Monitoring charts Hotelling

Multivariate monitoring charts based on Hotelling s statistic (T ) and squared prediction errors SPEx and SPEy) are constructed using the PLS models. Hotelling s statistic for a new independent t vector is [298]... 

If dependency exists. Hotelling 7 control chart is commonly used procedure for a multivariate process monitoring and controlling. For individual observations, suppose that there are m samples, each of size n=, and p is the number of quality characteristics observed in each sample. Let x be the sample mean vector and S be covariance matrix of these observations. The Hotelling 7 statistic is calculated as = x — (x — x). The phase I limits should be based on a beta distribution. 

Suppose that it is desired to use SPC techniques to monitor p variables, which are correlated and normally distributed. Let x denote the column vector of these p variables, x = col x, X2,..., Jc ]. At each samphng instant, a subgroup of n measurements is made for each variable. The subgroup sample means for the Ath sampling instant can be expressed as a column vector x(k) = col k), X2 k), Xp k) Multivariate control charts are traditionally based on Hotelling s statistic (Montgomery, 2009). 

Hotelling control chart If two or more features are monitored at the same time, monitoring these two quantities independently by applying two or more univariate control charts can be very misleading, especially if those features are correlated. On the opposite, the Hotelling control chart is designed for the monitoring of... 

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