Abstract Process capability indices C PU and C PL 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 C PU and C PL have been investigated extensively, but only restricted to cases with single samples. In this paper, we consider the estimation and capability testing of C PU and C PL based on multiple samples. We show that the proposed estimator of C PU and C PL 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.