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Some aspects of Hotelling’s \(T^2\) statistic for multivariate quality control. (English) Zbl 0948.62084

Ghosh, Subir (ed.) et al., Statistics of quality. Dedicated to the memory of Donald B. Owen. New York, NY: Marcel Dekker. Stat., Textb. Monogr. 153, 77-100 (1996).
From the aper: With the development of the distribution of the \(T^2\) statistic, H. Hotelling [C. Eisenhart et al. (eds.), Techniques of statistical analysis, 111-184 (1947)] made a major contribution to multivariate statistical theory and, ultimately, to multivariate statistical process control. Variations of the \(T^2\) statistic can be used for hypothesis tests about mean vectors, for multivariate outlier tests, and for multivariate control charts. Hotelling’s \(T^2\) statistic has played an important role in the development of multivariate quality control. The \(T^2\) statistic was introduced as a charting statistic for controlling the mean of a process. Although slow to be utilized initially, the \(T^2\) chart now is rapidly gaining popularity among quality practitioners. This is mainly due to the ready availability of personal computers and software that can perform the necessary calculations with ease.
For the entire collection see [Zbl 0913.00046].

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62H15 Hypothesis testing in multivariate analysis
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