In this paper, we consider the supplier selection problem for normally distributed processes with multiple independent characteristics based on process capability index CTPU. A two-phase testing procedure based on the quotient of two statistics is proposed to deal with the problem. We obtain the sampling distribution and the probability density function of the quotient. Several tables of the critical values for the testing procedure and decision making are provided. The required sample sizes for various capability requirements, magnitude of difference of two suppliers, and given power are also presented. A real application on TFT-LCD manufacturing processes is presented to demonstrate the efficacy of the proposed method.