# Prediction of Process Quality Performance Using Statistical Analysis and Long Short-Term Memory
## 1 Introduction  
The fourth industrial revolution (Industry 4.0) refers to the current trend of automation and data exchange in the manufacturing industry. It is a term for the developmental processes and chain of production in the management of manufacturing. In recent years, manufacturing processes have become more complex [1]. High complexity of manufacturing processes and continuously growing amounts of data lead to excessive demands on manufacturers with respect to production process monitoring and data analysis. Quality control has always been an integral part of manufacturing [2]. The internet of things (IoT) allows for data collection at every point of the manufacturing process, using networked sensors and intelligent devices and putting those technologies to use directly on the manufacturing floor, collecting data to drive artificial intelligence (AI) and predictive analytics [3, 4]. A huge increase in data volume has created a new paradigm in product quality management and predictive maintenance [5]. Not only does it rely on specific information pulled from each machine to analyze, detect, and predict potential problems, but it also increases productivity, improves product quality, and provides reliability tomanufacturers. Predictive maintenance, production monitoring, and quality control are intimately linked with each other [6,7]. It is essential to maintain manufacturing processes in a stable condition to achieve high productivity and reduce failures. Consider a manufacturing environment where most facilities repeatedly and periodically make the same products with certain properties. In this case, several process condition variables represent these properties that are used collectively to determine facilities' process capability and performance. The representative process condition variables are Cpk (Process Capability Index) and Ppk (Process Performance Index) [8, 9, 10, 11, 12], X-chart and R-chart [13, 14, 15], and production cycle time [16], which are described in detail in Section 3. We can determine the state of the manufacturing processes based on measuring these process condition variables between upper specification limit (USL) and lower specification limit (LSL). In other words, if the measures are in the normal scope, then a manufacturing process is in stable condition. Otherwise, it is unstable. One of the essential applications of utilizing process condition variables is predictive maintenance in smart manufacturing. That is, we can collect process condition variables over time by monitoring the states of product manufacturing and use these variables to predict possible failures, process capability, and performance in the future. Recently, deep learning algorithms have been actively studied in smart manufacturing to achieve predictive maintenance. Among deep learning algorithms, LSTM is especially appealing for predictive maintenance because it is suitable for learning complex sequences and functions over longer periods of time to detect failure patterns [17]. Even if there are many studies to measure the process capability and performance, the results are still not satisfactory. That is, the existing studies consider factors that do not fully reflect the manufacturing process of products or consider them separately. Considering that the smart manufacturing environment can accommodate the big data collected from various facilities, we need to understand the state of the process by comprehensively considering diverse factors contained in the manufacturing. In this paper, we propose a methodology for predicting process quality performance (PQP) using statistical analysis and LSTM. More specifically, this paper has two objectives. The first objective is to define a PQP as a new process capability and performance measurement tool by simultaneously considering the composite statistical process factors containing manufacturing cycle time analysis, process trajectory of abnormal detection, statistical process control analysis, and process capability control analysis.