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.