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Step-Down Analysis for Changes in the Covariance Matrix and Other Parameters

Summary: [This abstract is based on the authors' abstract.]It is shown how the elements of the covariance matrix and other higher order moments can be included in the step-down diagnostic analysis. The asymptotic normality of maximum-likelihood estimators is used to classify the parameters that describe the prior- and post-shift distributions into those for which there is evidence of a shift and those for which such evidence is lacking. This information can help identify the causes of the shift. In some cases it is more helpful to use standard deviations and correlation coefficients instead of variances and covariances. This approach, and application to distributions other than the multivariate normal, are discussed. The proposed methodology is illustrated with independent and identically distributed observations, but has broader applications.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Multivariate analysis,Shift point,Statistical process control (SPC),Stepwise procedures,Log-gamma distribution,Maximum likelihood estimate (MLE)
  • Author: Sullivan, Joe H.; Stoumbos, Zachary G.; Mason, Robert L.; Young, John C.
  • Journal: Journal of Quality Technology