This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances.