## 5 Discussion  
Figure 11 shows the probability distributions obtained from the fatigue characteristics for S355J2+C material for a stress amplitude \(S_{a}\) equal to 450 MPa and the number of samples \(n\) equal to 9, 21 and 30. It can be seen that the scatter of test results is lower for the smallest number of samples, \(n=9\). This is due to the lower value of the standard deviation \(\sigma\) than the other characteristics, which are shown in Table 3. It can be observed that this value increases as the number of samples increases. However, the \(S\)-\(N\) curve with a small number of specimens is more susceptible to being shifted by adding a new tested point. Additionally, the mean value is more incredible, which can be seen in Figure 11, where the mean value of fatigue life is underestimated for the fatigue curve with 9 specimens. Figure 10: Comparison of S–N characteristics for S355J2+C steel for 30, 21 and 9 samples. As could be expected, a lower value of the standard deviation was obtained, followed by a higher value of the correlation coefficient. However, the error calculated by Equation (5) and the error type II \(\beta\) calculated by Equation (7) are lower for a larger number of test points. So, the correlation coefficient cannot be a criterion for judging the quality of the estimated \(S\)-\(N\) curve. [PERSON] et al., in their paper [39], conducted tests for low alloy forged AISI 8630 M steel in a quenched and tempered condition of the same grade supplied by different suppliers. The tests were performed for alternating axial loading on specimens. They obtained a standard deviation value \(\sigma\) for the S-N characteristics of 0.159 \(\div\) 0.214. The \(\sigma\) for 0.72% steel, presented in Chapter 1, was 0.2166, so it is higher than was obtained for AISI 8630 M and S355]2+C steels. On the other hand, in the recommendations of the International Institute of Welding [40], one can find recommendations for \(n\) < 10 to adopt a \(\sigma\) value of 0.178 for geometrically simple structures between \(10^{4}\div 10^{5}\) cycles and 0.25 for complex structures up to \(10^{6}\) cycles. Based on the presented \(\sigma\) values, it can be concluded that the obtained results are in line with the literature data. In addition, it can be concluded that for a dataset smaller than 10 samples, the resulting scatter of test results (estimated \(\sigma\) value) is unreliable. Figure 11 shows the probability distribution for the S-N characteristics of S355]2+C steel for \(n\) = 9, with a standard deviation \(\sigma\) of 0.25 indicated by the International Institute of Welding [40]. Based on this distribution, with a probability of 5%, a value of 65,770 cycles (the logarithm value is 4.818) is obtained. However, for the probability distribution of \(S\)-\(N\) characteristics for \(S_{a}\) = 450 MPa and the number of samples \(n\) = 30, the fatigue life is 59,538 cycles (the logarithm value is 4.774). This gives a difference of 10% estimation error (the logarithm value is 0.9%). In contrast, the difference in the mean values of these two distributions yields a difference of 42% (169,528 for \(n\) = 9 and 119,035 for \(n\) = 30), and it is higher than the error according to Equation (5), which equals 6.3%. However, the difference in mean logarithm values is 3.03%. It is worth noticing that components with sharp notches have a smaller dispersion of fatigue life, which was shown in a paper [41]. So, using a large value of the standard deviation can reduce the overestimation/underestimation of mean values for notched elements. In addition, the graph in Figure 11 marks the area of rejection of the null hypothesis \(H_{0}\) stating that the mean value of the experiment is equal to the population value. Two-sided testing was adopted for \(\alpha\) equal to 10%. Figure 11: Comparison of S–N characteristic distributions for S\({}_{a}\) = 450 MPa for S355]2+C steel for 30, 21 and 9 samples. Figure 12 shows the dependence of test power on the number of samples.