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Figure 6.43. Equalized/synchronized batch trajectories of the reference set using DTW procedure in Figure 6.31.

where S is the estimated covariance matrix of scores and Fa,i-a,<x is the F-distribution value with A and I — A degrees of freedom in a significance level, I is the number of batches in the reference set, A is the number of PCs retained in the model.

Hotelling's T2 plot detects the small shifts and deviations from normal operation defined by the model. Statistical limits on the D-statistic are computed by assuming that the data follow a multivariate Normal distribution [254, 253]. D statistics (T2 can be written as the D-statistic) for end-of-batch SPM for batch i are tTS-it j di = 11 - i)2 ~ ba/2,(i-a-i)/2 (6.97)

where ta is a vector of A scores [254] and S is the (A x A) estimated covariance matrix, which is diagonal due to the orthogonality of the t scores [594]. The statistics aforementioned in Eq. 6.97 is called

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