayes’ setup outperforms classical approaches, particularly in smallsample settings, making the proposed methodology flexible and beneficial in concluding the study when the researcher’s foremost concern is the total number of failed items.OPEN ACCESS Received: 29/03/2025 Accepted: 21/05/2025 Accepted: 22/09/2025
Mohammed et al. (Wed,) studied this question.