A process capability index with asymmetric tolerances under fuzzy environment

Process capability indices (PCIs) are summary statistics to depict the process location and dispersion successfully and they can be used to show the process performance by producing PCIs. Although PCIs are generally used for a process which has a symmetric tolerance, it is a necessity to analyze some processes where the target value (T) cannot be defined at the midpoint of the specification interval (m). If the T does not locate on m which is called asymmetric tolerances, PCIs have some disadvantages in the casual use and interpretation of PCIs. For these cases, PCIs with asymmetric tolerances have been developed and applied successfully. In this paper one of the most used PCIs with asymmetric tolerances ̃C″pmk is analyzed and the fuzzy set theory is used to provide deep and flexible analysis. The fuzzy formulations of the index pmk ̃C″pmk, which is one of the most used PCI with asymmetric tolerances, are developed. Then a real case application from an automotive company is given.