Abstract
In a bivariate setting, misleading signals (MS) correspond to valid alarms which lead to the misinterpretation of a shift in the mean vector (resp. covariance matrix) as a shift in the covariance matrix (resp. mean vector). While dealing with bivariate output and two univariate control statistics (one for each parameter), MS occur when:
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The individual chart for the mean vector triggers a signal before the one for the covariance matrix, although the mean vector is on-target and the covariance matrix is off-target.
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The individual chart for the variance triggers a signal before the one for the mean, despite the fact that the covariance matrix is in-control and the mean vector is out-of-control.
Since MS can be rather frequent in the univariate setting, as reported by many authors, this chapter thoroughly investigates the phenomenon of MS in the bivariate case.
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Acknowledgements
The authors thank the financial support of Centro de Matemática e Aplicações (CEMAT) and Fundação para a Ciência e a Tecnologia (FCT). The first author was also supported by grant SFRH/BD/35739/2007 of FCT and would like to thank all the members of the Department of Statistics of the European University Viadrina (Frankfurt Oder, Germany) for their hospitality.
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Ramos, P.F., Morais, M.C., Pacheco, A., Schmid, W. (2013). Misleading Signals in Simultaneous Schemes for the Mean Vector and Covariance Matrix of a Bivariate Process. In: Oliveira, P., da Graça Temido, M., Henriques, C., Vichi, M. (eds) Recent Developments in Modeling and Applications in Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32419-2_23
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