Due to their effectiveness and simplicity of use, the process capability indices Cp, Cpk, and Cpm have been popularly accepted in the manufacturing industry as management tools for evaluating and improving process quality. Combining the merits of those indices, a more advanced index, Cpmk, is proposed that takes into account process variation, process centering, and the proximity to the target value, and has been shown to be a very useful index for manufacturing processes with two-sided specification limits. Most research works related to Cpmk assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when highly advanced measurement instruments are employed. Conclusions drawn regarding process capability are therefore unreliable and misleading. In this paper, we conduct a sensitivity investigation for the process capability index Cpmk in the presence of gauge measurement errors. We consider the use of capability testing of Cpmk as a method for obtaining lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that using the estimator with sample data contaminated by measurement errors severely underestimates the true capability, resulting in an imperceptibly smaller test power. To measure the true process capability, three methods for the adjusted confidence bounds are presented and their performances are compared using computer simulation.