There have been a number of process capability indices (PCIs) which are summary statistics to depict the process location and dispersion successfully proposed over the years for the purpose of assessing the capability of a process to meet certain specifications. Generally PCIs are used with symmetric tolerances when the target value (T) locates on the midpoint of the specification interval (m). Sometimes it is possible to meet the case target value does not located on mid-point (T not equal m) which called asymmetric tolerances. To analyze the process which have asymmetric tolerances, PCIs with asymmetric tolerances have been developed and successfully applied. Process incapability index (C-pp) is used both symmetric and asymmetric cases. In this paper, C-pp with asymmetric tolerances (C-pp '') is analyzed by using fuzzy set theory to obtain a deep and flexible analysis. To produce fuzzy process incapability index with asymmetric tolerances ((C) over tilde (pp)''), fuzzy process mean (mu) over tilde and fuzzy variance (sigma) over tilde (2), which are obtained by using the fuzzy extension principle, are used together with fuzzy specification limits (SLs) and target value (T). The proposed index (C) over tilde pp '' is applied in an automotive firm to analyze the capability of Volvo Marine motor's piston for diesel engine and the results prove that the fuzzy set theory brings an advantage which is including more information and flexibility to evaluate the process performance.