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Figure 4.11. Autoscaling of a set of reference trajectories about the mean trajectory (darker line).

This decomposition summarizes and compresses the data with respect to both X and Y variables and time into low dimensional spaces that describe the process operation which is most relevant to final product quality. T matrix carries information about the overall variability among the batches. The P and W convey the time variation of measured variables about their mean trajectories and weights applied to each variable at each time instant within a batch giving the scores for that batch. U represents the inner relationship between X and Y, and summarizes the Y variables (quality variables) with some information coming from the X block (process variables) . Q relates the variability of process measurements to final product quality [243, 434, 661].

MPLS will detect unusual operation based on large scores and classify a batch as 'good' or 'bad' as MPCA does and in addition, it will indicate if the final product qualities are not well predicted by process measurements when the residuals in the Y space [SPEy = Y2c=i c)2j are large. The W, P, and Q matrices of MPLS model bear all the structural information about how the process variables behaved and how they are related to the final quality variables. Implementation of this technique is discussed in Section 6.4.4.

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