Variation Charts for Multivariate Processes

Non-causal data-driven monitoring of the process correlation structure: A comparison study with new methods

“…(4). Levinson et al (2002) proposed a monitoring scheme based on the idea that, in a stable process, the covariance matrix estimated with the complete set of collected data should be approximately equal to the one obtained from the mean square of successive differences. To obtain the monitoring statistics, G, one has to calculate first the in-control sample covariance matrix, S 0 , from a reference data set with n 0 observations.…”

“…To obtain the monitoring statistics, G, one has to calculate first the in-control sample covariance matrix, S 0 , from a reference data set with n 0 observations. After that, the ith test sample covariance matrix, S 1,i , determined from a subgroup with n 1 observations is combined with S 0 in the pooled estimator of the covariance (Levinson et al, 2002),…”

“…However, the generalized variance is a rather ambiguous measure of multivariate variability, as quite different covariance matrices can lead to similar values for the determinant. Other approaches are based on the likelihood ratio test (LRT), as for example those found in the works of Alt and Smith (1988) and Levinson et al (2002). More recently, Yen and Shiau (2010) presented a control chart, based on LRT, specifically designed to detect an increase in process dispersion, which was later on extended to variations in both directions (increase and decrease) (Yen et al, 2012).…”

Test of covariance changes without a large sample and its application to fault detection and classification

“…To tackle this problem, one can alternatively apply the likelihood ratio test (LRT) which has a single test statistic only and possesses certain optimality property in detecting changes of parameters. Many other approaches have been also proposed to detecting change of covariance matrix, including GuerreroCusumano [1], Aparisi et al [2], Chan and Zhang [3], Levinson et al [4], Yeh and Lin [5], Yeh et al [6], Ghute and Shirke [7], Bodnar et al [8], among others. A detailed review of existing methods for detecting change of covariance matrix can also be found in Yeh et al [9].…”

On-line process monitoring using local measures of association: Part I — Detection performance

“…However, the underlying structure of collected data does change in such circumstances, and therefore its monitoring can be more effective to detect the abnormalities. For explicitly monitoring the multivariate process' dispersion (or correlation), typical approaches are based on subgroups of observations and usually employ the generalized variance (the determinant of the variance-covariance matrix) [16][17][18] or the likelihood ratio test [5,19,20]. Other approaches based on the conditional entropy [21], vector variance (which is the sum of the squares of all eigenvalues of the sample variance-covariance matrix) [22] and independent components obtained from the decomposition of the sample variancecovariance matrix [23] have also been proposed.…”