Detection and Interpretation of a Multivariate Signal Using Combined Charts

Abstract

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.

Keywords:

• Cluster of means
• Hotelling's T ² statistic
• Scatter matrices
• Wilks' W statistic

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62E15

Acknowledgments

The authors would like to sincerely thank the reviewers for many helpful comments and suggestions.

Notes

*Significant at α = 0.005.

*Significant at α = 0.005.

*Significant at α = 0.005.