# Prediction of Process Quality Performance Using Statistical Analysis and Long Short-Term Memory
## 3 Materials and Methods
### Composite Statistical Analysis of PPD
#### 3.2.1 Manufacturing Cycle Time Analysis  
Cycle time (Ct) is widely known as an essential measure of performance in the manufacturing industry [26]. Manufacturing cycle time (MCt) measures the duration of every  
Figure 2: Composite statistical analysis of PPA.  
process move in a production line [27]. Ct plays an essential role in controlling parameters in the manufacturing process. Specifically, as the manufacturing process may become complex, Ct makes it possible to improve the system by breaking the product cycle times into workpieces to understand the duration of each piece. In other words, operational workpieces can improve product cycle time and increase understanding of the duration of producing each product. In this paper, we propose an MCtA method to analyze duration patterns in producing good and defective products. The proposed MCtA contains four elements: workpiece cycle time (WCt), process cycle time (PrCt), process interval cycle time (PInCt), and production cycle time (PCt). Figure 3 demonstrates the MCtA proposed in this paper.  
From Figure 3, we can observe that typical manufacturing process contains several WCt, which is the duration of loading product components into machines. This loading process might start before or after the previous WCt end time. The calculation of WCt is given as in the following Equation (1):  
\[\text{WCt}=\sum_{i=0}^{n}\text{WCt}_{i}=\text{wet}_{i}-\text{wet}_{i} \tag{1}\]  
where \(\text{WCt}_{i}\) is the workpiece cycle time of the \(i\)th product and \(n\) is the total number of products in the manufacturing process. Besides, \(\text{wet}_{i}\) and \(\text{wet}_{i}\) are the start time and end time of the WCt for the \(i\)th product, respectively.  
PrCt is the duration for producing a single product that may contain many pieces. The calculation of PrCt is shown as in the formula Equation (2):  
\[\text{PrCt}=\sum_{i=0}^{n}\text{PrCt}_{i}=\text{pet}_{i}-\text{pst}_{i} \tag{2}\]  
where \(\text{PrCt}_{i}\) is the process cycle time of the \(i\)th product and \(n\) is the total number of products. \(\text{pst}_{i}\) and \(\text{pet}_{i}\) are the start time and end time of the PrCt for the \(i\)th product, respectively.  
In a typical manufacturing process, a product contains many pieces. PInCt refers to the duration of producing a piece of product. For an example, when an imbalanced pressure is in the process of producing a piece of product, this can cause product failure. A high-pressure value has a long duration, calculated by the following Equation (3):  
\[\text{PInCt}=\sum_{i=0}^{n}\text{PInCt}_{i}=\text{piet}_{i}-\text{pist}_{i} \tag{3}\]  
where PInCt\({}_{i}\) is the process interval cycle time of the \(i\)th product and \(n\) is the total number of products. \(\text{pist}_{i}\) and \(\text{piet}_{i}\) are the start time and end time of the PInCt for the \(i\)th product, respectively.  
Figure 3: Process of MCtA.  
PCt is the duration from the end of a process of one WCt in a machine to the start of another WCt in the same machine. The PCt is calculated by:  
\[\text{PCt}=\sum_{i=0}^{n}\text{PCt}_{i}=\text{wst}_{i+1}-\text{wst}_{i} \tag{4}\]  
where \(\text{PCt}_{i}\) is the production cycle time of the \(i\)th product and \(n\) is the total number of products; \(\text{wst}_{i+1}\) and \(\text{wst}_{i}\) are the start time of the production cycle for the \((i+1)\)th and \(i\)th products, respectively.  
The aforementioned elements (i.e., WCt, PrCt, PInCt, and PCt) enable us to analyze the time it takes to perform one repetition of any product, generally measured from the starting point of one product in a machine to the starting point of another product in the same machine.