## 5 Conclusions  
This paper introduces a novel method designed to provide a simple yet effective prognostic algorithm, particularly suitable for real-world situations where obtaining multiple sets of degradation data is very difficult. To achieve this, a stepwise linear regression method is proposed to approximate nonlinear degradation behavior. The proposed method demonstrates higher accuracy while reducing computational time by a factor of 50 to 60 compared to that of a typical ANN, which is one of the simplest models among its variations. Additionally, while the median prediction error from the ANN increases sig  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Methods** \\ **(Calculation Time)** \\ \end{tabular} } & \multirow{2}{*}{**Percentile**} & \multicolumn{5}{c}{**Error (\%)**} \\ \cline{3-7}  & & **2600 Cycle** & **2700 Cycle** & **2800 Cycle** & **2900 Cycle** & **3000 Cycle** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Proposed method \\ (34 s) \\ \end{tabular} } & 5 & 0.61 & 2.60 & 0.25 & 0.09 & 0.11 \\  & 50 & 12.20 & 11.05 & 4.34 & 1.55 & 0.81 \\  & 95 & 66.10 & 33.23 & 14.52 & 7.93 & 2.31 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} ANN \\ (2145 s) \\ \end{tabular} } & 5 & 17.76 & 6.62 & 5.52 & 1.60 & 0.41 \\  & 50 & N/A & N/A & 15.52 & 5.54 & 2.18 \\ \cline{1-1}  & 95 & N/A & N/A & N/A & 13.20 & 3.97 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of prediction error percentiles for the proposed method and ANN using 97 data sets at a noise level of 2 mm.  
Figure 13: Prediction results using 97 data sets at a noise level of 2 mm: (**a**) RUL prediction from the proposed method; (**b**) RUL prediction from the ANN; (**c**) prediction error from the proposed method; (**d**) prediction error from the ANN.  
nificantly when the noise level in the data doubles, the proposed method remains robust and consistent.  
Although the prediction performance of the ANN in this study could potentially be improved by fine-tuning hyperparameters related to the training process, the effort required may outweigh the benefits. Furthermore, while the ANN may outperform the proposed method if multiple sets of degradation data are available, obtaining even a single degradation data set is highly challenging in practice. Thus, given the practical constraint of having only a single degradation data set, the proposed method is promising for real-world applications. It offers consistently high accuracy, simplicity of implementation, and most notably, computational efficiency compared to the ANN.  
In real-world scenarios, however, degradation data are often obtained as sensor signals (e.g., vibration, current, and voltage) rather than being directly measured. To further enhance the practicality of the proposed method under this condition, a feature extraction step will be considered in future studies.  
This study has been conducted with the support of the Korea Institute of Industrial Technology as \"Development of Core Technologies for a Working Partner Robot in the Manufacturing Field (kitech EO-24-0007)\" and the Industrial Technology Innovation Program (RS-2024-00422721, Development of safe and reliable XAI-based robotic workcell safety sensors and control modules) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea).  
Not applicable.  
The data presented in this study are available in Section 4.1.1. Data Generation.  
The author declares no conflicts of interest.