Process Capability indices (PCIs) such as Cp and Cpk  are commonly used measures to evaluate a manufacturing processes performance. The validity of these measures is based on that quality characteristics data under evaluation is normality distributed and the manufacturing process in under statistical control. The   measure considers the process data is centering the specification band. However, it lacks to evaluate a process off-centering the given specification band. The Cp and Cpk  measure which is 2nd generation considers the off-centering issue of any process being evaluated for its performance. Addressing the indeterminate and incomplete information about the different specification limits (SLs), the process capability indices Cp and Cpk  is designed under the neutrosophic fuzzy environment. The neutrosophic fuzzy SLs contains three different aspects of membership degrees such as truth, indeterminacy, and falsity degrees which is more flexible to the fuzzy based approaches. Furthermore, the proposed neutrosophic PCIs Cp and Cpk  is implemented on the rubber parts manufacturing company. The results show the more reliable values of PCIs while dealing with the indeterminacy degree present in the SLs. The wide range of getting different SLs is also benchmark findings of the proposed neutrosophic PCIs study. The conclusions and future work scope is also furnished in an efficient manner.