Gauge measurement errors and multivariate capability indices

Univariate capability indices have been investigated extensively with or without considering the measurement errors, but for multivariate case, the study of process capability in the presence of measurement errors for quality characteristics are comparatively neglected. Since the correctness of data relies very much on the gauge measurement accuracy, therefore evaluating the capability indices by ignoring the measurement errors would not be reliable. In this paper, we consider the multivariate process capability index (MCp) by adding the measurement error as a source of variation in the data and study the statistical properties of obtained capability index. Implementing the results on a real example, show that the gauge measurement capability has a noticeable effect on the estimating and testing results of the process capability.