1. Introduction
The control chart is an essential tool to monitor whether the manufacturing process is in control or not. There are several key practical efficiencies of using the control chart. First, it is an effective tool for improving the stability of manufacturing processes [
1,
2]. Second, it provides indicative information which can effectively prevent potential defects [
3]. Third, the information on manufacturing system ability is provided [
4].
As first proposed by Shewhart, a control chart is composed of two elements: three straight lines parallel to the horizontal axis and sampled observations in chronological order [
5]. The traditional control chart is widely used, but there are still some limitations: (1) Analysis methods based on traditional judgment rules cannot point out all abnormal situations. (2) It only focuses on whether the observations are within limits or not, and it cannot provide potential information of previous observations. (3) It cannot provide more clues of abnormal situations, so it is difficult to find out assignable causes. With the development of statistical process control (SPC) and computer technology, the appearance of control chart patterns (CCPs) overcomes these limitations of the traditional control chart. The CCP is composed of continuous points that reflect fluctuations in manufacturing processes [
6]. As such, the application of a CCP is exceptionally useful for a rapid diagnosis of any abnormal causal pattern and then for the formulation of a treatment scheme.
Fifteen types of CCPs are introduced in the Statistical Quality Control Handbook [
7]. The normal pattern (NOR), cycle pattern (CYC), upward trend pattern (UT), downward trend pattern (DT), upward shift pattern (US), downward shift pattern (DS) and system pattern (SYS) are basic patterns, while the remaining types are combinations of a single pattern and some other special patterns. Since each type of abnormal pattern corresponds to a particular assignable cause [
8], control chart pattern recognition (CCPR) dramatically reduces the search scope for abnormal causes. In practice, the type of CCP always corresponds to some specific assignable causes. Thus, CCPR can quickly recognize anomalies in charts, making it an important tool for narrowing the search scope of abnormal causes. The workload of inspectors will be significantly decreased. Developing the CCPR scheme is important for finding out the assignable cause.
In the past, most studies have concentrated on improving the recognition accuracy of CCPs. The rule-based expert system method was originally proposed by Alexander and Jagannathan, who proved that the CCP could be explained and analyzed according to artificial experience [
9]. With this breakthrough, excessive false alarms emerged as a critical defect of the system. Subsequently, despite the abundance of research into these problems, recognition accuracy remained low [
10]. With the development of computer technology, machine-learning algorithms have been employed in the CCPR field. For example, artificial neural networks [
11], support vector machine (SVM) [
12,
13,
14], random forest [
15], decision tree [
16,
17], fuzzy systems [
12] and other algorithms have performed well for CCPR. As a result, recognition accuracy improved dramatically so that a multilayer perceptual neural network identified six types of CCPs with an accuracy of 99.15% [
18]. Ranaee, Ebrahimzadeh and Ghaderi [
19] applied an improved particle swarm algorithm to optimize SVM, and the recognition accuracy is 99.58%. Kalteh and Babouei [
20] suggested an adaptive neuro-fuzzy inference system recognition method based on the intelligent application of shape and statistical features. Meanwhile, a chaotic whale optimization algorithm was used to optimize every layer of the classifier, allowing the recognition accuracy to reach 99.77%.
In the literature, most of the existing research assumes that observations at different time points are normal, independent and identically distributed (NIID). Unfortunately, this assumption cannot satisfy flow industries [
21], as for instance, there could be autocorrelation in chemical, pharmaceutical or metallurgical industries. Moreover, with the development of sensor technology, more and more advanced acquisition systems have been employed in production to collect process data [
22]. Due to the acquisition method of high-frequency data, the time interval is extremely short between adjacent observations, and as a result, there is an inevitable autocorrelation [
23].
If the NIID-based CCPR models are directly employed to monitor the autocorrelated process, there will be a great number of false alarms. At present, there are several studies considering autocorrelated processes in CCPR. Cheng and Cheng [
24] used a ruled-based neural network as a classifier to identify five types of abnormal CCPs in autocorrelated processes and employed the Haar discrete wavelet transform for decorrelation and feature extraction. Lin, Guh and Shiue [
25] proposed a CCPR model based on SVM for the online recognition of seven abnormal CCPs. The simulation results indicated that the method based on SVM had a better performance compared with the learning vector quantization (LVQ) network. In another study, Yang and Zhou [
26] developed an integrated neural network based on the LVQ network. Every individual backpropagation network was trained to identify each pattern with the specific autoregressive coefficient, and the outputs of all backpropagation networks were combined by the LVQ network. In these papers, the process mean was assumed to be the first-order autoregressive (AR(1)) process, and the discrete autoregressive coefficients (−0.9, …, 0.9) were selected to represent various autocorrelated levels. Shao et al. [
27] proposed a two-stage framework to recognize seven kinds of both single and concurrent CCPs by assuming the autocorrelated processes, and the accurate identification rate is employed to evaluate the performance. De and Pham [
21] first considered that the inherent noise was expressed by the AR(1) model and applied a pattern generation scheme (PGS) to generate datasets. Then, the CCPR model based on the NIID assumption was used to recognize CCPs in autocorrelated processes. Compared with the NO-PGS and PGS datasets, it becomes clear that the former scheme has great recognition accuracy. However, given that a host of samples were discarded when PGS was applied to generate CCP samples, this recognition rate is overestimated.
The existing researches on CCPR have established the autocorrelated model in two ways: one assumes that the process mean follows an AR(1) model, and the other assumes that the inherent noise follows an AR(1) model. If both the process mean and the inherent noise obey the AR(1) model, the two models are equivalent when the process mean is set to zero. In other instances, when the process mean is described by the AR(1) model, there will be a remarkable deviation that can be monitored and recognized easily. For this reason, it is important to identify CCPs in tiny autocorrelated processes by assuming that the inherent noise follows AR(1).
In this paper, a novel scheme is proposed to recognize the control chart patterns in autocorrelated processes, in which the one-dimensional convolutional neural network (1DCNN) is utilized to extract features, and the grey-wolf-optimizer-based support vector machine (GWOSVM) is used as the classifier. The novel scheme provides a very appealing option for the CCPR at a wide range of autocorrelation levels and different types of patterns. Experiments show that the proposed scheme is comparable for some levels of autocorrelation and better for overall accuracy. The rest of this study is organized as follows.
Section 2 introduces the basic concepts comprising the convolutional neural network (CNN) and SVM algorithms.
Section 3 describes the proposed scheme, and
Section 4 contains a series of experimental results and discussions. Finally,
Section 5 presents the conclusion.
3. The Proposed 1DCNN-GWOSVM Scheme
A novel scheme to recognize CCPs is proposed for autocorrelated processes, and
Figure 2 shows the flowchart. In detail, the 1DCNN is employed to extract features from autocorrelated CCP inputs, while the SVM optimized by the GWO algorithm is utilized as the classifier to recognize which type the input CCP belongs to. For the sake of simplicity, this paper refers to the proposed scheme simply as the 1DCNN-GWOSVM scheme. The proposed scheme is implemented in three stages.
Stage 1: Data Generation. As discussed in one review [
32], due to the lack of fully documented public databases, 41 out of 44 papers evaluated the performance of the CCPR models by simulated data, while only 3 papers implemented real data in their studies. In this study, a large number of CCP samples are generated by the Monte-Carlo method, which is usually applied to generate CCPs both for training and testing. In this study, the process mean, inherent noise and abnormal disturbances components were utilized to generate the data points for the seven CCPs [
21]. The specific expressions are given by the following:
where
represents the observation at time,
;
indicates the process mean;
represents the inherent noise at time,
; and
represents an abnormal disturbance.
The inherent noise is assumed to follow the AR(1) model, which is given by the following:
where
indicates the inherent noise at time,
;
is autoregressive coefficient;
is a white noise and obeys the standard normal distribution; and
.
Based on Equations (1) and (2), the expressions of different typical CCPs are defined below.
The NOR pattern is expressed by the following:
The CYC pattern is expressed by the following:
where
and
represent the amplitude and period of a cycle, respectively.
The UT and DT patterns are expressed by the following:
where
is the slope of a trend, the UT pattern employs the mark “
” and the DT pattern applies the mark “
”.
The US and DS patterns are expressed by the following:
where
represents the shift position,
indicates the shift magnitude, the US pattern generated employs the mark “
” and the DS pattern applies the mark “
”.
The SYS pattern is expressed by the following:
where
represents the systematic departure.
In this study, eight datasets at different autocorrelation levels were generated to validate the performance of the proposed 1DCNN-GWOSVM scheme.
Stage 2: Extract features. The CCPs generated from Stage 1 served as the inputs of the 1DCNN model. Two convolution layers and two pooling layers were alternatively used to select, extract and optimize the features of CCPs. The fully connected layer was used to expand and splice together the features that were extracted from the convolution and pooling layers. The ReLU activation function was used in the convolution layer, while the average pooling function was utilized in the pooling layer. In order to make the extracted features more prominent, the weights, biases and parameters of the convolution and pooling layers were optimized by the backpropagation algorithm. The extracted features were then output in the fully connected layer. The structure diagram of the 1DCNN feature extraction is shown in
Figure 3.
Stage 3: Build the GWOSVM classifier. The SVM is employed as the classifier, and the features extracted from Stage 2 serve as the inputs. For the SVM classifier, the penalty term and the kernel function parameter
g have a great impact on its classification performance. The GWO algorithm [
33] is a new intelligence optimization algorithm inspired by the predatory activity of grey wolves, such as hunting, encircling and attacking their prey. Its advantages are its strong convergence, its few parameters and its readiness for implementation, accomplished through its simulation of social hierarchy and predatory behavior. Therefore, the parameters of SVM are optimized by the GWO algorithm to gain the optimal parameters, abbreviated as the GWOSVM classifier.
The proposed 1DCNN-GWOSVM scheme aims to recognize a CCP and identify its type in actual manufacturing processes. Identifying the type of abnormal CCP greatly narrows the search scope of the abnormal cause. The type of each CCP corresponds to possible causes [
20,
34], which are shown in
Table 1.