The Group Selection problem is an essential problem in the supplier selection process. The objective of the problem is to select a subset of suppliers containing the best among multiple candidate suppliers. Manufacturers should procure parts from the selected suppliers to produce high-quality products. Lin, C.J., W.L. Pearn, J.Y. Huang, and Y.H. Chen [2017. “Group Selection for Processes with Multiple Quality Characteristics.” Communications in Statistics–Theory and Methods. doi:10.1080/03610926.2017.1364392] considered the problem under multiple quality characteristics, and proposed the Modified Bonferroni method and the Multiple Comparisons with the Best (MCB) method to tackle the problem. The two methods, however, may select different subset containing the best depending on the magnitude of the differences among the k estimated C T pk index values. In this paper, we derive the power function for the Modified Bonferroni method, and compare the power of the two methods with extensive simulations. The results show that the MCB method is more powerful than the Modified Bonferroni method when the actual number of the best process is one. On the other hand, the Modified Bonferroni method significantly outperforms the MCB method when the actual number of the best process is greater than one. The results provide practitioners with useful reference about the properties of the two methods for supplier selection.