# Prediction of Process Quality Performance Using Statistical Analysis and Long Short-Term Memory
## 3 Materials and Methods
### Composite Statistical Analysis of PPD
#### 3.2.4 Process Capability Control Analysis  
Process capability control (PCC) is well known and widely used as the criteria of choice to measure manufacturing process performance. PCC has achieved acceptable levels of results of significantly lower costs and higher productivity [9; 10]. PCCA is used to analyze production process quality, which enables manufacturers to understand process quality in real-time [9; 10]. Furthermore, the capability (Cp) and Cpk formulates the results of PCCA, and are mostly used in manufacturing industries to improve production quality with product design specification limits. Specification limits are set by manufacturers to observe the behavior of production processes, as well as the capability of machines. These limits demonstrate how capable the production process is of producing products and can determine whether a process is working within the specification requirements. Figure 5 shows the results of PCCA, determined by the LSL and USL.  
The specification limits are designed by manufacturers for each machine depending on its capability. The average \(\mu\) is the median of the process condition; \(\tau\) is the number of the target products of one day. Cp is calculated using the specification limits and the standard deviation, whereas Cpk is calculated using the specification limits, the standard deviation, and the process mean. They are calculated by the following formulas [8]:  
\[\mathbf{Cp}=\frac{\mathbf{U}\mathbf{S}\mathbf{L}\mathbf{S}\mathbf{L}\mathbf{S }\mathbf{L}}{6\sigma} \tag{13}\]  
\[\mathbf{Cpk}=(\mathbf{1}-\mathbf{k})*\mathbf{cp} \tag{14}\]  
Equation (13) shows the formulas to calculate Cp. Here, \(\sigma\) is the standard deviation of the process condition values. If the average values of the process are within the specification limits, the calculated results can measure whether a process is feasible. Table 1 shows the criteria of process capability.  
Equation (14) is a formula to calculate Cpk. Here, \(k\) is calculated using Equation (15), and it represents the relationship between Cp and Cpk.  
Figure 5: Process capability control analysis.  
\[\mathbf{k}=\frac{\frac{\textbf{(USL+LSL)}}{2}-\mathbf{u}}{\frac{\textbf{(USL-LSL)}}{2}} \tag{15}\]  
where \(u\) is the number of target products of a machine. The calculated result of Cpk is used to determine whether the process is feasible when the average values of the process depart from the median of the specification limits. CpK considers when the average of the processes might not be between the specification limits. Table 2 shows the criteria of Cpk.  
As shown in Tables 1 and 2, if the calculated results of Cp and Cpk are less than \(1\), the process is unfeasible and does not meet the design specification. Conversely, if the calculated results are greater than or equal \(1\), the process is feasible and meets the specifications. Cpk can never be greater than Cp. It is possible to have equal values when the actual process average falls in the middle of the design specifications.