Abstract: The effect of measurement error on the performance of two control chart schemes, derived from the sample generalized variance and an unbiased likelihood ratio test for monitoring multivariate process variability, is investigated. It is demonstrated that the performance of the sample generalized variance chart based on surrogate quality characterisics is not proportionally invariant to changes in the covariance matrix of the true quality characteristics, even though it is proportionally invariant when no measurement error exists. Further, it is shown that for the sample generalized variance chart, the power to detect a change in the covariance matrix under measurement error could be larger than that under no measurement error. On the other hand, the control chart obtained from the unbiased likelihood ratio test does not seem to have this undesirable property. For this chart, under certain assumptions, measurement error results in reduced power to detect changes in the covariance matrix of the true quality characteristics. Bivariate examples of both charts are considered to demonstrate the possible scenarios.
Key words and phrases: Control limits, likelihood ratio test chart, measurement error, multivariate process variability, proportionally invariant, sample generalized variance chart.