Journal of Industral Engneerng Internatonal July 008, Vol. 4, No. 7, 04 Islamc Azad Unversty, South Tehran Branch An artfcal Neural Network approach to montor and dagnose multattrbute qualty control processes S. T. A. Nak* Professor, Department of Industral Engneerng, Sharf Unversty of Technology, Tehran, Iran Abstract M. Nafar Department of Industral Engneerng, Sharf Unversty of Technology, Tehran, Iran One of the exstng problems of multattrbute process montorng s the occurrence of hgh number of false alarms (Type I error). Another problem s an ncrease n the probablty of not detectng defects when the process s montored by a set of ndependent unattrbute control charts. In ths paper, we address both of these problems and consder montorng correlated multattrbutes processes followng multbnomal dstrbutons usng two artfcal neural network based models. In these processes, outofcontrol observatons are due to assgnable causes comng from some shfts on the mean vector of the proporton nonconformng of the attrbutes. Model one, whch s desgned for postvely correlated attrbutes, conssts of three neural networks. The frst network not only detects whether the process s outofcontrol, but also determnes the drecton of shfts n the attrbute means. In ths stuaton, the second and the thrd networks dagnose the process attrbute/s that has/have caused the outofcontrol sgnal due to ncrease or decrease n proporton nonconformng, respectvely. Model two s desgned for negatvely correlated attrbutes and conssts of two neural networks. The frst network s desgned to detect whether the process s outofcontrol and the second one dagnoses the attrbute/s that make/s the sgnal. The results of fve smulaton studes on the performance of the proposed methodology are encouragng. Keywords: Neural Networks; Montorng; Multattrbute; Qualty control. Introducton and lterature revew Montorng s an effort to reduce varablty and mprove processes n ndustres. In many manufacturng or servce companes, some characterstcs of processes cannot be measured numercally, but may be classfed as conformng and nonconformng. These characterstcs are called attrbutes and the montorng task becomes dffcult when there are more than one attrbute of nterest, especally when some correlaton exst between them. There exst many possble applcatons of multattrbute montorng n servce or ndustres, n whch there are more than one correlated defecttype n the product. As an example, n an electroncboard producton company the numbers of weakly soldered and oversoldered bases n a board are two negatvely correlated qualty attrbutes that must be montored smultaneously. In another example, the numbers of leak ponts on ether the sde seam or the bottom panels of 00 orange juce concentrate cans are two postvely correlated qualty attrbutes. In a servce ndustry, the numbers of employee paychecks that are erroneous or dstrbuted late durng a pay perod are usually two negatvely correlated qualty attrbutes that are of nterest to montor smultaneously. Moreover, n many multvarate processes, n order to reduce the nspecton costs, we may be nterested n classfyng the varables wth go and nogo gauges as conformng or nonconformng attrbutes. In these cases, f there s a correlaton between the qualty varables t wll project tself n the classfed attrbutes; justfyng the applcatons of multattrbute control charts. Although multvarate statstcal process control s recevng an ncreasng attenton n the lterature, lt * Correspondng author. Emal:nak@sharf.edu
S. T. A. Nak and M. Nafar tle work has been done to deal wth multattrbute processes. Patel [6] consdered tme dependent and tme ndependent observatons followng multvarate Posson and multvarate bnomal dstrbutons, respectvely. Assumng normalty for the dstrbuton of the observatons by large sample szes and fxed covarance structure, he proposed a G statstc, approxmately dstrbuted as χ dstrbuton, as the base of hs proposed control chart. Lu et al. [9] presented a multvarate np control chart (MNP) based on the X statstc defned as the weghted sum of the nonconformng unts. They also proposed a score statstc (Z) to recognze the outofcontrol sgnal and showed that the MNP chart was more senstve than a set of unattrbute np charts. The lmtaton of ths technque was the dependences between the sample szes and the value of nonconformng tems of all process attrbutes. Jolayem [7] addressed an economc desgn of multattrbute control chart based on J approxmaton (Larpkattaworn [8] and Jolayem [6]) and Gbra ([] and []) model, who assumed that the assgnable causes are ndependent and that they do not overlap each other. When the proportons of nonconformtes n each qualty category were known or estmated usng a base perod, Marcucc [0] used a MultNomal dstrbuton to develop a control chart; but snce not all multattrbute processes follow MultNomal dstrbuton, ths method s not always applcable. Garde and Ratthall 0] by assumpton of MultNomal dstrbuton for multattrbute processes used a MPtest to determne f the parameters of the dstrbuton changed. In ther method to do the MPtest, the magntude of the parameters of nterest must be defned n advance. Decsons n the desgn of multattrbute process montorng due to ts complexty cannot be easly attaned wth classcal statstcal process montorng. For ths reason, the research studes n ths feld are progressvely drected toward the use of new approaches and methods developed n some areas of the Artfcal Intellgent (AI) world lke Artfcal Neural Networks (ANN) and fuzzy logc. Many qualty engneers and researchers are famlar wth the successful applcatons of Artfcal Neural Networks, whch have been appled to statstcal process control (SPC) snce late 980s n montorng unvarate and multvarate processes (see Pugh [8], Cheng [6], Saka et al. [0], and Nak and Abbas []). One of the man reasons for the applcatons of ANN to SPC s to automate SPC charts nterpretaton. However, whle most of these applcatons have focused prmarly on unvarate control charts, lttle effort has been devoted to multvarate control charts. Pugh [9] proposed a backpropagaton neural network for detectng unvarate process mean shfts. Cheng [5] studed performance comparson between artfcal neural network and ShewhartCUSUM scheme n detectng unnatural patterns of a process usng a multlayer perceptron (MLP). Guo & Dooley [] recommended network models that can dentfy postve changes n the process mean and varance. Whle Hwarng and Hubele [5] developed backpropagaton networks to dentfy unnatural patterns on Shewhart X control charts, Chang and Aw [] proposed a neuralfuzzy network to detect and classfy mean shfts. Moreover, Chang & Ho [4] expanded neural network models to detect and classfy the magntude of varance shfts and also developed a combned neural networks control scheme for montorng mean and varance shfts wth a combnaton of Chang & Ho [4] and Chang & Aw [] models. Artfcal neural networks have also been appled to control and montor multvarate processes. Martn & Morrs [] proposed a fuzzy neural network as an alternatve approach for dentfyng outofcontrol causes n a multvarate process. Wlson et al. [] used appled Radal Bass Functon (RBF) network n a multvarate process. Nak & Abbas [] used a multlayer perceptron to pattern classfcaton when there was a sgnal n multvarate control charts. In multattrbute process montorng there are two broad research categores:. Montorng the proportons of several correlated nonconformtes. Controllng the number of several correlated defecttypes Whle t s common practce to assume a multvarate bnomal dstrbuton for the frst category, n the second category we usually assume a multvarate Posson dstrbuton. Larpkattaworn [8] proposed a neural network to montor processes wth two postvely correlated attrbutes and compared ts performance wth the ones from the MNP and multvarate normal approxmaton technques. He assumed that the varancecovarance matrx assocated wth the process attrbutes was unchanged from process to process. He employed the desgn of experments technque and presented three scenaros llustratng decsonmakng rules to select the best method to be used n a partcular process. In a more recent research n ths area, Nak and Abbas [] based on a smple approach that almost elmnates the exstng correlatons be
An artfcal neural network to montor and dagnose... tween the attrbutes, presented a methodology to montor multattrbute processes, and presented a rectangular regon for the montorng purposes. Moreover, Nak and Abbas [4] developed a methodology to derve control lmts on the attrbutes based on the bootstrap method n whch they buld smultaneous confdence ntervals on the attrbutes. Then, based upon the ncontrol and outofcontrol average run length crtera they nvestgated the performance of the proposed method usng smulaton. Ths paper descrbes the applcablty of ANN approach n multattrbute process montorng. Ths tool, n fact, ntroduces an nnovatve approach, whch s fundamentally based on a knowledge not drectly vsble by the user. However, t s able to be stored through a smpler and more ntutve tranng process. We propose two neural network based models to both montor and dagnose multattrbute processes n whch there exst more than one correlated process attrbutes. These models consst of two and three neural networks, respectvely. The frst network n both models nvestgates whether the process s n ncontrol or outofcontrol condton. The second and the thrd network n model and the second network n model show the status of the attrbutes. Although t s correct that the use of the control chartng method s easy, there s not any control chartng methods avalable n the lterature that counts for the possble correlaton between the attrbutes n multattrbute processes. The one that exsts uses the approxmate multnormal probablty dstrbuton, whch may not be approprate. Besdes, the proposed neural network method not only s desgned to detect mean shfts, but also t s capable of dagnosng the attrbutes that have been shfted. The latter case s an mportant contrbuton of the proposed methodology n process montorng. It s true that t may requre more effort to tran the network, but once t s traned, t can easly be appled n practce. The practtoners may vew the method as a black box such that when they nput the values of the attrbutes they can see f the process s outofcontrol, and f yes, whch attrbute(s) s n outofcontrol condton. In Secton, we brefly ntroduce the neural network modelng and ther tranng processes. The data generaton and preprocessng comes n secton three. Secton 4 contans the neural network modelng of the multattrbute qualty control problem, the proposed network archtecture, and ts tranng process. The performance evaluaton by smulaton technque comes n Secton 5. Fnally, concluson and recommendatons for future research s presented n Secton 6.. Neural Networks Artfcal Neural Networks (ANN) modelng s an optmzaton tool for the output processes (responses). They mmc bologcal neural networks to model and solve a varety of problems arsng n predcton or forecastng, functon approxmaton, pattern classfcaton, clusterng, and categorzaton. A neural network, whch conssts of a number of nterconnected nodes called neurons, plays lke a computatonal algorthm for nformaton processng (Pao [5] and Saka et al. [0]). In pattern classfcaton applcaton of the ANN, we usually assgn an observaton to a predentfed pattern. There are two stages n pattern classfcaton, namely, characterstcs dentfcaton stage and classfcaton stage. In the former, we select the basc characterstcs of a pattern that dstngushes t from the others. We wll later use them as a crteron for decsonmakng process. In the latter, we desgn a classfcaton machne such that t takes the characterstcs as nput and produces patterns as output. As many researchers have proposed several classfcaton machnes so far, there are many topologes of the ANN n pattern classfcaton. Studes show that the Multlayer Perseptron (MLP) network wth error back propagaton has better performance than that of tradtonal statstcal classfcaton methods (Saka et al. [0]). MLP s a neural network that does nonlnear classfcaton and has three layers: the nput layer, the output layer, and the hdden layer. Input layer dstrbutes nput to all neuron n the hdden layer, whch contans the sgmod transfer functon. The task of the output layer s to determne the pattern (Pao [5]). Desgn and mplementaton of an ANN s fulflled n three steps. In the frst phase, we tran the network usng a set of nputs and desred outputs (known as tranng set). After tranng, we employ another set of nputs and outputs to check the valdty of the model. If the obtaned error of the valdty specfcaton phase s acceptable, the mplementaton phase wll begn. The network tranng process s an mportant task that needs to be addressed before network mplementaton. There are two general types of tranng process, namely, the supervsed and the nonsupervsed process. In the supervsed tranng process, n whch the user plays an mportant role as the network learns, a set of tranng nputs wth a correspondng set of targets are gven and the network s traned to adjust the weghts such that a measure of performance s satsfed. However, n a nonsupervsed process, whch s of two types (renforcement learnng and unsuper
S. T. A. Nak and M. Nafar vsed learnng), a set of nputs wthout any target s avalable and the network s traned by lettng t contnually adjust tself to new nputs and fndng relatonshps wthn data... MultLayer Perceptron and Back Propagaton neural networks Perceptron Neural Network (PNN) s perhaps the most popular network archtecture n use today and s dscussed at length n most neural network textbooks (e.g., Bshop []). An mportant class of the PNN s multlayer feed forward perceptron (MLP) network. In ths type of network, we arrange the unts n a layered feed forward topology, where the unts each perform a based weghted sum of ther nputs and pass ths actvaton level through a transfer functon to produce ther output. The network therefore has a smple nterpretaton as a form of nputoutput model, wth the weghts and thresholds (bases) as the free parameters of the model. In order to tran a MLP network wth error back propagaton (BP), n the frst step one needs to generate suffcent data contanng all of the classfed patterns. In the second step, one uses the data as nput to the network and compares the output of the network wth a prespecfed target. Then, n the thrd step, based upon some performance crtera, such as the mean squared error; the error beng the dfference between the target value and the output, the error back propagaton algorthm modfes the weghts (W s) and the threshold values or bases (b s). The tranng process goes to the next step and so on untl ether an acceptable value for the mean squared error s acheved or a prespecfed number of cycles (epochs) s reached. In other words, Error backpropagaton learnng conssts of two calculatng passes, feedforward and feedback, through the dfferent layers of the network. In the forward pass, an actvty pattern (nput vector) s appled to the sensory nodes of the network and ts effect propagates through the network layer by layer to produce a set of output as the actual response of the network, fnally. Durng the forward pass, the synaptc weghts of the networks are all fxed and n the backward pass the weghts are adjusted n accordance wth an errorcorrecton rule. Ths error s then propagated backwards through the network to make outputs close to the targets (Haykn [4] and Chowdary [7]). Backpropagaton networks are often appled n pattern recognton and classfcaton problems. Although the number of nput and output unts s defned by the problem, the number of hdden unts to use s far from clear. A good startng pont s to use one hdden layer and trade the number of unts n t. For a good reference on the detals of the feedforward and the feedback equatons of the BP algorthm, we may refer to Haykn [4]. Fgure shows a typcal structure of a MLP wth k neurons n ts nput layer, one hdden layer wth one neuron and m neurons n the output layer, n whch learnng s supervsed and error back propagaton algorthm s used. Such networks can model functons of almost arbtrary complexty, wth the number of layers and unts n each layer, determnng the functon s complexty. Important ssues n MLP desgn nclude specfcaton of both the number of hdden layers and the number of unts n these layers (see Haykn [4] and Bshop []). MLP networks have successfully solved some dffcult problems wth a supervsed error backpropagaton tranng algorthm (see Patterson [7], Haykn [4], Fausett [9], and Chowdary [7]). Modern secondorder algorthms such as conjugate gradent descent and LevenbergMarquardt (see Bshop []) are substantally faster for many problems; however, back propagaton s easer to understand and stll has advantages n some crcumstances... Reslent backpropagaton Multlayer networks typcally use sgmod transfer functons n ther hdden layers. These functons compress an nfnte nput range nto a fnte output range. Sgmod functons are characterzed by the fact that ther slopes must approach zero, as the nput becomes large. Ths causes a problem when we use the steepest descent to tran a multlayer network wth sgmod functons, because the gradent can have a very small magntude and, therefore, cause small changes n the weghts and bases, even though they are far from ther optmal values. Envronment Input layer k Bas Hdden layer Bas Output layer Fgure. Topology of one hdden layer MLP. m Envronment
An artfcal neural network to montor and dagnose... 4 The purpose of the reslent backpropagaton tranng algorthm s to elmnate the harmful effects of the partal dervatves magntudes. Only the sgn of the dervatve s used to determne the drecton of the weght update; the magntude of the dervatve has no effect on t. The sze of the weght change s determned by a separate update value. Whenever the dervatve of the performance functon wth respect to that weght has the same sgn for two successve teratons, the update value for each weght and bas s ncreased by a factor. However, t s decreased by a factor whenever the dervatve wth respect to that weght changes sgn from the prevous teraton. If the dervatve s zero, then the update value remans the same. Whenever the weghts are oscllatng, the weght change s reduced. If the weght contnues to change n the same drecton for several teratons, then the magntude of the weght change ncreases (Demuth et al. [8]). We have chosen to use ths algorthm for ths research.. Data generaton and preprocessng In order to tran a neural network, a set of proper data along wth ts target values s requred. To generate data from say a R valued random vector X d wth margnal cumulatve dstrbuton functons F (.) = P(X.), =,...,d () and correlaton matrx X Σ = ( (, j) :, j d). () X Caro and Nelson [] presented the NORTA procedure based on the followng transformaton functon: X = FX [ Φ( Z )], FX [ Φ( Z )],..., FX [ Φ( Z )] k k () where Z = ( Z, Z,..., Z ) T k s a multnormal vector wth correlaton matrx Σ, Φ (.) s the cumulatve Z X X X k probablty dstrbuton functon of a standard normal random varable, and F, F,..., F are the desred margnal dstrbutons. The correlaton matrx ( Σ X ) s set to ensure that X wll have prescrbed correlaton matrx of desrable data and the transformaton technque ensures that X has the desred margnal dstrbuton F. X T In other words, the NORTA procedure to generate random devates from a ddmensonal random vector X takes the followng steps: d ) Generate an R standard multvarate normal random vector Z= Z,..., Z ) wth correlaton matrx Σ. Z ( d ) Compute the vector X = (,,..., ) X X X d where X = F ( Φ (Z )) ; =,,..., d and Φ(.) s the cumulatve probablty dstrbuton functon of a standard normal random varable. Then F (u) = nf { x : F (x) u }. In ths research, we assume the margnal probablty dstrbuton of the correlated qualty attrbutes to be bnomal... Data preprocessng In order to mprove the effcency of the tranng process, the generated nput data are usually preprocessed. One of these preprocessng methods s scalng the nput data to fall wthn the nterval of [,] by the followng equaton: [ p p ] mn( ) pn =, (4) [max( p) mn( p)] where p s the nput matrx, pn s the scaled nput matrx, mn( p) s the mnmum nput vector, and max( p) s the maxmum one. Then, the unscalng task may be performed usng the followng equaton: p = 0.5( pn + )[max( p) mn( p)] + mn( p).(5) 4. Neural Network modelng of a multattrbute qualty control process Although ANNs have been ntroduced for several decades, ther use n multattrbute process montorng area s qute recent and ther applcatons are stll very few. In ths research, n order to montor a multattrbute qualty control process and dagnose the shfts n the attrbute means we propose two models. The frst s desgned for stuatons n whch the attrbutes are postvely correlated and have a common drecton n the mean shfts. Otherwse, the second model s suggested for negatvely correlated attrbutes. T
5 S. T. A. Nak and M. Nafar In ths study, multlayer backpropagaton perceptron networks are chosen. The number of nput nodes n all archtectures represents the number of characterstcs of the process under consderaton. The only node n the output layer of the frst network represents the status of the process (ncontrol or outofcontrol). In the second and the thrd network, the output nodes represent the status of the attrbutes under study; hence, the number of output nodes n these networks s equal to the number of attrbutes. The default number of the layers n the hdden layer s set to be two (Haykn [4]). However, by a tralanderror method, n some nstances n the tranng process one layer seemed to be good enough. Fgure shows the proposed neural networks to montor correlated multattrbutes processes. In order to montor a multattrbute qualty control process, frst the preprocessed observatons are appled to the network. Ths network s traned such that when the process s ncontrol, the output becomes very close to 0. However, f the process s outofcontrol and at least one attrbutemean has postve shft, t returns a value close to, and Observatons fnally the output s almost f the process s outofcontrol and at least one attrbutemean has a negatve shft. Then, networks and determne whch attrbute mean/s has/have a postve or a negatve shft, respectvely. In processes n whch some attrbutes have postve and some have negatve meanshfts, as n cases of negatvely correlated attrbutes; model s unable to detect the shfts. In ths stuaton, the observatons are appled to model, whch conssts of two networks. The frst network returns almost 0 and when the process s ncontrol or outofcontrol, respectvely. The second one determnes the attrbute(s) causng outofcontrol sgnal. In other words, the output of ths network shows the status of the attrbutes. For example an output vector of approxmately [ 0] correspond to a stuaton n whch the frst attrbute has postve meanshft, the second one has negatve meanshft, and the thrd one s under control. Fgure shows the proposed neural networks (model ) to montor negatvely correlated multattrbutes processes. Fgure. The neural network model to montor and dagnose postvely correlated multattrbute processes (Model ). Observatons Network Network Is process n control? Yes No Is process n control? Postve shft Negatve shft No Network Network Network Sgnal dagnoss Sgnal dagnoss Yes Fgure. The neural network model to montor and dagnose negatvely correlated multattrbutes processes (Model ).
An artfcal neural network to montor and dagnose... 6 4.. Network tranng process In ths research, the reslent back propagatontranng algorthm ntroduced n Secton. s chosen for the tranng process. Not only ths algorthm s generally much faster than the standard algorthms based on the steepest descent methods, t also requres a modest amount of memory. Moreover, t has shown good performances n pattern recognton problems (Demuth et al. [8]). The reslent backpropagaton algorthm s not very senstve to the settng of the tranng parameters, so some of the networks parameters such as the number of epochs and the network MSE are chosen randomly for best results. Adaptve learnng rate and momentum constant are selected accordng to a computer experment that has been conducted n pattern classfer to llustrate the learnng behavor of a multlayer percpetron. These values are 0. for the learnngrate and 0.5 for the momentum constant. The transfer functon n the hdden layers s selected to be the sgmod functon. The flow chart of the tranng process for multattrbute montorng shown n Fgure 4 has been employed whle developng the Reslent Back Propagaton Artfcal Neural Networks n Matlab computer package envronment. The traned networks for montorng have been smulated and tested for ther valdty. Whle testng the networks, varous patterns have been appled to t. The output generated from the neural network models s compared to the desred output. In the tranng process of the frst network n Model, frst we tred 00 ncontrol and 00 outofcontrol patterns for processes wth two and three attrbutes. An Outofcontrol pattern s a set of observatons wth both postve and negatve shfts around the process mean. However, the performance of the network n terms of both ncontrol and outofcontrol average run length were not desrable smultaneously. Hence, we employed 000 and 000 ncontrol patterns for processes wth two and three attrbutes, respectvely. The number of outofcontrol patterns n both cases was 00. The tranng process of network and ncluded 00 and 700 outofcontrol patterns wth two and three attrbutes, respectvely. These outofcontrol data had postve mean shfts for network and negatve mean shfts for network. Whle the frst network n Model was traned by 000 ncontrol and 00 outofcontrol patterns, the second network was traned by 800 outofcontrol data sets on two attrbutes. Outofcontrol patterns n both networks are a set of observatons wth both postve and negatve shfts around the process mean. In all tranng processes, we estmated the varancecovarance matrx of the attrbute means assumng changes n the varances and no changes n the correlatons and reached the MSE of approxmately 0 4 by tral and error. 5. Performance evaluaton In Model and, the performance of the network s measured by ncontrol and outofcontrol average run length (ARL). An ncontrol average run length (ARL 0 ) s the average number of samples that must be taken before a sample ndcates an outofcontrol condton when, n fact, the process s n control. An outofcontrol average run length (ARL ) s the average number of samples taken to detect a shft n the mean of a process, when the process s n a partcular outofcontrol condton. For network n Model and and network n Model, the percent of the tmes the networks detect the true outofcontrol attrbute(s) s selected as a measure to evaluate ther performance n the followng smulaton experments. 5.. Smulaton experment (Model ) In the frst smulaton experment we nvestgate a MultBnomal dstrbuton wth two postve correlated attrbutes and parameters as p = 0., n = 0, ρ = 0. 5, p =0. 5, and n = 0. Tables, and show the performance of network,, and of Model, respectvely. In these tables and the ones for the other smulaton experments, there are empty cells referrng to stuatons n whch ther correspondng data could not be observed from a process. For example n Table the data followng a MultBnomal dstrbuton whose attrbute means are shfted could not be generated because ther nonconformng proportons become negatve. The and rows n the Table have the same descrpton as mentoned. In addton, the entres n these tables are estmated from 0000 replcatons. The results of Tables, and show that n ths smulaton experment the networks possess good performances.
7 S. T. A. Nak and M. Nafar Start Tranng Patterns Increase Tranng Patterns No Network Tranng and Valdaton MSE<=Specfed Accuracy Yes Feed the Test Patterns and Valdaton MSE<=Specfed Accuracy Fgure 4. The flow chart of the tranng process. No Yes Increase Network Complexty Stop
An artfcal neural network to montor and dagnose... 8 Table. The performance of network n smulaton experment. Noshft + + + + + + ARL.47 68.49 6.4..4 Table. The performance of network n smulaton experment. + + + + + + + + + + + + Correct detecton 0.49 0.5 0.64 0.74 0.7 0.8 0.6 0.8 0.9 Table. The performance of network n smulaton experment. Correct detecton 0.59 0.57 0.65 0.78 0.80 0.98 Table 4. The performance of network n smulaton experment. Noshft + + + + + + ARL.0.78 7.5 8 0.00.78.06 Table 5. The performance of network n smulaton experment. + + + + + + + + + + + + Correct detecton 0.48 0.48 0.6 0.55 0.57 0.90 0.57 0.6 0.99 Table 6. The performance of network n smulaton experment. Correct detecton 0.47 0.49 0.7 0.56 0.6 0.97 0.77
9 S. T. A. Nak and M. Nafar Table 7. The performance of network n smulaton experment. Noshft + + + + + + + + + ARL.44.0 7.7.99.4.4 Table 8. The performance of network n smulaton experment. + + + + + + + + + + + + Correct detecton 0.8 0.9 0.7 0.9 0.4 0.45 0. + + + + + + + + + + + + Correct detecton 0.44 0.4 0.9 0.6 0.65 0.64 0.44 + + + + + + + + + + + + Correct detecton 0.45 0.6 0.50 0.7 0.8 0.7 0.6 Table 9. The performance of network n smulaton experment. Correct detecton 0.4 0.8 0. 0.5 0.5 0.4 0. Correct detecton 0.55 0.6 0.4 0.8 0.8 0.76 0.9
An artfcal neural network to montor and dagnose... 0 Table 0. The performance of network n smulaton experment 4. + + + Noshft + + + + + + ARL.. 9..8. Table. The performance of network n smulaton experment 4. + + + + + + + + + + + + Correct detecton 0.4 0. 0.46 0.49 0.7 0. 0.0 + + + + + + + + + + + + Correct detecton 0.57 0.9 0.7 0.79 0.6 0.5 0.48 + + + + + + + + + + + + Correct detecton 0.69 0.9 0.88 0.88 0.4 0.7 0.59
S. T. A. Nak and M. Nafar Table. The performance of network n smulaton experment 4. Correct detecton 0.48 0.4 0.40 0.67 0.49 0.56 0.5 Table. The performance of network n smulaton experment 5. + + + + + ARL.78 8.76 7.66.97.8 5.0 + + + + + + + ARL 4.0.79..7.7.0 Noshft ARL 7.00 Table 4. The performance of network n smulaton experment 5. + + + + + + Correct detecton 0.4 0.8 0.0 0.44 0.40 0.8 0.7 0.8 + + + + + + Correct detecton 0.94 0.55 0.46 0.90 0.79 0.9 0.49 0.78 + + + + + + Correct detecton 0.64 0.94 0.44 0.5 0.97
An artfcal neural network to montor and dagnose... 5.. Smulaton experment (Model ) In ths example, we consder a MultBnomal dstrbuton wth two negatve correlated attrbutes and parameters of p = 0. 4, n = 5, ρ = 0. 6, p = 0., and n = 5. Tables 4, 5 and 6 show the performance of network,, and n ths experment, respectvely. Once agan relatvely good performances are observed n ths experment. attrbutes and parameters p = 0. 4, n = 5, ρ = 0.6, p = 0., and n = 5. Tables and 4 show the performances of network and n ths experment, respectvely. The results of Table 5. show that the desgned network works relatvely well n term of n and outofcontrol average run lengths. However, from Table 4 we see that the probablty of detectng the correct attrbute(s) s not very good. 5.. Smulaton experment (Model ) Three postve correlated attrbutes wth Mult Bnomal dstrbuton and the parameters p =0., n = 0, p =0. 5, n = 0,.00 0.9 0.4 ρ = 0.9.00 0.4, p = 0. 8, and n = 0 are 0.4 0.4.00 studed n ths experment. Tables 7, 8 and 9 show the performance of network,, and n ths experment, respectvely. Agan good performances are observed. However, n term of the probablty of correct detecton, sometmes the performances are not very good. 5.4. Smulaton experment 4 (Model ) The fnal example of experment wth model nvolves a MultBnomal data wth both negatve & postve correlatons between the attrbutes and parameters p =0., n =, p =0., n =,.00 0. 0.57 ρ = 0..00 0.9, p =0. 6, and n =. 0.57 0.9.00 Although, Table 0 shows good performances of network n term of the n and outofcontrol average run length, the results of networks and n Tables and show that sometmes these networks do not perform very well n term of the probablty of correct detecton. 5.5. Smulaton experment 5 (Model ) In ths smulaton experment we employ model on the data obtaned for the second smulaton experment n whch there are two negatvely correlated 6. Concluson and recommendatons for future research Montorng processes n whch there are several correlated qualty attrbutes s a complex problem. In ths paper, we proposed two neuralnetworkbased models wth three and two networks, to montor multattrbutes processes. As the three networks n model were traned usng fewer data sets, they were not able to effcently detect dfferent scenaros of mean shfts n the mean of negatvely correlated attrbutes. As a result, for the dagnoss purpose n negatvely correlated multattrbutes processes, we desgned and proposed model. The frst network n both models was desgned to dentfy the status of the process under consderaton; the second and the thrd network n model were desgned to detect the attrbute(s) causng postve and negatve shfts n the process mean, respectvely. We showed that the proposed models possessed a desrable ncontrol average run length n dfferent smulaton experments and could detect dfferent scenaros of meanshfts relatvely fast. However, n term of the probablty of correct detecton, sometmes they do not perform very well. As a result, ths study has shown that a properly developed ANN model provdes a vald alternatve for montorng multattrbute qualty control problems. The reslent back propagaton artfcal neural network models demonstrated n ths paper s an nnovatve approach fundamentally based on AI, whch s not drectly vsble to the user. However, t s able to solve the complex problem through a smpler and supervsed feed forward BP tranng process. The practtoners may vew the method as a black box such that when they nput the values of the attrbutes they can see f the process s outofcontrol, and f yes, whch attrbute(s) s n outofcontrol condton. The potental of ANN as a multattrbute montorng tool s usually based on a large sample sze. The generalzaton capabltes of ANNs are hghly dependent on the number of patterns n the tranng set.
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