Chi-Square quantile-based multivariate variance monitoring for individual observations

ABSTRACT

Under the normality assumption, some statistics for monitoring a multivariate process variance for individual observations can be used to detect a variance shift, but the distribution of their in-control run length has a high variance as well as the median that is extremely smaller than the mean, which leads to many false alarms in the in-control process. In this paper, we propose a chi-square quantile-based monitoring statistic which is free of the problems. The numerical experiments show that the proposed monitoring statistics outperform the existing monitoring statistics in terms of the detection of a shift for the variance.

KEYWORDS:

• Chi-square quantile
• Covariance matrix
• Individual observations
• Multivariate variance monitoring

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30

Acknowledgement

This author thanks the editor and referees for their suggestions, which improved the presentation of the paper.

Funding

This work was supported by the Dong-A University research fund.