A new two-parameter inverted Gompertz distribution with an upside-down bathtub-shaped failure rate is investigated in the presence of incomplete (censored) data. Reliability experimenters favor employing censoring strategies to collect data in order to strike a compromise between the time needed to complete the test, the required sample size, and the cost. Recently, an adaptive Type-II hybrid progressively censoring strategy has been proposed to improve the effectiveness of statistical inference. Therefore, using this strategy, this study explores the classical and Bayesian estimates of the inverted Gompertz distribution. The distribution parameters, reliability, and hazard functions are estimated using maximum likelihood and Bayesian estimation methods. On the presumption that the gamma priors are independent, symmetric and asymmetric loss functions are used to create the Bayesian estimation. The Markov chain Monte Carlo approach is used to collect samples from the entire conditional distributions and then acquire the Bayes estimates since the joint posterior distribution has a difficult shape. The highest posterior density and asymptotic confidence intervals are also obtained. Through simulated research, the efficacy of the various recommended strategies is contrasted. The best progressive censoring schemes are also shown, and various optimality criteria are investigated. Two real data sets, representing the lifetimes of mechanical components and the Boeing 720 jet airplane, are also looked at to show how the recommended point and interval estimators may be used. When the experimenter's main concern is the number of failures, the results of the simulation research and data analysis showed that the proposed scheme is adaptive and highly useful in concluding the experiment.