A new two-parameter weighted-exponential (WE) distribution, as a beneficial competitor model to other lifetime distributions, namely: generalized exponential, gamma, and Weibull distributions, is studied in the presence of adaptive progressive Type-II hybrid data. Thus, based on different frequentist and Bayesian estimation methods, we study the inferential problem of the WE parameters as well as related reliability indices, including survival and failure functions. In frequentist setups, besides the standard likelihood-based estimation, the product of spacing (PS) approach is also taken into account for estimating all unknown parameters of life. Making use of the delta method and the observed Fisher information of the frequentist estimators, approximated asymptotic confidence intervals for all unknown parameters are acquired. In Bayes methodology, from the squared-error loss with independent gamma density priors, the point and interval estimates of the unknown parameters are offered using both joint likelihood and the product of spacings functions. Because a closed solution to the Bayes estimators is not accessible, the Metropolis–Hastings sampler is presented to approximate the Bayes estimates and also to create their associated highest interval posterior density estimates. To figure out the effectiveness of the developed approaches, extensive Monte Carlo experiments are implemented. To highlight the applicability of the offered methodologies in practice, one real-life data set consisting of 30 failure times of repairable mechanical equipment is analyzed. This application demonstrated that the offered WE model provides a better fit compared to the other eight lifetime models.