## 1 Introduction
In a case study involving shaft and hole assembly, the hybrid approach demonstrated a cost reduction of approximately 45.8% compared to conventional selective assembly methods. However, this method has a limitation, namely that it is difficult to apply to processes with low flexibility in the process structure. [PERSON], [PERSON], and [PERSON] designed a selective assembly algorithm that deals with the design tolerances of holes and shafts [20]; they categorized the dimensional boundaries of each shaft and hole into groups of nonbasic mating sizes and further subdivided them into clearance fit, interference fit, and transition fit. Depending on the case, they applied specific process techniques such as re-machining, measurement, assessment, and marking. [PERSON] proposed a simulation model for selective assembly [21] and introduced a block diagram of the information control system to optimize the process and improve accuracy [22] by employing a selective assembly algorithm and a complementary five-step block diagram comprising a measuring device, an estimation subsystem, a control subsystem, a communication channel, an output device, and an assembly machine, and error reduction and efficiency improvement were achieved. [PERSON] and [PERSON] presented algorithms based on statistical figures and the z-group to increase matching accuracy [23]. The above studies focused on single-parameter selective assembly, indicating the need to expand this framework to multiparameter assembly systems. [PERSON] and [PERSON] proposed the density-based prioritization (DBP) algorithm to minimize surplus parts by prioritizing the selection of parts according to their dimensional density [24]. This algorithm has significant benefits in increasing the matching rate while reducing the computational complexity of the assembly process. This is suitable for a process where parts are continuously fed, such as ball bearings, and a combination of parts is selected in a short time to produce the assembly result. However, a critical limitation of this algorithm is its lack of considering how close the assembled dimensions are to the ideal dimensions. This can lead to a uniform distribution of assembled dimensions within the tolerance band, significantly limiting the process capability, which is a measure of a process's ability to produce parts within specified tolerances. Considering the inherent limitations of the DBP approach, in this study, we introduce the predominance preferential selection (PPS) algorithm; this algorithm addresses the surplus parts issue and improves process capability. Unlike the DBP algorithm, the PPS algorithm incorporates a novel technique of grouping priorities into specific units, treating them as equivalent in priority. This methodology ensures that from the available combinations of parts with the same priority, the combination of parts with dimensions closest to the ideal dimensions is selected. Such an approach naturally resolves the above-mentioned process capability problem by promoting a distribution of assembled dimensions that are tighter and more aligned with the ideal dimensions. The PPS algorithm can also be applied to multiple-slot row structures because of its improved versatility and scalability compared with other algorithms. In contrast, the DBP algorithm, which was designed for assembly facilities employing a one-slot row, exhibits difficulties in prioritizing parts across multiple components because of the conflicting priority orders in assembly facilities employing more than one slot row. By grouping priorities, the PPS algorithm seamlessly integrates multiple priority orders into a unified sequence; thus, it can be applied to complex assembly facilities that feature multiple-slot rows. Its scalability is particularly important in modern manufacturing lines, which increasingly rely on the efficient assembly of multiple components to meet high precision and quality standards.