A control chart pattern recognition system using a statistical ...

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206 J.-H. Yang, M.-S. Yang / Computers & Industrial Engineering 48 (2005) 205–221 for monitoring variations in the product manufacturing process. However, these control charts do not provide pattern-related information because they focus only on the latest plotted data points. In other words, only the last point on the chart is examined rather than the trend in the process over time. The value of average run length (ARL) is usually used to measure the frequency before the process is out-of-control. ARL is generally defined as the average number of points in a control chart until an out-ofcontrol signal occurs. Under a normal distribution N(m,s 2 ) assumption with its mean m and variance s 2 ,it is called out-of-control when its value is outside the range of G3s from the mean m. In general, it is unavoidable due to a random noise even though in a regular condition. For example, when we have a production process that the quality of products is under the N(0,1) assumption, the probability P(X%K3 or XR3)Z0.0027 such that 1/0.0027z370.4. Thus, ARL under the N(0,1) assumption is around 370.4. Similarly, for mZ0.5 with s 2 Z1, ARL is around 155.2. The ARL value for other mean shift m with s 2 Z1 is shown in Table 1. We can see that ARL will be decreasing when a mean shift m is increasing. We know that the smaller ARL exhibits out-of-control signal more often. In this case, it is not good for detecting abnormal process behavior with a Shewhart control chart because it is variable due to a mean shift m. Therefore, the control chart pattern recognition is important for recognizing unnatural patterns in control charts. Control chart pattern recognition has the capability to recognize unnatural patterns. In general, there are six unnatural patterns in control charts. They are upward trend, downward trend, upward shift, downward shift, cycle and systematic variation. These patterns present the long-term behavior of a process. If any of these patterns appears, something has occurred in the process such as a change of raw materials, equipment damage or the state of workers. If we can have such information on hand and then make decisions on the process, it will help us prevent failures appearing in the future. There have been many studies on control chart pattern recognition (see Al-Ghanim & Ludeman, 1997; Cheng, 1997; Guh & Hsieh, 1999; Pham & Oztemel, 1994; Yang & Yang, 2002). Recently, Guh (2003) proposed a hybrid artificial intelligence technique that consists of three major sub-systems so that it can be well used to build a real time SPC system. Most of these studies are considered for recognizing a single unnatural control chart pattern. However, in most real control chart applications, normal points may appear before abnormal points so that a change point from normal to abnormal may occur at any point in control charts. If we do not have a mechanism for recognizing such change patterns, we may incorrectly obtain the classification results. Therefore, under these circumstances, even though we have a good classification method for the control chart pattern recognition, we may still make an incorrect decision. Table 1 Average run length with a mean shift m m ARL 0 370.4 0.5 155.2 1 43.9 1.5 15 2 6.3 2.5 3.2 3 2
J.-H. Yang, M.-S. Yang / Computers & Industrial Engineering 48 (2005) 205–221 207 Another practical situation is concurrent patterns where two unnatural patterns may exist together. For recognizing concurrent unnatural patterns, Guh & Tannock (1999) used a back-propagation network (BPN) learning to perform the recognition for these concurrent control chart patterns. Although this BPN has a learning structure with a good network construction, the approach to the control chart pattern recognition is slow and complicated with a learning process. In this paper we propose a simple mechanism to recognize these unnatural patterns. The statistical correlation coefficient approach is used to construct a control chart pattern recognition system. By adding a threshold criterion, we can recognize these unnatural patterns even though they may change from normal to abnormal at any point in control charts. The remainder of this paper is organized as follows. In Section 2 we explain why a statistical correlation coefficient method is proposed and then present the proposed approach with the training and classification algorithms. Some simulation results and their comparisons are presented in Section 3. In Section 4, we present the performance for recognizing concurrent control chart patterns. Conclusions will be stated in Section 5. 2. The proposed control chart pattern recognition system Since control chart pattern recognition is an important step for industrial production processes, many researchers have made efforts toward finding various efficient methods for recognizing unnatural patterns in control charts. Hwarng and Hubele (1993) used a back-propagation neural network technique for detecting X-bar control charts. Cheng (1997); Guh and Hsieh (1999) used a neural network approach for recognizing an unnatural control chart pattern. Pham and Oztemel (1994) constructed a pattern recogniser using a learning vector quantization (LVQ) network. Yang and Yang (2002) created a fuzzy-soft LVQ to promote the recognition rate for control chart patterns. In order to decrease the number of reference vectors for each pattern used to identify different variation quantities, Al-Ghanim and Ludeman (1997) constructed a so-called ‘matched filter’ using a correlation analysis technique based on an inner pattern vector product. For concurrent control chart pattern recognition, Guh and Tannock (1999) proposed a back-propagation approach. In this section, we will propose a statistical correlation coefficient approach for the recognition of unnatural control chart patterns. The so-called matched filter approach involves obtaining a prototype for each pattern, called a ‘reference vector’ after the training algorithm is finished. Al-Ghanim and Ludeman (1997) evaluated the correlation between reference vectors and the input vector using the inner product. Let x and y be two random vectors with x 0 Z[x 1 .x n ] and y 0 Z[y 1 .y n ]. Then the inner product between x and y is defined as hx; yi Z x 0 y Z X x i y i : (1) Their inner-product correlation technique got good results in recognizing trend, cycle and systematic patterns. However, this method is poor in recognizing shift patterns. This is because the inner product presents the consistency in positive and negative components values in two vectors, but each component at the same position with an opposite sign will counteract the final inner product value. For example, if there are two vectors with nearly positive components, the inner-product correlation will become worse.
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