# Control Chart Concurrent Pattern Classification Using Multi-Label Convolutional Neural Networks
## 1 Introduction  
Control charts are a statistical process control (SPC) tool used to determine if a manufacturing or business process is behaving as intended. When a non-random pattern appears on the control chart, it suggests that there exist one or more assignable causes which will gradually deteriorate the process/product quality. The presence of assignable causes requires instant investigation of the process, including the identification of root causes and implementing corrective actions. It was recognized that non-random patterns can provide relevant information about process diagnosis. [PERSON] [1] pointed out that every non-random pattern is mapped to a set of assignable causes. Therefore, if the pattern type can be correctly recognized and identified, it will help to diagnose the possible causes of the manufacturing process problem. The statistical quality control manual of the Western Electric Company [2] first described the non-random patterns that often appeared on control charts, and proposed a set of zone tests for analyzing the patterns. Figure 1 illustrates several representative examples of control chart patterns. A normal pattern (NOR) only exhibits random variations (Figure 1a). In stratification (STRA), the points tend to cluster around the center line. Figure 1b illustrates an example of stratification. In systematic variations (SYS), a high point is always followed by a low one or vice versa (Figure 1c). A cycle (CYC) can be recognized by a series of high portions or peaks interspersed with low portions or troughs. A typical example is shown in Figure 1d. A trend is characterized by a continuous movement in one direction. Figure 1e illustrates an upward trend (UT) and Figure 1f a downwardtrend (DT). A shift is a sudden or abrupt change in the average of the process. Figure 1g depicts an upward shift (US) and Figure 1h a downward shift (DS). In a mixture (MIX) pattern, the points tend to fall near the high and low edge of the pattern with an absence of points near the center (Figure 1i). A mixture is caused by the combination of data from two or more distributions. [PERSON] [3,4] also proposed a set of runs rules for analyzing non-random patterns of control charts. Zone tests and runs rules are usually referred to as sensitizing rules or supplementary rules [1]. These rules are easy to use and have been adopted in many statistical packages (e.g., Minitab). However, the application of the aforementioned sensitizing rules is not without its drawbacks, because no one-to-one mapping between the rules and non-random patterns exists [5]. In response to the limitations of the sensitizing rules, many researchers have applied pattern recognition to the analysis of control chart patterns [5, 6, 7, 8]. In the past, researchers have used machine learning (ML) algorithms to build pattern classifiers to identify non-random patterns in manufacturing process data. The task is commonly referred to as control chart pattern recognition (CCPR). [PERSON] and [PERSON] [9] comprehensively reviewed the literature on the application of neural networks to SPC. [PERSON] and [PERSON] [10] and [PERSON] [11] reviewed the literature on the application of neural networks in CCPR. [PERSON] and [PERSON] [12] discussed recent research on control chart patterns and proposed some directions for future research. With the development of the industrial internet of things (IIOTs) and artificial intelligence (AI), collecting process data and applying intelligent decision-making models for analysis have become more feasible than before. Researchers have focused on using advanced methods to improve the accuracy of CCPR. In the following, we provide a summary and analysis of the relevant publications on the topic of control chart pattern recognition. In research on CCPR, the pattern can be expressed in the form of original data or features [12]. Most methods that use features have relied on hand-crafted features, including shape features [13, 14, 15], multi-resolution wavelet features [16] and statistical features [17].