## 6 Conclusions  
Process Capability Indices (PCIs, which are commonly adopted by the industry, are functions of accuracy index \(\delta\) and precision index \(\gamma\). Accuracy index \(\delta\) focuses on measuring the degree to which process mean \(\mu\) deviates from process target value \(T\). As the value is closer to 0, the process is more accurate. Precision index \(\gamma\) mainly represents the size of process variation. As the value is smaller, the process variation is smaller. That is to say, the process Is more precise. It is obvious that accuracy index \(\delta\) and precision index \(\gamma\) are two important parameters of the process capability index, as well as two important indices for evaluating the process quality level. For example, when \(|\delta|\leq 1.5/k\) and \(\gamma\leq 1/k\), then the process quality reaches the \(k\)-sigma quality level [20]. Raising the process precision and process accuracy can increase the values of process capability indices as well. Therefore, the \(\delta-\gamma\) control charts were derived to monitor process accuracy and precision based on in-control data. This study used the unbiased estimator of accuracy index \(\delta\) to derive the three-sigma control chart of index \(\delta\) and discovered the upper control limit, the center limit, and the lower control limit. Similarly, this study employed the unbiased estimator of precision index \(\gamma\) to derive the three-sigma control chart and found the upper control limit, the center limit, and the lower control limit. Table 1 provides the values of items \(b_{n}\), \(A_{n}\), \(B_{n}\), and \(B_{n}^{\prime}\) to help the quality control engineer figure out the control limits of these two control charts, so as to monitor the process accuracy and precision. When the process precision and accuracy became stable, the statistical testing method proposed by this study was applied to the evaluation of process capability. Then, according to the normal process, it was learned that the sample mean and the sample variation were independent. In this paper, the \(100(1-\alpha)\%\) confidence region of \((\delta,\gamma)\) was first derived, and then confidence interval \(CR_{\delta}\) for index \(\delta\) and confidence interval \(CR_{\gamma}\) for index \(\gamma\) were defined based on this confidence region. Subsequently, this study made the testing rules based on \(CR_{\delta}\) and \(CR_{\gamma}\). First, considering the definition of the six-sigma quality level, we examined whether the process could reach the six-sigma quality level. Second, when the process failed to reach the six-sigma quality level, the statistical testing method of accuracy and precision indices was adopted to come up with a direction for process improvement, such as correcting the direction of process deviation and deciding whether to reduce process variation. Finally, this study presented an empirical case to prove the feasibility of the proposed model. To sum up, we have provided a mechanism for monitoring, evaluating, and improving the normal process quality through the statistical testing method, which has the following advantages and functions:  
1. The accuracy and precision control charts developed by this study can assist quality control engineers with the calculation of the control limits of these two control charts, so that they can supervise the accuracy and precision of the process. 2. The statistical testing method and the definition of the six-sigma quality level can help evaluate whether the precision and accuracy of the process meet the required level and decide whether to make improvements. 3. Accuracy index \(\delta\) and precision index \(\gamma\) are not only two important parameters of the process capability index but also two important indices for evaluating the process quality level. Therefore, when the process accuracy and precision reach the required level, then both the process capability and the six-sigma quality level can meet requirements.