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Journ al of Scientific & Industrial Research Vol . 60, November 200 I , pp 860-862 Recognition of Control Chart Patterns Using Self Organization Models J Srini vas •• M Ananda Rao and G Rambabu Deparment of Mechanical Engineering, Andhra University, Yisakhapatnam 530 003 Received: 08 May 2001; accepted: 20 August 2001 The study proposes the use of self organizing neural networks for accurate and speedy detection of control chart pattern s in order to achieve tight control of the process and ensuring good product qu ality. Control charts used in statisti ca l process control can exhibit six principal types of patterns. Apart from the normal patterns , all other patterns indicate abnormalit ies in th e process. which mu st be corrected to bring the process under control. Hence, accurate identification of control chart pattern is essential in modern industry. Unlike conventional tool s that require a prior knowledge of the problem, the network class ifies in a pure intuitive manner. Further the network is noise-tolerant. The training and classificatio n results of the neiwork are presented. Introduction Present strategy of recognition of patterns in signal identification and image processing requires knowledgebased software. One of such pattern recognition problem is the identification of industrial control charts, where it is frequently necessary to monitor the process within the control limits . Statistical Process Control (SPC) makes use of control charts to access whether a particular process is functioning correctly. In 1924, Walte r Shewhart designed the first control chart and gave a rationale for its use in process monitoring and control. Critical process variables are to be periodically sa mpled and average values of each sample is plotted on a mean control chart. Abnormaliti es in the process can be identified as unu sual developments in the control charts. Based on the nature of the variation in the control chart, basically six main types of patterns have been identifi ed. These are normal , upward sh ift, downward shift , increasing trend, decreasing trend and cyclic. Correct identification of these patterns is important to achieve earl y detection of potential problems and maintaining the quality of the process under observation . Wh en a process is operatin g normally i.e., its co ntrol chart shows a normal patte rn , its variables fl uctuate within a range. All other pattern s indicate th at the process is abnormal. There are numerous sc hemes in the identification of control chart patterns, which can be divided broadly into two types: *Author for correspondence ( i) By the use of statistical classification and heuristic methods 1 and (ii) By the use of neural network s. For automatic identification o f control c hart patterns, many neural network s 2· 4 were e mplo yed. Supervised neura l network s can be succ essfu ll y employed but these ty pes of network s cannot be easily retrained to identify new pattern s. T he network has to be trained again from starting with both original trainin g data and new-patterns to be identified. This class ical stability-plasti city dilemma can be overcome by usin g self-organi sing neural networks havin g an expandab le layer of class neurons 5 . After training, if additional new input patterns are required to be learned, they will , first of all, be tested against the establi shed class neurons. If they can be acco mm odated in th e e neurons with out degrading the information already encoded in them, then they will be learn ed by the neurons. Ot herwi se, new class of neurons will be created to cater for th ese addit ional new input vectors, so that th ey can be a part of th e kn owledge encoded in the neural network, whil e not affecting the already stored class ifi cation inform ati on. This capability of incre mental learn ing is a desirabl e feature of an on-line classifier required for rapid detect ion of abnormal process behaviour. In thi s paper, a competiti ve lea rning algorithm 6 is used for learn ing th e netwo rk. wh ich is app li ed to process-control problem. X61 SRINIVAS et al.: RECOGNITION OF CONTROL CHART PAlTERNS Outputs (pattern classes) -Normal -~==~~====~~~~ O~. 0.6 Cydic 0.-4 0.2 °f---~--~--~--~Ar~ -0.2 -0.04 ---.J -0.6 ~--------- (a) --Increaoing trend '--Decreasing trend 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Inputs I, ( Process mean) Figure I-Present Kohonen's neural network topology Network o t----r---~.L-- Sketch of the present network is presented in the Figure 1. The network consists of two layers, the input layer and the output layer. The neurons of the two layers are fully connected. In addition, each neuron of the output layer is connected laterally to indicate lateral inhibition. Input pattern (l) is processed through neurons of input layer after normalization. The connection weights must also be normalized. The products of input vector and the weights of an output node give the output of that node. Output is calculated for all the nodes of output layer. The output having the highest value is the winner. Training is based on a 'winner take all' strategy. Therefore, weights corresponding to the output node Wi; with maximum output (0) are updated according to the J Eq.(l). wnew.] . = W0 ld -I . + at] - W0 ld ,j .) , ... (I) where a is learning rate, which varies from 0 to I and controls the rate of learning. An a== I means that it learns a new example as soon as it is presented. It, however, forgets all previous examples of that class. Similarly, a==0 means that the network does not learn at all and it classifies new examples based on previous experiences only. The number of input units depends on required resolution of the input patterns. Output units are equal to the desired number of classes. The network can be initialized to any value of weights and an initial value of a is kept close to I. It can be reduced gradually as the network learning progresses. After satisfactory classification a value of a=O can be set. Identification of Patterns The network is presented with the control chart patterns of a process and is expected to organize itself to .0.1 -02 .0.3 ~~~r---\-1 (b) -- Upward sI>ft -- Downward shift 0.8 0.6 0.4 0.2 0f---~---r----r--~~~ -0.2 -04 j .0.6 ...J '------------ ( C) Figure 2- Six basic control chart patterns classify the input patterns according to their trends. Using appropriate mathematical equations I, analytically generates the six-basic control chart patterns. The parameters like process mean, standard deviation are predefined. The classification is carried out purely intuitively by the network without any prior knowledge of attributes like number of zero crossings. Three sets of each type of control-chart are generated with a simple program and all these values are normalized with corresponding Euclidian norm. The normalized mean values as a function of sample size are plotted randomly and are shown for all the six basic patterns in Figure 2. Present network has ten input nodes to accept the sampled data for ten different samples. The initial value of learning rate has been set to 0.9. The network converged to six control chart patterns as soon as at least one example from each representative group was presented. The corresponding connection weights of the network after learning are shown in Figure 3. From Figure 3, it can be noticed that weight vectors are following inputs very accurately. Several trials have J SCI IND RES VOL 60 NOVEMBER 2001 862 --cyclic -+-lncreasm.. trend - - Upshift -downshift Table 2-Ability of the network to identify new patterns Sl No. l_ _ _ _ -0.4 -0.6 .L__ _ _ _ _ _ _ __ _ __..J 2 Experiment number Pattern Output winning node 3 Cyclic 2 2 Upw ard shift 5 ______. Figure 3- Patterns captured in.connection weights Table !-Output of the network for new problem Normalized output Output No. 0.6400 0.9990 0.0360 0.4830 0.2887 Pattern 3 (Increasi ng trend) 0.2348 0.0370 0.8859 0.5527 0.6459 Pattern 4 (decreasing trend) 0.6043 0.4830 0.5500 1.070 0. 5480 Pattern 5 ( pward shift) 0.0504 0.0442 0.8859 0.5214 1.0000 Pattern 6 {down wa rd shift) 1.000 0.6404 0.0671 0.6043 0.8353 0.4467 0.3368 0.566 0.3773 0.258 Pattern I (Normal) Pattern 2 (Cycli c) 5 0.2580 0.4467 0.3736 0.5662 0.1634 6 1.0000 I 2 3 4 been conducted to test the robustness of the network for convergence. The network classified the sample values of new problems, i.e., sample values at different location s of time (in control chart equations) accurately. Table I shows normalized output of network for different patterns for a definite sample value set. As evident from Table I, appropriate output nodes are noticed to be c lear winners for all the patterns. Network performed similarly for other examples presented to it. To test whether the present network has an ability to di scover a new pattern the pre-calculated sampled values are presented at two different times. Results of the identification of new patterns are shown in the Table 2. Two of the basic control charts viz., up-shift and cyclic patterns are presented as new patterns and the network has classified them appropriately. The training and classification are found to be stabl e even when the data contains di sturbances (noi se). The sample values measured at manufacturing sites, contain inaccuracies . Network is able to di stingui sh between noi se and a new pattern and diagnose correctly the data with noi se as the new pattern . Significant limitation of the present network is that the number of output nodes determines the maximum number of clas e . Network is not able to create a new class on its o wn, wh en all available class ifications are occupied by previous input patterns. Conclusions For control chart pattern classification, se lforganising neural network model has been utilized. Based on the Euclidian di stance-firin g ru le, the netw o rk classified the patterns very accurate ly. Th is network is highly noise-tol erant. Thi s is very desirab le property when plant-data is available. References 2 3 4 5 6 Evans J R & Lindsay W M, Computlnd Eng, 14( 1988) 335. Guo Y & Dooley K J, lnt 1 Prod Res, 30( 1992) 1655 . Guh R S & Hsieh Y C, Comput lnd Eng, 36( 1999) 97. Chang S I & Aw C I, lnt 1 Prod Res, 34 ( 1996) 2265 . Mukherj ee A, 1 Com put Civil Eng, ASCE, 14 ( 1997) 74. Ko ho ne n J, Self organizing associative memory (SpringerVerlag, New York) 1988.