A new process capability index for asymmetric specification limits

Most commonly seen process capability indices (PCIs) such as C-p, C-pk and C-pm are appropriate only for symmetric specification limits and should not be used for the process with asymmetric tolerances. For asymmetric tolerances, it seems that C-pmk has been the best alternative heretofore. However, C-pmk may not be applicable to the search for the prior candidate to improve. In addition, when the specification limits can be changed, we may not compare the process capability properly between before and after the change point with C-pmk. In this paper a new measure is proposed for asymmetric specification limits, which modifies C-pmk with the numerator min[USL-E(X),E(X)-LSL] replaced by E[min(USL-X,X-LSL)]. The new process capability index, C-pio, adds up the contribution of individual observations to the manufacturing process. The properties of C-pio are investigated and its estimator, C-pio, is provided. It is proved that rootn( C-pio --> C-pio) has an asymptotic normal distribution under the assumption that the fourth moment is finite. Finally two examples of its application are included.