Multivariate EWMA control charts for monitoring the variance-covariance matrix

Abstract

We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

“…Several univariate procedures have been properly extended to monitor multiple quality characteristics of a normally distributed process (see, for example, Cheng and Mao, 5 Khoo, and 6 Thaga and Gabaitiri 7 ). For additional multivariate CCs with memory, the interested reader is referred to the articles of Xie, 8 Cheng and Thaga, 9 Jeong and Cho, 10 and Chen et al 11 When the question comes to the simultaneous surveillance of both mean and variance, a popular approach is to use two distinct statistics, one for the mean and one for the variance, which are plotted on the same chart (Spiring and Cheng 12 ); another approach, suggested by Cheng and Mao, 5 makes use of a single combined plotting statistic. Alternatively, the use of two-chart monitoring schemes has been suggested, which consist of separate mean and variance charts with appropriate control limits (CLs) adjusted to the overall false alarm rate FAR (see, for example, Levinson et al, 13 Reynolds and Stoumbos, 14 and Maboudou-Tchao and Hawkins 15 ).…”

“…Several univariate procedures have been properly extended to monitor multiple quality characteristics of a normally distributed process (see, for example, Cheng and Mao, Khoo, and Thaga and Gabaitiri). For additional multivariate CCs with memory, the interested reader is referred to the articles of Xie, Cheng and Thaga, Jeong and Cho, and Chen et al . When the question comes to the simultaneous surveillance of both mean and variance, a popular approach is to use two distinct statistics, one for the mean and one for the variance, which are plotted on the same chart (Spiring and Cheng); another approach, suggested by Cheng and Mao, makes use of a single combined plotting statistic.…”

Πολυδιάστατα Διαγράμματα Ελέγχου Διεργασιών Και Εφαρμογές

“…Ενώ, ο Xie (1991) και οι Cheng and Thaga (2005) παρουσίασαν ένα πολυδιάστατο διάγραμμα EWMA και ένα διάγραμμα CUSUM. Περισσότερα πολυδιάστατα διαγράμματα ελέγχου EWMA, έχουν προταθεί από τους Jeong and Cho (2012) και Chen et al (2005).…”