A multivariate control chart for simultaneously monitoring process mean and variability

Authors:
Jiujun Zhang;Zhonghua Li;Zhaojun Wang
Affiliations:
Department of Mathematics, Liaoning University, Shenyang 110036, PR China and LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.