Multivariate Capability Index (MCp) with Presence of Gauge Measurement Errors

Process capability indices have been widely used in the manufacturing industry for measuring process reproduction capability according to manufacturing specifications. Properties of the univariate processes have been investigated extensively, but are comparatively neglected for multivariate processes where multiple dependent characteristics are involved in quality measurement. Since the quality of data on the process characteristics relies very much on the gauge measurement accuracy, therefore the capability indices of the process by ignoring the measurement errors would not be reliable. In this paper, we consider the multivariate process capability index (MC_p) by adding the measurement error as a source of variation in the data and show that we obtain a better estimation of the (MC_p) and the results are more accurate with respect to the case of ignoring the measurement error in the data collection.