ο€  Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 22 - 24 22 Recognition of Concurrent Control Chart Patterns in Auto- correlated Processes Using Support Vector Machine Chau-Chen Torng * , Chon-How Hwang Department of Industrial Engineering and Management, National Yunlin University, Yunlin, Taiwan. Received 16 February 2016; received in revised form 18 March 2016; accept ed 09 April 2016 Abstract Control chart pattern recognition (CCPR) is an important issue in statistical process control because unnatural control chart patterns (CCPs) e xhibited on control charts can be associated with specific causes that adversely affect the manufacturing processes. In recent years, many mach ine learning techniques have been su c- cessfully applied to CCPR. However, such ex- isting research for CCPR has mostly been d e- veloped for identification of basic CCPs (Sh ift Patterns, Trend Patterns, Cyclic Pattern and Systematic Pattern). Little attention has been given to the identification of concurrent CCPs (two or more basic CCPs occurring simultan e- ously) which are co mmonly encountered in practical manufacturing processes. In addition, these e xisting researches also assume the pro- cess data are independently and identically dis- tributed which may not be appropriate for cer- tain manufacturing processes. This study pro- poses a support vector machine (SVM) approach to identify concurrent CCPs for a mu ltivariate process with autocorrelated observations which can be characterized by a first order autoregres- sive (AR(1)) mode l. The nume rical results in- dicate that the proposed model can effect ively identify two concurrent identical CCPs but for those cases involving one trend pattern and one shift pattern, their recognition accuracy deteri- orates to around 20% to 50% depending on the autocorrelation coeffic ients used in the data model. Ke ywor ds : control chart pattern, support vector machine, autocorrelation process 1. Introduction The effectiveness of the use of control charts depends on the ability to recognize patterns. The common types of CCP e xhib ited on statistical process control charts have been formalized in early literature. In most literature, the fo llo wing seven typical types of basic CCP, i.e ., Up ward and Downwa rd Sh ift Pattern (USP and DSP); Upward and Down ward T rend Pattern (UTPand DTP); Cyclic Pattern (CP); Systemat ic Pattern (SP); Natural Pattern (NP), are usually ad- dressed. Identificat ion of unnatural patterns canfacilitate early detection of an out -of-control process and the diagnostic search process by narrowing down the set of possiblecauses that must be investigated. For instance, shift patterns may indicate changes in materia l, mach ine or operator, while trend patternsmay indicate tool wear. Cyclic patterns may ind icate voltage fluctuation in power supply [1-3]. There is a crucia l need for an auto matic and effective analysis and interpretation methodol- ogy for control chart pattern recognition (CCPR), which enables indication of the real state of the manufacturing process. CCPR studies consist of the description, the identification, the e xp lic it classification, and the e xtraction of patterns in data. In recent years, many mach ine learning techniques have been successfully applied to CCPR. Ho wever, such e xisting research for CCPR has mostly been developed for identifi- cation of basic CCPs (Sh ift Patterns, Trend Patterns, Cyclic Pattern and Systematic Pattern). Little attention has been given to the identifica- tion of concurrent CCPs (two or more basic CCPs occurring simu ltaneously) wh ich are commonly encountered in practical manufac- turing processes. In addition, these e xisting researches also assume the process data are independently and identically distributed which may not be appropriate for certain manufactu r- ing processes. For those processes involving continuous manufacturing operations (including the manufacture of food, chemicals, and paper * Corresponding aut hor. Email: t orngcc@yuntech.edu.tw Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 22 - 24 23 Copyright Β© TAETI and wood products), the consecutive observ a- tions of product characteristics are often highly correlated. The purpose of this paper is to propose a support vector machine (SVM ) approach to identify concurrent CCPs for a mu ltivariate process with autocorrelated observations. 2. Method This study uses simu lations to generate the required sets of CCP e xa mp les for tra ining, testing, and performance evaluation of the pro- posed model. The mathemat ical e xp ressions for CCP generation are e xp ressed in a general form that consists of process mean, common cause variation and special d isturbance from assign a- ble causes. The equations and parameters used to generate the data points are shown in Table 1. Table 1 CCP equations and parameters pat t erns equat ions paramet ers Nat ural pat t ern π‘₯𝑖 = πœ‡ + π‘Ÿπ‘–πœŽ =0, =1 T rend pat t ern π‘₯𝑖 = πœ‡ + π‘Ÿπ‘–πœŽ + 𝑑 Γ— 𝑖  26.0,10.0ο‚±οƒŽt Shift pat t ern π‘₯𝑖 = πœ‡ + π‘Ÿπ‘–πœŽ + 𝑒 Γ— 𝑠   10 0.3,0.1 oru s ο€½ ο‚±οƒŽ Cyclic pat t ern π‘₯𝑖 = πœ‡ + π‘Ÿπ‘–πœŽ + π‘Ž Γ— sin 2πœ‹π‘‘ 𝛺  0.3,0.1οƒŽa Syst emat ic pat t ern π‘₯𝑖 = πœ‡ + π‘Ÿπ‘–πœŽ + 𝑑(βˆ’1) 𝑖  0.3,0.1οƒŽd The follo wing equations are used to simulate the autocorrelated data. 𝑋1𝑑 = πœ‡ 1 + πœ™11 𝑋1 ,π‘‘βˆ’1 +πœ™12 𝑋2 ,π‘‘βˆ’1 + πœ€1𝑑 (1) 𝑋2𝑑 = πœ‡ 2 + πœ™21 𝑋1 ,π‘‘βˆ’1 +πœ™22 𝑋2 ,π‘‘βˆ’1 + πœ€2𝑑 (2) where πœ™π‘–π‘— are autocorrelated coefficients , and πœ™11 = {1.0, 0.7 0.4, 0.1}, πœ™22 = {1.0, 0.7, 0.4, 0.1}. For tra ining and testing the concurrent pat- terns, a SVM based on radial basis kernel fun c- tion is chosen inthis study. Related para meters C and Ξ³ for this ke rnel were varied in the fixed ranges [2-5, 25]. Using the simu lated training and testing exa mp les, the optima l (C, Ξ³) was determined as [1, 0.03]. The observation win- dow sizes of 24 and 32 are selected according to the suggestions by Guh and Tannock [4] and Hachicha and Ghorbel [1]. 3. Results and Discussion The concurrent CCPs we re a co mbination of any t wo of the basic unnatural CCPs. Thus, 13 types of concurrent CCP, na me ly USP mixed with UTP (USP+UTP), USP mixed with DTP (USP+DT P), USP mixed with CP (USP+CP), USP mixed with SP (USP+SP), DSP mixed with UT P (DSP+UTP), DSP mixed with DTP (DSP+DT P), DSP mixed with CP (DSP+CP), DSP mixed with SP (DSP+SP), UTP mixed with CP (UTP+CP), UT P mixed with SP (UT P+SP), DTP mixed with CP (DT P+CP), DT P mixed with SP (DTP+SP), CP mixed with SP (CP+SP) are addressed in this study. Table 2 Accuracy of CCPR Simu lation results in Table 2 show that the rate of accuracy for patterns of UTP, DTP, UTP+USP, UTP+DSP, UTP+SP, DTP+USP, DTP+DSP, DT P+SP is worse than the other patterns. It is noticed that if the trend pattern was mixed with other patterns, their recognition performance would decrease. 4. Conclusions In this paper, a support vector mach ine ap- proach is proposed to identify concurrent CCPs for a mu ltivariate process with autocorrelated observations which can be characterized by Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 22 - 24 24 Copyright Β© TAETI afirst order autoregressive (AR (1)) model. The numerical results indicate that the proposed model can effectively identify two concurrent identical CCPs but for those cases involving one trend pattern and one shift pattern, their reco g- nition accuracy deterio rates to around 20% to 50% depending on the autocorrelation coeffi- cients used in the data model. Acknowledgement The support of the Minister of Education (Taiwan), under Grant MOST 104-2221-E- 224- 026 is gratefully acknowledged. References [1] W. Hachicha and A. Ghorbel, β€œA survey of control-chart pattern-recognition literature (1991–2010) based on a new conceptual classification scheme,” Co mputers & In- dustrial Engineering, vol. 63, no. 1, pp.204-222, 2012. [2] L.J. Xie, N. Gu, D.L. Li, and Z.Q. Cao, β€œConcurrent control chart patterns recogni- tion with singular spectrum analysis and support vector machine,” Co mputers & Industrial Engineering, vol. 64, no. 1, pp. 280-289, 2013. [3] W. A. Yang, W. Zhou, W. Liao, and Y. Guo, β€œIdentification and quantification of co n- current control chart patterns using ex- treme -point symmetric mode deco mpos i- tion and e xtre me learn ing mach ines ,” Neurocomputing, vol. 147, pp. 260-270, 2015. [4] R. S. Guhand J. Tannock, β€œRecognition of control chart concurrent patterns using a neural network approach,”International Journal of Production Research, vol. 37, no.8, pp.1743-1765, 1999.