In this paper, we consider the supplier selection problem which deals with comparing two one-sided processes and selecting the one that has a significantly higher capability value. We present an exact approach to tackle the supplier selection problem. Testing hypotheses with two phases for comparing two processes are considered. Critical values of the tests are calculated to determine the selection decisions. Sample size required for a designated selection power and confidence level is also investigated. The results provide useful information to practitioners. The proposed approach generalizes the existing method by not requiring equal sample sizes for the two processes. An application example on comparing two wavelength division multiplexer (WDM) manufacturing processes is presented to illustrate the practicality of our approach to actual data collected from the factories.