Summary: Process capability indices (PCI) have become an integral part of statistical quality control. During the past three decades various process capability indices have been proposed. Several authors have studied the distributions and inferential characterizations of these indices. Recently a new process capability index, \(C_{pnst}\), has been proposed by B.C. Gupta [J. Combinat. Inf. Syst. Sci. (2004); to appear]. We show that the proposed PCI has an asymptotic normal distribution. Interval estimation and testing hypothesis of the process capability will be discussed along with a numerical example based on a real life data set.