## 2 Case Introduction  
This study used bearing connectors processed by a small-scale machinery factory in central Taiwan for a case study. The company's standard operation process was subjected to situation analysis. The case company first purchases raw materials and examines whether the materials meet its quality requirements. Before conducting the numerous processes, parameter setting for the machine tools involved is conducted. Additionally, the selection of cutters is also of great importance. Subsequently, the manufacturing process can be conducted, and a measuring instrument can be used to examine whether the products are within the acceptable tolerance range following the manufacturing process. Products can be packaged and shipped if they pass the inspection. The manufacturing process for the bearing connector is introduced in the following, and the flow chart of the manufacturing process is depicted in Figure 2.  
Explanation of the entire manufacturing process is as follows:  
1. Raw material procurement and inspection: The material is stainless steel, and it is examined for rust or defects. 2. Parameter setting: According to product characteristics, suitable cutters and rotation speeds are selected. Subsequently, CNC program codes are entered to control the automatic manufacturing process of machine tools. 3. External diameter cutting: A lathe is used to conduct processing, with a rotation speed of 3000 rpm. During heavy cutting, the cutters can wear out easily. To ensure processing quality, cutters are given individual codes for easier monitoring of processing time and cutter condition. 4. Internal diameter cutting: The lathe is set at 1500 rpm, and the processing time of cutting the internal diameter of a workpiece to the required tolerance is approximately five minutes. 5. Thread carving: The lathe's rotation speed is set at 2000 rpm and the feeding rate is 20 threads per minute. A cycle involves moving a milling cutter precisely and steadily around the circumference of a workpiece in relative rotation. The grooves that are formed initially guide the forward movement of the milling cutter. 6. Finished product inspection: Examine whether the external diameter, internal diameter, and threads of the product have become deformed due to the cutting. Additionally, whether the product meets the specifications is examined. Products that fail to meet the specifications are eliminated to ensure product quality. 7. Packaging and shipping: protective measures are implemented on products to avoid rusting or friction-induced damage, and products can be shipped after packaging. These steps indicate that bearing connectors are associated with three quality characteristics, namely the internal diameter, external diameter, and threads. These are the key quality items that manufacturers must examine after the whole manufacturing process is completed. Therefore, this study first focused on these crucial nominal-the-best quality characteristics and provided evaluation indices corresponding to manufacturing process quality and time. As mentioned previously, the study of [PERSON] et al. [17] was referenced for the manufacturing time performance index, and the Six Sigma quality indices proposed by [PERSON] et al. [8] were used for quality evaluation. Additionally, an evaluation model concerning both manufacturing time performance and process quality was constructed for the manufacturing process of bearing connectors. The objective was to improve the manufacturing process quality and manufacturing time performance of bearing connectors. A detailed explanation regarding the processing of bearing connectors has been provided in the previous section. Bearing connectors are key components that affect the stability of machine tools, and their process quality directly affects the operational quality of the bearing, which in turn affects the quality of machine tools.