When conducting engineering life tests, it is common to collect necessary data from multiple production lines simultaneously. However, traditional methods are inadequate for analyzing this type of data, which is crucial for assessing reliability performance. In this study, we employ a newly proposed methodology called a joint Type-II hybrid censoring plan for gathering data from two production lines. We apply this plan to analyze three real-world engineering data sets when the parent distribution of the populations of interest is the Nadarajah–Haghighi distribution with varying shape and scale parameters. We consider two estimation approaches, maximum likelihood and Bayesian methods, to obtain point and interval estimates of the model parameters. The Bayesian estimates are obtained using the squared error loss function and the Markov Chain Monte Carlo procedure. To assess the performance of these different estimation methods, we conduct a simulation study that incorporates various testing plans. Finally, three engineering applications are considered to show the applicability of the offered methodologies.