Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed.