| Since the development of control charts by Shewhart in 1926, it has become a common practice to rely on statistical control schemes to monitor a process. During the past decades, a number of multivariate procedures have been developed to monitor a process mean vector; included among those, the Chi-square control chart by Alt (1974), the Multivariate CUSUM by Croisier et al., and the Multivariate EWMA by Lowry et al. Very little is published on multivariate control charts for monitoring the covariance matrix. Alt (1985), Alt and Bedewi (1986), and Alt and Smith (1988) propose three control charts. The first one is based on the likelihood ratio test for testing whether the covariance matrix Σ is equal to a given covariance matrix Σ0. The second and third charts are based on the generalized sample variance, denoted by |S|. All three of these procedures are Shewhart-type charts. This dissertation uses an EWMA approach based on the log transformation of the sample generalized variance. Properties of the EWMA chart based on the generalized sample variance are presented. ARL tables and plots are generated to facilitate the design of an optimal EWMA control chart. It is shown that the optimal EWMA procedure performs better than the Shewhart one in terms of its ability to quickly detect small shifts in process variability. |
