A model for correlated quality variables with measurement error is presented. It is shown that the performance of multivariate control charting methods based on measured covariates is not directionally invariant to shifts in the mean vector of the underlying process variables, even though it may be directionally invariant when no measurement error exists. An expression for the power of the χ2 chart under measurement error is given as an illustration. Bivariate examples of the χ2 chart are considered for which power curves are developed.
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Linna et al. (2001) studied this question.
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