Info

Variable No.

Figure 6.48. MPLS model VIP statistics. Important variables on projection are variables 5 (glucose concentration), 7 (biomass concentration), 8 (penicillin concentration), 9 (culture volume), 13 (generated heat) and 14 (cooling water flow rate).

of time for initial fast assessment before the real Y is available. New batch data are processed with MPLS model at the end of the batch as shown in Eqs. 6.115 and 6.116 after proper equalization/synchronization, unfolding and scaling, resulting in multivariate SPM charts (Figures 6.50 and 6.51) for detection and diagnosis. Figure 6.50 summarizes several statistics to compare new batch with the reference batches. Figures 6.50(a) and 6.50(b) indicate that there is a dissimilarity between the new batch and the NO batches in both process and quality spaces. Scores of the new batch in both spaces fall outside of the in-control regions defining NO in figures 6.50(c) and 6.50(d). These charts suggest that an unusual event occurred in new batch and should be investigated further. To find out when the process wnet out-of-control and which variables were responsible SPE\ chart and a variety of contribution plots are used (Figure 6.51). SPEx chart of process space in Figure 6.51(a) reveals a deviation from NO and process goes out-of-control around 570th observation. The overall variable contributions to SPEx in Figure 6.51(b) over the course of batch run indicate that variable 9

Figure 6.50. MPLS-based end-of-batch monitoring results.

(culture volume) has changed unexpectedly, hence the deviation. Variable contributions to SPEx for a specified time interval can also be calculated to zoom the interval when out-of-control situation is observed. Figure 6.51(d) shows average variable contributions to SPE* between 570th and 690th measurements. Variables 3, 6 and 9 are found having the highest contributions to deviation for that interval of out-of-control. A further analysis can be performed by calculating contributions to process variable weights. Since weights (W) bear information about the relationship between process and product variables, variable contributions to weights will reveal variable (s) that are responsible to out-of-control situation with respect to product quality. These contributions can be calculated similar to SPEx contributions. Figure 6.51(c) shows overall absolute variable contributions to the weights over the course of the batch run. Variables 3, 6, 7, 10, 13

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