# Control Chart Concurrent Pattern Classification Using Multi-Label Convolutional Neural Networks
## 1 Introduction
Classification methods include rule-based methods [6], decision trees [18, 19], neural networks [5, 20, 21], and support vector machines [22, 23]. Recently, deep learning (DL) techniques have demonstrated strong capabilities in time series classification, and many studies have begun to focus on the application of deep learning techniques to the classification of control chart patterns [24, 25, 26, 27, 28]. Studies have focused on the identification of basic non-random patterns and, increasingly, on the identification of concurrent patterns (which are combinations of two or more basic patterns appearing simultaneously) [21, 23, 29, 30, 31]. A concurrent pattern  
Figure 1: Typical examples of control chart patterns. indicates that the manufacturing process is affected by multiple assignable causes. To identify concurrent non-random patterns, researchers have often performed pre-processing to smooth the data or extract features. Some examples of pre-processing methods include a wavelet analysis [29; 32; 33], independent component analysis [34], and singular spectrum analysis [35; 36]. This study proposed a novel method of classifying single and concurrent non-random patterns on control charts through the use of a convolutional neural network (CNN) to build a multi-label classifier. To the best of our knowledge, this study is the first to apply a multi-label CNN classifier to control chart concurrent pattern classification. The main ideas of using multi-label CNN are explained as follows. CNNs are most commonly applied to computer vision [37; 38; 39]. Recently, researchers have demonstrated that it is possible to apply CNNs not only to image recognition tasks but also to time series classification tasks [40; 41], which is called one-dimensional convolutional neural network (1D CNN). The primary advantage of CNNs is their ability to automatically learn the important features of a dataset without any hand-crafted feature extraction. The end-to-end classification system performs feature extraction jointly with classification. More importantly, CNN has the ability to learn the translation invariance features from the input [42; 43]. For CCPR, the translation invariance means that the classifier can recognize the pattern regardless of where it appears in the window. This characteristic is extremely important when considering the dynamic nature of the non-random patterns [12]. In previous work, researchers have generally applied multi-class classifiers to concurrent CCPR. This is because a concurrent pattern is treated as a single pattern class. Because a concurrent pattern possesses multiple features, the classification algorithm must allow each sample to have more than one class label. The introduction of multi-label classification into concurrent CCPR is advantageous because the multi-label classification algorithm can predict more than one class label and has a chance of being partially correct; at least one nonrandom pattern being reported is preferable to no pattern being reported. In this study, a multi-label 1D CNN was developed to analyze control chart patterns, and a series of experiments were conducted to assess the performance of the multi-label 1D CNN. The CNN was evaluated using real-world data and datasets from previous studies against traditional classifiers. The method presented here may contribute to the implementation of smart SPC. The organization of the paper is as follows. Section 2 presents the proposed end-to-end multi-label 1D CNN architecture and a brief description of the traditional classifiers evaluated in this study. Subsequently, a set of performance metrics suitable for multi-label classification is given. Section 3 details the evaluation of the proposed approach against traditional classifiers. Section 4 presents the application of the proposed approach to real-world data from industry. Finally, the study is concluded and directions for future research are discussed.