The process capability index (Cp) measures the amount of dispersion a process involves relative to the limits of specification. This paper considers sixteen different available confidence intervals for estimating the population process capability index. A simulation study under different conditions has been conducted to compare the performance of the estimators. Our vast simulation records reveal that both augmented large sample (ALS) and modified augmented large sample (MALS) intervals have better coverage probability and shorter average width in all simulation conditions. We expect that the results of this paper will contribute to the literature on process capability and will guide the researchers to select an interval estimator when they are interested to estimate the population process capability index.