# An Applicable Predictive Maintenance Framework for the Absence of Run-to-Failure Data
## 6 Additional Experiment  
To verify the reliability of the proposed method, additional experiments were conducted. One additional experiment was a simple experiment investigating how the RUL was predicted, and an isolation forest was used as a comparison method [31; 32]. Isolation forest is a tree-based ensemble method, which is widely used in outlier detection. The hyper-parameter of the isolation forest was selected through grid search, and the number of trees used was 500. The isolation forest outputs a probability value. In this case, the theoretically possible value is between 0 and 1, but in practice, the normal data have a value of about 0.5. Therefore, the failure threshold of this model is defined as the average of these, 0.75. In the general principles of reliability theory, this is a more sensitive threshold because it is assumed that about 15% of the total length are data in which failure occurs [33]. The experiments were all conducted under the same conditions as in the Sections 4 and 5. As the training data for regression, 10 min of data for the pump and 1 week of data for the robot arm were used, respectively. This was settled according to data length. The test samples consisted of data 1 h before failure for each pump, and 1 month before failure for each robot arm, and this was presented by the engineer. Hence, this figure is the starting point of the RUL prediction that the engineer wants to know. Root Mean Square Error (\(RMSE\)) and Mean Absolute Error (\(MAE\)) are used as measurements for evaluating performance [34; 35], which can be computed by the following equations:  
\[RMSE =\frac{1}{n}\sqrt{\sum_{i=1}^{n}d_{i}^{2}} \tag{8}\] \[MAE =\frac{1}{n}\sum_{i=1}^{n}\lvert d_{i}\rvert \tag{9}\]  
where \(n\) is the total number of test data samples. \(d_{i}=RUL_{i}^{{}^{\prime}}-RUL_{i}\) is the difference between the predicted RUL and the actual RUL for the \(i\)-th test data sample. All experiments were performed 10 times, the average was calculated, and the result is shown in the Table 2.  
Table 2 shows the experimental results of the proposed method and the comparative method according to the measurements. The proposed method outperformed with 6 datasets and 6 datasets out of 7, where we used RMSE and MAE as measurements, respectively. In pump cases, the proposed method alternately showed good results in RMSE and MAE. In pump case 1, the threshold was somewhat inaccurate, resulting in relatively \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Pump**} & \multicolumn{2}{c}{**Pump**} & \multicolumn{2}{c}{**Robot Arm**} & \multicolumn{2}{c}{**Robot Arm**} & \multicolumn{2}{c}{**Robot Arm**} & \multicolumn{2}{c}{**Robot Arm**} & \multicolumn{2}{c}{**Robot Arm**} \\  & **Case 1** & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 3**} & \multicolumn{2}{c}{**Case 4**} & \multicolumn{2}{c}{**Case 5**} \\ \hline
**Method** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline Proposed method & 378.67 & 158.07 & 47.64 & 15.72 & 92.08 & 68.82 & 78.32 & 57.75 & 116.89 & 71.59 & 336.05 & 90.90 & 20.65 & 5.01 \\ Isolation forest & 888.69 & 509.43 & 42.38 & 37.54 & 231.30 & 221.70 & 84.23 & 67.35 & 120.89 & 111.29 & 456.76 & 206.77 & 278.68 & 125 \\ \hline \end{tabular}
\end{table} 
Table 2: The result of additional experiment. poor results. In the robot arm cases, the proposed method showed better results in all cases. These results indicate the effectiveness of the proposed method. In particular, in robot arm 5, the threshold was fit, so an accurate result could be obtained. On the contrary, the reasons isolation forest produced poor results are as follows.