## 4 Results and Discussion  
First, one baseline vehicle was selected for each engine displacement. Vehicles Y1.1 and Y2.1 presented the lowest MIS and the best battery SOH. Thus, vehicles with the same engine displacement were evaluated against the baseline vehicle. The DCCAC was calculated for the pairs Y1.1,Y1.2 and Y1.1,Y1.3 for 1.5L engine displacement. Pairs Y2.1,Y2.2, Y2.1,Y2.3, and Y2.1,Y2.4 were evaluated for 2.0L engine displacement. Figure 3 shows the results for 1.5L engine displacement. All the batteries are in good SOH. The DCCAC for the pair Y1.1,Y1.2 exhibits a steady increase from 0.0613 at \(n=4\) to 0.5880 at \(n=285\), indicating a progressively stronger correlation as the box size increases. This behavior was noticed in batteries operating under similar conditions. For the pair Y1.1,Y1.3, the DCCAC follows a similar trend but reaches a higher value of 0.8829 at  
Figure 2: DCCAC results interpretation: Zone A is defined by the 95% confidence interval upper limit (UL) and 95% confidence interval lower limit (LL) and represents the statistically non-significant area, calculated using the method proposed by [PERSON] et al. [65]. Zone B corresponds to the statistically significant area, where meaningful correlations can be observed. Batteries with good SOH should have all computed DCCAC results within Zone B, indicating significant cross-correlation with the reference battery. \(n=285\), indicating a strong cross-correlation between these two vehicles. Despite the 32-month usage period of the Y1.3 battery, the results suggest that it retains a stable voltage profile comparable to that of a new battery. The highlight in Figure 3 is the pattern of the rising curve for batteries with good SOH, demonstrating how the cross-correlation strengthens from short- to long-term scales. The results for 2.0L engine displacement are presented in Figure 4. Only the baseline and Y2.3 vehicles have batteries in good condition of use, with adequate SOH. The DCCAC increases from 0.0210 at \(n=4\) to 0.7263 at \(n=285\) for the Y2.1,Y2.3 pair. The pair Y2.1,Y2.2 and Y2.1,Y2.4, both featuring vehicles with deteriorated SOH, present weak and statistically non-significant DCCAC values across all time scales. Even in the case of Y2.4, where the battery was recently recharged, the DCCAC remains low. This suggests that recharging a battery with degraded SOH does not restore its ability to sustain voltage stability under load. The lack of significant correlation in these cases highlights a fundamental deterioration in battery performance, further reinforcing the effectiveness of DCCAC in identifying failing batteries. In contrast, the rising curve trend seen in Figure 3 is also observed in Figure 4 for the pair Y2.1,Y2.3, reinforcing that batteries with good SOH maintain a consistent and increasing cross-correlation coefficient from short- to long-term scales. Finally, it was verified that the method cannot be applied to compare different engine displacements using a unique baseline engine as a reference. Figure 5 evaluates the pairs Y2.1,Y1.2 and Y2.1,Y1.3 against the 95% confidence intervals. Vehicle Y2.1, with a 2.0-L engine, serves as the baseline for this analysis, while Y1.2 and Y1.3 are 1.5 L engine vehicles with batteries in good SOH. Initially, DCCAC values for the pair Y2.1,Y1.2 are not statistically significant, as they fall between the UL and LL for almost all boxsizes. As the boxsize increases (\(n\geq 224\)), DCCAC values exceed the UL, indicating statistically significant positive cross-correlation. For the pair Y2.1,Y1.3, DCCAC values are significant for smaller box sizes (\(n>38\)), but become statistically insignificant afterward, almost mimicking the other analyzed pair for the remaining box sizes. However, unlike the r  
Figure 3: DCCAC of the following vehicle pairs: Y1.1,Y1.2 and Y1.1,Y1.3. Vehicle Y1.1 is the baseline for this analysis. The 95% confidence interval upper limit (UL) and 95% confidence interval lower limit (LL) are also presented.