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Misleading signals in joint schemes for the mean vector and covariance matrix
Author(s) -
Cabral Morais Manuel,
Schmid Wolfgang,
Ferreira Ramos Patrícia,
Lazariv Taras,
Pacheco António
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2598
Subject(s) - covariance matrix , covariance , statistical process control , control chart , joint (building) , estimation of covariance matrices , matrix (chemical analysis) , process (computing) , chart , mathematics , computer science , scatter matrix , multivariate statistics , multivariate normal distribution , statistics , algorithm , engineering , architectural engineering , materials science , composite material , operating system
In multivariate statistical process control, it is recommendable to run two individual charts: one for the process mean vector and another one for the covariance matrix. The resulting joint scheme provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both process location and spread. The multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart of the joint scheme. Consequently, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa. Compelling results are provided to give the quality control practitioner an idea of how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals that will likely lead to a incorrect diagnostic of which parameter has changed.