This research conducts a systematic literature review and case study analysis to compare the Design of Experiments (DOE) and Active Learning (AL) methods in the context of machine learning within manufacturing and mechanical engineering. The objective is to evaluate the efficacy of these data-gathering methods in informing Supervised Machine Learning models. The review began with a search yielding 1280 documents, culminating in a final selection of 35 articles after meticulous screening and eligibility checks. The findings illustrate that DOE methods provide comprehensive insights into process variables, while AL methods offer significant efficiency gains by requiring less data to achieve similar or improved model performance. Case studies demonstrate the practical applications and highlight the potential of a hybrid approach that integrates the thoroughness of DOE with the efficiency of AL. The research identifies gaps in the current literature, particularly in the real-world application of AL and its integration with emerging technologies. The conclusion suggests that future research should focus on developing sophisticated AL models to navigate the increasing complexity of manufacturing environments and that a nuanced approach to selecting data-gathering methods is crucial.