6.
Process or Product Monitoring and Control
6.5. Tutorials 6.5.4. Elements of Multivariate Analysis
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Hotelling's |
A multivariate method that is the multivariate counterpart of
Student's |
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Univariate |
Recall, from Section 1.3.5.2,
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Generalize to |
When |
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Distribution of |
It is well known that when |
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Result does not apply directly to multivariate Shewhart-type charts |
Although this result applies to hypothesis testing, it does not apply
directly to multivariate Shewhart-type charts (for which there is no |
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Three-sigma limits from univariate control chart | When a univariate control chart is used for Phase I (analysis of historical data), and subsequently for Phase II (real-time process monitoring), the general form of the control limits is the same for each phase, although this need not be the case. Specifically, three-sigma limits are used in the univariate case, which skirts the relevant distribution theory for each Phase. | ||
Selection of different control limit forms for each Phase | Three-sigma units are generally not used with multivariate charts, however, which makes the selection of different control limit forms for each Phase (based on the relevant distribution theory), a natural choice. |