Stochastic Ordering in the Qualitative Assessment of the Performance of Simultaneous Schemes for Bivariate Processes

Abstract

Misleading signals (MS) are likely to happen while using a simultaneous scheme to control the mean vector (μ) and the covariance matrix (Σ) of a bivariate process. They correspond to valid signals that lead to a misinterpretation of a shift in μ (resp. Σ) as a shift in Σ (resp. μ). Following previous work, focused on the quantitative assessment of the probabilities of misleading signals (PMS) in simultaneous schemes for bivariate processes, we now make use of stochastic ordering to qualitatively assess the impact of changes in μ and Σ in those probabilities.

Keywords:

• Bivariate processes
• Misleading signals
• Simultaneous schemes
• Statistical process control

Subject Classifications:

• 60E15
• 62P30

ACKNOWLEDGMENTS

The first author was supported by grant SFRH/BD/35739/2007 from the Fundaço para a Cincia e a Tecnologia (FCT). This work received financial support from Portuguese National Funds through FCT within the scope of the projects PEst-OE/MAT/UI0822/2011 and PTDC/MAT-STA/3169/2012.

We are grateful to the Editor, an anonymous Associate Editor, and an anonymous referee for sharing their enthusiasm with us.

Notes

Recommended by Nitis Mukhopadhyay