Abstract: Supplier selection is an important part of supply chain management. In the initial stage of production setting, the decision-maker usually faces the problem of selecting the “best” one(s) from available manufacturing material suppliers. For this purpose, process capability indices (PCIs) are commonly used in the literature to rank the suppliers under selection; and among these PCIs, Cpk could be the most popular one. This problem of selecting the best supplier(s) has received considerable attention in the literature but mainly from the frequentist point of view. In this paper, we tackle the so-called group supplier selection problem via the Bayesian approach, namely selecting a group of suppliers that would include the supplier of the largest Cpk value with a high level of confidence in a Bayesian sense. Based on the observed data and available prior information, we develop a practical procedure for the group supplier selection, which is useful for practitioners operating in-plant applications.