## 4 Method 1: FVA Approach Based on FZG Research
Within method 1, the limited-life region is estimated by calculating, for each load level, the 50% experimental lifetime \(N_{50\%}\) by assuming a log-normal distribution of the failure load cycle numbers [23]. This is performed using a log-normal probability grid, with the definition of the single failure probability for each data point based on the order approach defined by [PERSON] [59]. On the other hand, a more simplified approach is to calculate \(N_{50\%}\) from the lifetime of the n individual tests according to Equation (3) [25]:  
\[\log(N_{50\%})=\frac{1}{n}\sum_{i=1}^{n}\log(N_{i}) \tag{3}\]  
That is, calculating the average lifetime. Once the 50% curve has been estimated, the 1% gear failure probability lifetime \(N_{1\%}\) is calculated for each load level as:  
\[N_{1\%}=10^{(\log{(N_{50\%})}-2.33\cdot s_{log}} \tag{4}\]  
where \(s_{log}\) is the typical logarithmic standard deviation, the trend of which is shown in Figure 6. Then, both the 50% experimental and the 1% gear curve are calculated by fitting a line through the estimated \(\log(N_{50\%})\) and \(\log(N_{1\%})\). According to this method, the standardized calculation method as per ISO 6336-3 [6] can still be applied. Therefore, the life factor \(Y_{NT}\) is used to multiply \(\sigma_{F0\infty,1\%,MG}\). The choice between a horizontal endurance line and the presence of the secondary slope for a number of load cycles > 3 million depends on the experience and the criticality within the field of application. The FVA guideline 563 I [25] also describes the sampling strategy adopted (i.e., allocation and numerosity). According to this guideline, six different load levels are to be selected (if possible), two of which should be in the limited-life range. The load levels for the determination of the endurance limit must be equally dist  
Figure 6: Logarithmic standard deviation considering failure load cycle numbers in limited-life range for peened gears according to [PERSON] [23]. 38 data points are suggested for a high numerosity experimental campaign. However, the standard allocation is between 20 to 24 test runs. The FVA guideline 563 I [25] also suggests that half of the specimens should be located in the endurance limit region while the remaining should be distributed among the load levels, aiming to have at least two load levels with a higher numerosity. Experimental campaigns with low numerosity are still possible, especially when the focus is primarily on the endurance limit. The runout level (i.e., the limiting load cycle number) is set to 6 million load cycles in pulsator tests. An example of the application of this procedure is shown in Figure 7, where the dotted curve represents the 50% experimental SN curve while the continuous curve is the 1% gear curve. Here it is possible to observe the effect of the hypothesis of a not-constant deviation for the limited life. Indeed, the slopes associated with the limited life slightly vary. Similar to Figure 1, a shaded area has been included to represent the possible choices of \(\mathbf{Y_{NT}}\). The term \"Exp\" refers to the 50% curve estimated considering the experimental point while the term \"Gear\" refers to the gear SN curve (at 1% failure probability).