Properties of multivariate process capability in the presence of gauge measurement errors and dependency measure of process variables

Nowadays process capability has been extensively studied as a mean of summarizing process performance relative to a set of specification limits. Most of the research papers related to process capability indices have assumed that there are no gauge measurement errors. Unfortunately, such an assumption does not reflect real situations accurately even with highly sophisticated advanced measuring instruments. In this paper, we study the behavior of multivariate process capability index (MCpMCp) in the presence of gauge measurement errors. In addition, the effect of correlation coefficient and measurement capability on the statistical properties of the estimated MCpMCp are also studied. The results indicate that correlation coefficients of process variables will notability change the statistical behavior of the multivariate process capability in the presence of gauge measurement errors. With the adjusted confidence intervals and suitable estimation method the more accurate testing procedure for MCpMCp by considering different values of correlation coefficient is obtained.