The concept of convex order, which pertains to the arrangement of observations in a dataset, holds significant academic value and finds extensive application across diverse disciplines such as health and engineering. It serves as a robust mathematical tool for the purpose of ranking and comparing distinct alternatives. Nevertheless, the extent to which its performance aligns with the "new better than used" criterion remains mostly ambiguous. The objective of this study is to examine and analyze the exponential property of the idea of new better than used in convex ordering (NBUC), based on the concepts of aging and classes of life distributions. To examine its ramifications in the disciplines of health and engineering. For this purpose, a new test statistic for
testing exponentiality versus NBUC property. Some efficiency criteria for the proposed test are estimated and compared with previous tests. Finally, real data examples are used as practical applications for the proposed test.