Recently, improved Type-II adaptive progressive censoring has been introduced to ensure that the experimental duration does not exceed a certain time and that the test concludes once a predetermined number of failures are recorded. This paper addresses the problem of estimating the unknown parameters as well as the reliability and hazard rate functions of the proposed lifetime Nadarajah-Haghighi distribution when the collected data are obtained from the proposed censoring plan. For each unknown parameter of life, using maximum likelihood and Bayes inference methods, both point and interval estimators are derived. The approximate confidence intervals are acquired based on the asymptotic normality of the maximum likelihood estimators. Under the assumption of independent gamma priors, the Bayes estimators cannot be obtained in closed form, therefore, the Markov-Chain Monte-Carlo approximation technique via the Metropolis–Hastings algorithm is utilized to evaluate the Bayes point estimates and to create their credible interval estimates. To compare the efficiency of the different proposed estimators, in terms of root mean squared-error, mean relative absolute bias, and average interval length values, extensive Monte Carlo simulations are implemented. Ultimately, to show how the acquired estimators can be applied in a real-life engineering scenario, a real data set consisting of eighteen failure times for electronic devices is analyzed.