A Process Capability Index $C_{pd}$ Consistent with the Proportion of Nonconforming Items

불량률과 이치하는 공정능력 지수 $C_{pd}$

Process capability indices (PCI) $C_p\;C_{pk},\;C_m,\;and\;C_{pmk}$ are widely used to evaluate the process performance. The PCI's have been evolved to consider the 'off targetness' more adequately. However, all of these indices are found to be inconsistent with the proportion of nonconforming items, in some cases. That is, the PCI for a process may result in higher value even when the proportion of defectives increases. For these reasons, we propose a new capability index, $c_{pd}$, which is consistent with the defect rate. The characteristics of the new PCI, $c_{pd}$ are investigated with respect to the existing PCI's. Some statistical properties of an estimator for $c_{pd}$ are also investigated by a Monte Carlo simulation. Sensitivity study under minor deviation from normality is also performed to show the robustness of $c_{pd}$. A good estimator for $c_{pd}$ is under study.