A method for obtaining multivariate control procedures based on a loss function is proposed and studied. This involves constructing a function that measures the extent of "out of control" conditions associated with any configuration of paramenter values, and then basing a control chart on a sequence of sample statistics whose expected values are equal to this function. The method is illustrated by obtaining cumulative sum procedure for bivariate and trivariate normal distributions.
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Mohebbi et al. (1989) studied this question.
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