Identifying the mean vector of bivariate process

Control charting is the most important part of implementing SPC. However, this usually makes some incorrect control limits in multivariate setting when the variables are highly correlated. This study proposes the joint X charts identifying the directions of out-of-control variables about bivariate when the joint non-central chi-square statistic (NCS) charts monitor the mean shift in bivariate control chart. Firstly the joint NCS charts can detect the variable or group of variables that cause the signal and then the joint X charts recognize the direction(s). Once the joint NCS charts and the proposed charts signal simultaneously, the user can be provided more details of the out-of-control variable. That makes technician and/or engineering analyze and correct them more conveniently and speed up the research about monitoring and diagnosing of multivariate process.