on the multivariate variation control chart

multivariate control charts such as hotelling`s t^ 2 and x^ 2 are commonly used for monitoring several related quality characteristics. these control charts use correlation structure that exists between quality characteristics in an attempt to improve monitoring. the purpose of this article is to discuss some issues related to the g chart proposed by levinson et al. [9] for detecting shifts in the process variance-covariance matrix. they use a g statistic which is distributed as a chi-square with p(p+1) / 2 degrees of freedom where p denotes the number of variables under study. the authors show through simulation that the chi-square distribution only holds for certain cases. the results could be important to practitioners who use g chart for monitoring purposes.