Process capability indices (PCIs) have been extensively used to evaluate and measure whether the process meets the specifications and they provide quality assurance and guide a principal for quality improvement. The index Cpk is the most popular index and is widely used in the manufacturing industry for manufacturing yield evaluation. However, typical evaluations of Cpk depend heavily on the assumption of normal variability. When the underlying distributions are non-normal, the capability evaluations are highly unreliable. In the paper, we apply four various bootstrap methods to construct lower confidence bounds of CNpk for non-normal processes. We also propose an approximately unbiased estimator of CNpk for the non-normal processes. Comparisons among the four bootstrap methods with different estimators are provided.