## 5 Discussion  
### Discussion on the Results of Dataset 1  
As previously mentioned, the experimental accelerated life test data included seven run-to-failure tests, classified into two groups according to the type of final observed failure (Table 3). This subsection describes the application of the results of the FT estimation by the three models in Section 4.1 to these run-to-failure tests in order to compare their outputs. The graphs in Figure 11 illustrate the trends for the vibration peak feature for three tests corresponding to inner race failure. In these graphs, three proposed values for the FT using the three models described in Section 4.1 are shown. The EoL estimation of each model is depicted by a star (*) on the trend. As can be seen, the estimated EoLs of the first and second models were close together and represent more conservative failure points than the third model. However, all of the models prevented unstable vibration. Also, the third model provided a more extended lifetime. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **PCC** \\ \hline Peak amplitude & 0.9548 \\ \hline Peak-to-peak amplitude & 0.9548 \\ \hline Root mean square & 0.9053 \\ \hline Standard deviation & 0.9053 \\ \hline Shape factor & 0.8669 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Correlation of time signal features with PC\({}_{1}\). Figure 10: Estimated FT distribution for dataset 2. Similarly, the trends for the vibration peak in the four tests with the rolling element failure are shown in Figure 12. In this figure, it can be seen that the first and second models estimated the same EoL for all four tests. The third model also estimated a similar EoL in three tests out of four. However, in one test (test 7), the EoL estimated by model 3 was somewhat later than the two other models. The results of the three FT estimation models with regard to useful life for the seven tests are given in Table 12. The parameter \(\Delta\) is used to show the difference in useful life between the proposed models and the predetermined test stop criterion. The reader should note that this difference does not represent the error of the models presented in this paper since the predetermined criterion is just an assumption for stopping the tests and not the ideal. Figure 11: Comparison of the FT models in the tests for inner race faults. The highest value of \(\Delta\) was obtained in test 2. Comparing the vibration trends from all seven tests reveals the different behavior of the REB degradation in test 2. The vibration trend started to grow gradually from the beginning of its life. Furthermore, this REB had a relatively short life. The lack of a healthy stage in this test (unlike in the others) led to the high value of \(\Delta\). Comparing the degradation trends for two groups of data shows that the degradation data included a soft failure stage when the growing defect was on the inner race. However, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Mode**} & \multirow{2}{*}{**Test No.**} & \multirow{2}{*}{
\begin{tabular}{c} **Test Duration** \\ **(s)** \\ \end{tabular} } & \multicolumn{4}{c}{**Useful Life (s)**} & \multicolumn{4}{c}{**\(\Delta\) (\%) 1**} \\ \cline{3-8}  & & & **Model 1** & **Model 2** & **Model 3** & **Model 1** & **Model 2** & **Model 3** \\ \hline \multirow{3}{*}{Inner race} & 1 & 10,961 & 9804 & 10,490 & 10,830 & 10.56 & 4.30 & 1.20 \\  & 2 & 4181 & 342 & 342 & 1482 & 91.82 & 91.82 & 64.55 \\  & 4 & 26,448 & 24,530 & 25,230 & 25,750 & 7.14 & 4.61 & 2.64 \\ \hline \multirow{3}{*}{Rolling element} & 3 & 81,535 & 78,660 & 78,660 & 78,660 & 3.53 & 3.53 & 3.53 \\  & 5 & 30,450 & 27,550 & 27,550 & 27,550 & 9.52 & 9.52 & 9.52 \\  & 6 & 6498 & 6032 & 6032 & 6032 & 7.17 & 7.17 & 7.17 \\  & 7 & 5546 & 4596 & 4596 & 5192 & 17.13 & 17.13 & 6.38 \\ \hline \hline \end{tabular}  
* \({}^{1}\)\(\Delta=1\)–useful life/test duration.  
\end{table} 
Table 12: The effect of FTs on REB useful life. Figure 12: Comparison of the FT models in the tests for rolling element faults.