Abstract

It is important to monitor more than two correlated quality variables at the same time in the industrial manufacturing and service processes. It leads to the multivariate statistical process control becoming a popular research area for researchers. This paper aims at constructing a new exponentially weighted moving average (EWMA) control chart with variable dimension (VD) quality variables in order to monitor the process covariance matrix for the VD multivariate normal distributed processes. The VD dispersion control chart is thus first developed and studied. Moreover, the proposed novel VD dispersion control chart is independent of the out-of-control process mean vector. It overcomes the problem in many existing covariance matrix control charts of assuming that there are no shifts in the process mean vector which, depending on the existence of shifts in mean, can lead to an increased false alarm rate. The properties of the charting statistic and the out-of-control dispersion detection performance of the proposed VD dispersion control chart are investigated. Compared to the fixed dimension dispersion control chart, the VD dispersion control chart can provide a good option when some of all quality variables are hard to measure and with high measurement costs, and perform better out-of-control dispersion detection performance. Moreover, the proposed VD dispersion control chart is very sensitive to changed variances and/or variance and covariances, but not for only changed covariances. An example of a semiconductor data set is adopted to illustrate the application of the proposed control charts.