Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

• Published in: International journal of advanced manufacturing technology Vol. 45; no. 7-8; pp. 772 - 785
• Main Authors: Machado, Marcela A. G., Costa, Antonio F. B., Marins, Fernando A. S.
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01-12-2009; Springer Nature B.V
• Subjects: Bivariate analysis; CAE) and Design; Computer-Aided Engineering (CAD; Control charts; Covariance matrix; Engineering; Industrial and Production Engineering; Mathematical analysis; Matrix algebra; Matrix methods; Mechanical Engineering; Media Management; Monitoring; Original Article; Statistical tests; Mean vector; Covariance matrix; Bivariate processes; Control charts
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-009-2018-7

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the
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| charts. However, these charts have two drawbacks: (1) the
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| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint
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| charts in signaling processes disturbances.