A new version of the three-parameter Weibull model, called the new extended Weibull (NEW), has been introduced in the literature to provide an increased or inverted bathtub failure rate. In a survival context, adaptive progressive Type-Ⅱ censoring encourages the statistical inference's efficiency and minimizes the overall testing period during a lifetime experiment. By gathering a NEW sample from the proposed strategy, both likelihood and Bayesian inferential evaluations for the NEW model parameters of life were derived. For each unknown subject, asymptotic confidence intervals by normality and the log-transformed-normality approximations were constructed. Given independent uniform and gamma density priors against squared-error and general-entropy loss functions, Bayesian point and credible estimations were created utilizing several Monte-Carlo Markov-Chain techniques. To appreciate the usefulness of the acquired estimators, a comprehensive simulation analysis was performed by offering different experimental scenarios. To examine the superiority of the proposed model and to exhibit the viability of the proposed approaches in real practice, a pair of data examples, one based on the strength (in gigapascal) of carbon fibers and the other based on the failure times of conductors, were analyzed and the results were observed.