In this paper, we consider a supplier selection problem, which compares two glass substrate processes with multiple lines and selects the one that has a higher capability. A test statistic obtained by a subtraction method is employed to establish a hypothesis test with two phases. Critical values of the test are obtained to determine the selection decisions. Sample sizes required for various designated selection powers and confidence levels are also investigated. Practitioners can use the proposed method to make reliable decisions. This paper presents a real-world case of a glass substrate process. The selection procedure uses data to reach a decision in supplier selection. We compare the results of the division method to the proposed subtraction method. The results show that the proposed subtraction method is indeed more powerful than the division method.