This study deals with a novel category of life distributions called the new better than renewal used in moment generating function (NBRUmgf) class. It delves into the connections between this form of aging and established aging categories, along with its relevance in a shock model. Additionally, it explores how this aging concept remains consistent through certain reliability operations which is consider a very important tool in reliability engineering. The research computes Pitman's asymptotic efficiencies for this testing procedure, comparing them with alternative methods. Furthermore, the study furnishes a comprehensive table of percentiles for the test statistic associated with this proposed method. Furthermore, in order to showcase the relevance of the study's conclusions, we utilize distinct real-world datasets, which illustrate the effectiveness of our test across various types of real data.