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Abstract
Recently there has been a growing interest in multivariate statistical process control in which the simultaneous control of several related quality characteristics is considered The detection of a shift in the in-controi mean vector has already been studied in depth assuming that the p variables to be controlled are distributed as a p-multivariate normal. However, very little attention has been paid to the detection of shifts in the dispersion of the variables, i. e., shifts in the in-control covariance matrix ∑,0. The use of a chart which consists of plotting values of the generalized variance, |S|, is recommended in the bibliography, but its statistical properties are not well known In this paper we shall study the distribution of |S| and we shall show how to obtain a suitable control limit. The power of the chart wiii be studied and we shall show that it only depends on |∑1|/|∑0| where ∑1 is the out-of-control covariance matrix.
