## 7 Evaluation Study: Comparison between the Two Models  
The simplest comparison between method \(1\) and method 2 is the direct comparison between the curves estimated with the two different approaches. Figures 10-14 show the outcomes of these two elaboration methods for five different pulsator test experimental campaigns. Several cases have been studied, obtaining similar results. For the sake of simplicity, only five of them are shown. For all the experimental campaigns, the solutions of method 2 have been verified by adopting the Likelihood Profile (LP) and Likelihood Ratio (LR). Experimental points shown in Figure 10 to Figure 13 were taken from the FZG database [24] while those in Figure 14 were obtained at POLIMI [27; 28]. The SN curve comparison has not been extended to other Section 3 methodologies because they require specific data that are not available. Figure 10: Comparison of two estimation methods for exemplary campaign A from experimental FZG database [24]. Figure 9: Pulsator test database [24; 27; 28; 56; 65; 66; 67; 68]. By looking at the gear SN curves shown in Figures 10-14, it seems that there is no relevant difference between the two estimation techniques as the estimated curves are close to each other, especially if \(Y_{NT}\) according to ISO 6336-3 [6] is selected on the conservative side in the long-life range. The good agreement between the models allows us to re-affirm the validity of the two models: Despite the usage of completely different statistical tools, the final gear curves are different but, most importantly, they are coherent with each other. Figure 11: Comparison of the two estimation methods for exemplary campaign B from experimental FZG database [24; 66]. Figure 12: Comparison of the two estimation methods for exemplary campaign C from experimental FZG database [24]. The first difference between the two estimation methods is the different positions of the fatigue knee. Especially for the Exp. curves, method 2 always estimates the knee above the one estimated by method 1. This different position is related to the different estimations of the complete SN curve. On the one hand, according to method 1, the fatigue knee is estimated as the intersection of the line describing the limited-life and the long-life regions. On the other hand, according to method 2, the fatigue knee location depends on the two estimated CDF parameters (\(N_{e}\) and \(\sigma_{e}\)) and the CDF elaboration. However, neither method 1 nor method 2 present a smooth passage between the two regions. This aspect is taken into account within more complex SN curve estimation methods (e.g., [68; 69; 70; 71; 72; 73]). Their application within the case of pulsator test elaboration is the subject of current research. Figure 14: Comparison of the two estimation methods for exemplary campaign E from [27; 28]. Figure 13: Comparison of the two estimation methods for exemplary campaign D from experimental FZG database [24] (Orig.) and excluding an outlier data point (Mod.). The main difference between the two estimation methods is the model sensitivity concerning the presence of outliers, and method 2 results in being more sensitive than method 1. This is depicted in Figure 13, where one experimental point (i.e., the one indicated by the arrow) can be considered an outlier as it has a lifetime almost 5 times higher than the one of the other experimental runs obtained at the same load level. This outlier has been defined by a graphical analysis of the test data and adopted here as an example. On the one hand, concerning method 1, the only effect the outlier has is that, at such a load level, \(N_{50\%}\) (i.e., Equation (3)) changes, with consequences on the estimated \(N_{1\%}\) (i.e., Equation (4)); the lines describing the experimental and gear-limited life vary accordingly (see the relatively slight difference between the pink and the black line). As limited-life and long-life regions are estimated differently, this outlier does not affect the latter.