## 5 Conclusions  
As a follow-up to the DBP algorithm, we developed the PPS algorithm to improve the quality of selective assembly processes and optimize computation efficiency. PPS is based on sorting components within slots according to their dimensional similarities and grouping them to assign search priorities. By narrowing the search space, PPS reduces the computation time to one-sixth, significantly improving computational efficiency. Furthermore, by ensuring dimensional diversity within slots, PPS increases the matching rate from 95.11% to 97.09%, leading to a 40% reduction in surplus parts. Additionally, we introduced metrics to validate the potential drawbacks of the PPS algorithm, such as increased tolerance variance, to cross-verify its performance. Apart from performance improvement, the main advantage of the PPS algorithm is its flexibility. Since PPS is based on component dimensional similarities for sorting and grouping, it can be widely applied to selective assembly processes employing slot structures and quality control metrics that are value- or dimension-based. Although this study focuses on a two-dimensional selective assembly process, the proposed PPS algorithm can be easily adapted to handle slot structures with more than two dimensions by making minimal modifications. In summary, PPS is a robust algorithm that achieves both computational efficiency and improved matching rates across a variety of selective assembly applications. Furthermore, its adaptability makes it suitable for addressing additional variables such as the integration of new assembly lines. However, in this study, the PPS algorithm was not tested in real-time operations in an actual production environment. Although the algorithm incorporates priority-based search to reduce computation time, its feasibility for integration with factory PLCs was not validated. Furthermore, it was not tested in a wide range of manufacturing environments; \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Ordinary Algorithm** & \
\begin{tabular}{c} **PPS** \\ **(Stride 5-3)** \\ \end{tabular} &
\begin{tabular}{c} **PPS** \\ **(Stride 2-2)** \\ \end{tabular} \\ \hline Computation time [ms] & 0.060 \(\pm\) 0.237 & 0.022 \(\pm\) 0.150 & 0.010 \(\pm\) 0.099 \\ Matching rate [\%] & 95.11 & 96.54 & 97.09 \\ Cpk & 1.76 & 1.43 & 1.15 \\ Adjusted matching rate [\%] & 95.10 & 96.50 & 97.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Results. Figure 5: Assembled product clearance distribution. (**a**) Ordinary algorithm. (**b**) PPS (stride 5-3). (**c**) PPS (stride 2-2). therefore, additional testing and further research are required to address these limitations. To this end, we will test and improve our algorithm through continuous collaboration with the aforementioned ball bearing manufacturer. Conceptualization: K.S., H.S., and K.J. ; methodology: K.S., H.S., and K.J. : software: K.S. and H.S. ; validation: K.S., H.S., and K.J. ; formal analysis: K.S., H.S., and K.J. ; investigation: K.S., H.S., and K.J. ; resources: K.J. and H.S. ; data curation: K.S. and H.S. ; writing--original draft preparation: K.S., H.S., and K.J. ; writing--review and editing: K.J. and H.S. ; visualization: K.S. and H.S. ; supervision: K.J. ; project administration: K.J. ; funding acquisition: K.J. All authors have read and agreed to the published version of the manuscript. This research was supported by \"Regional Innovation Strategy\" through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (2021 RIS-003). It was also supported by the Ministry of Science and ICT (MSIT), Korea, under the Information Technology Research Center support program (IITP-2024-RS-2024-00438409) supervised by the Institute for Information & Communications Technology Planning & Evaluation (IITP). Not applicable. Data Availability Statement: Data were obtained from NSK Korea Co., Ltd. (Changwon Plant) and are available from the authors with the permission of NSK Korea Co., Ltd. (Changwon Plant).