Variable sample size control chart for monitoring process capability index C_pm

Process capability indices (PCIs) provide numerical measures of process reproduction capability and are effective tools for quality assurance. In the present paper, we develop a variable sample size control chart, namely VSSC_pm, to monitor PCIs for industry manufacturing to improve product quality. We setup the control limits; determine the upper and lower warning limits, fixed sample size, central region sample size, and warning region sample size for the control chart; and apply them to monitor PCI C_pm. We also use the average run length (ARL) as a monitoring performance indicator. To increase the in-plant applicability of the proposed method, we tabulate the performance value of the ARL for various commonly used situations. We perform a sensitivity analysis to study the effects of model parameters on the monitoring performance and then present an example to illustrate the proposed procedure.