Multivariate control chart for controlling variability – A comparative study

Abstract

Control chart is an important technique for statistical process control. In most of the practical situations data are collected on more than  one characteristic under study. Hence multivariate control chart has drawn the attention of quality control practitioners. For successful  implementation of multivariate control chart, two different charts are to be constructed. One is for controlling mean and another is for  controlling variance-covariance matrix or ∑ matrix. For effective implementation of control chart for mean, one need to establish that  variability is under control. Hence control chart for controlling variance-covariance matrix is playing an important role in multivariate  control chart. There are several control charts available in the literature which can be used for controlling ∑ matrix. In this article, we have  discussed different such control charts and studied their performance with respect to their ability to detect the shift in the  components of ∑ matrix. Out of control average run length (ARL) is considered as a measure for this purpose and the best method to  detect the shift have been identified under different conditions.