Process capability indices CPU and CPL are developed in the manufacturing industry to provide quantitative measures on process potential and performance, for processes with one-sided specification limits. Statistical properties of the estimators of CPU and CPL have been investigated extensively, but only restricted to cases with single samples. In this paper, we consider the estimation and capability testing of CPU and CPL based on multiple samples. We show that the proposed estimator of CPU and CPL are indeed the uniformly minimum variance unbiased estimators (UMVUEs). A simple procedure based on a hypothesis testing using the UMVUE is developed for the practitioners to use for judging whether a stable process meets the preset capability requirement.