(a) MPLS model blocks for predicting product quality

(b) MPLS model blocks for predicting progress of the batch

Figure 6.75. MPLS modeling with using different unfolding approaches.

Development of Online Process Performance Monitoring Framework. This online monitoring framework in this work is based on unfolding a three-way array by preserving the variable direction. However, it is also incorporated with the conventional MPLS technique when online/offline quality prediction and end-of-batch monitoring are aimed. To differentiate the two MPLS techniques depending on different type of unfolding, the conventional technique that preserves batch direction is called MPLSB (Figure 6.75(a)) and the one that preserves variable direction is called MPLSV (Figure 6.75(b)). MPLSV relies on information at a specific time. The history of the batch up to that time is not considered in contrast to the MPLSB framework. In this respect, it is similar to a Shewhart chart while MPLSB is similar to a CUSUM chart.

A reference data set that contains good batches presenting normal operation is used in the model development. Equalization and alignment of trajectories are required if batches in this reference set are of different lengths using alignment techniques discussed in Section 6.3. Data alignment using an indicator variable (IV) can be performed in different ways. If there exists an indicator variable that other process variables can be measured against its percent completion, variable trajectories in the reference set are re-sampled by linear interpolation techniques with respect to this indicator variable. As an alternative method, (especially when such an indicator variable is not available), an MPLSV model can be developed between the process measurements matrix X and local time stamps vector z of the individual batches in the reference set (Figure 6.75(b), y = z).

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