# Multivariate Analysis of Transient State Infrared Images in Production Line Quality Control Systems
## 4 Temporal Evolution of Principal Components in Exemplary Production Line Application
It is evident that in this example PC3 and PC4 are the only components that enable quick classification after just 4 min (Figure 8). On the other hand, the separation between classes for these PCs decreases with time (Figures 9-11) and they do not allow us to perform reliable classification for times greater than 10 min (Figure 12). Figure 8: Representation of devices by PC1–PC8 for acquisition time equal to 4 min. Figure 7: Exemplary infrared images of devices belonging to: (**a**) class G—non-defective devices; (**b**) class E—defective devices with faulty evaporator; (**c**) class B—defective devices with other than evaporator faults. The classification can be made after about 5 min depending on the device model. It is two times less than the time indicated in some other publications [8,9]. Moreover, tests proved that it is even easier to detect some faults, e.g., evaporator defects (class E, Figures 8-12), on the base of infrared images taken during the transient state (for times less than 10 min). As for the classification efficiency, the analysis of Figures 8-12 reveals that one of the faulty devices belonging to class E cannot be correctly classified using PCA approach. It must be noticed that its infrared image, presented in Figure 7b, is very similar to the image of a non-defective device presented in Figure 7a. Therefore, the final efficiency is equal to 95.2%. Figure 10: Representation of devices by PC1–PC8 for acquisition time equal to 7.5 min. Figure 9: Representation of devices by PC1–PC8 for acquisition time equal to 5 min. In Figures 8-12, it can be noticed that class B can be separated for almost all PCs and all acquisition times--in 18 considered cases out of 20 comparing to 6 for the class G and E assuming acceptable level of classification efficiency to be equal at least 95%. As it has been already suggested, it is not possible to point out the best PCs before performing a preliminary analysis of the data. Table 1 shows the time dependence of the total variance of data covered by each PC. Can it be helpful to choose the best PCs? In order to answer this question, the relative changes of total variance values covered by each PC have been presented in Figure 13. It has been assumed that the PC total variance values for \(t=240\) s are  
Figure 11: Representation of devices by PC1–PC8 for acquisition time equal to 10 min. Figure 4:0 Representation of devices by PC1–PC8 for acquisition time equal to 15 min. reference values. Two groups of PCs can be distinguished. The first group, for which the relative value changes are less than \(\pm 15\%\), includes PC1, PC4, PC5 and PC7. The second group, for which the relative value changes are higher than +25% and less than +55%, includes PC2, PC3, PC6 and PC8. The variance for the PC1 is decreasing with time when the other values are non-monotonically increasing (PC2-PC3 and PC5-PC8) or stay at the same level (PC4). Two PCs with the best classification power for each acquisition time have been indicated by yellow background in Figure 4:1 It seems that there is no simple rule that could be used to select PCs for classification on the base of the time dependence of the variance for each PC.