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doi: 10.3934/jimo.2020150

Integration of cuckoo search and fuzzy support vector machine for intelligent diagnosis of production process quality

College of Management Science, Chengdu University of Technology, Chengdu 610059, China

* Corresponding author: Xudong Chen

Received  October 2019 Revised  July 2020 Published  October 2020

Fund Project: The work is supported by by the [Soft Science Project for Science & Technology Department of Sichuan Province #1] under Grant [number 20RKX0474]; [Soft Science Project for Chengdu Science and Technology Agency #2] under Grant [number 2020-RK00-00179-ZF]; [Sichuan Civil-military Integration Research Center #3] under Grant [number JMRH-1807]

The quality of High-tech products usually influenced by numerous cross-correlation quality characteristics in production process. However, traditional quality control method is difficult to satisfy the requirement of monitoring and diagnosing multiple related quality characteristics. Scholars found that the diagnosis effect of support vector machine method is better than others. But, constructing fuzzy support vector machine for diagnosis by calculating the sample membership degree from the sample point to the class center is vulnerable to the influence of sample noise points because it will lead to low accuracy rate. Therefore, this paper focus on exploring the issue about the abnormal pattern and intelligent diagnosis of interrelated multivariable process quality, by taking the multivariable quality characteristics of capacitor as research object. Using multivariate exponentially weighted moving average (MEWMA) control chart to joint monitor the multiple quality characteristics. Constructing a fuzzy support vector machine (FSVM) based on cloud calculative model and cuckoo search (CS) for intelligent diagnosis on abnormal pattern. The result showed that the diagnostic accuracy rate for sample data is 97.42%. In instance analysis, the average diagnosis accuracy rate is 95.60%. It verifies the CS-FSVM model has a good diagnosis performance.

Citation: Huiqin Zhang, JinChun Wang, Meng Wang, Xudong Chen. Integration of cuckoo search and fuzzy support vector machine for intelligent diagnosis of production process quality. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020150
References:
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Z. Bo, Research on automatic processing quality control method based on support vector machine, Chongqing University. Google Scholar

[3]

H. M. BushP. ChongfuangprinyaV. C. ChenT. Sukchotrat and S. B. Kim, Nonparametric multivariate control charts based on a linkage ranking algorithm, Quality Reliability Engrg. Internat., 26 (2010), 663-675.  doi: 10.1002/qre.1129.  Google Scholar

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Z.-Y. Chang and J.-S. Sun, Adaptive EWMA control chart statistical economic design, Control Decision, 31 (2015), 1715-1719.   Google Scholar

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C.-S. Cheng and H.-T. Lee, Diagnosing the variance shifts signal in multivariate process control using ensemble classifiers, J. Chinese Institute Engineers, 39 (2016), 64-73.  doi: 10.1080/02533839.2015.1073662.  Google Scholar

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Z.-Q. ChengY.-Z. Ma and J. Bu, Variance shifts identification model of bivariate process based on LS-SVM pattern recognizer, Comm. Statist. Simulation Comput., 40 (2011), 274-284.  doi: 10.1080/03610918.2010.535625.  Google Scholar

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X. Y. ChewM. B. C. KhooS. Y. Teh and P. Castagliola, The variable sampling interval run sum $\bar{X}$ control chart, Comput. & Industr. Engrg., 90 (2015), 25-38.  doi: 10.1016/j.cie.2015.08.015.  Google Scholar

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S. HeW. Jiang and H. Deng, A distance-based control chart for monitoring multivariate processes using support vector machines, Ann. Oper. Res., 263 (2018), 191-207.  doi: 10.1007/s10479-016-2186-4.  Google Scholar

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J. Jiadong and F. Yuncheng, A new control diagram based on characteristic structure of covariance matrix, China Management Sci., 3 (2011), 123-133.   Google Scholar

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M. B. C. KhooZ. WuP. Castagliola and H. C. Lee, A multivariate synthetic double sampling $T^2$ control chart, Comput. & Industr. Engrg., 64 (2013), 179-189.  doi: 10.1016/j.cie.2012.08.017.  Google Scholar

[22]

T.-F. Li, S. Hu, Z.-Y. Wei and Z.-Q. Liao, A framework for diagnosing the out-of-control signals in multivariate process using optimized support vector machines, Math. Probl. Engrg., 2013 (2013). doi: 10.1155/2013/494626.  Google Scholar

[23]

W. LiX. PuF. Tsung and D. Xiang, A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection, Comput. & Industr. Engrg., 103 (2017), 116-130.  doi: 10.1016/j.cie.2016.11.024.  Google Scholar

[24]

Y. LiY. LiuC. Zou and W. Jiang, A self-starting control chart for high-dimensional short-run processes, Internat. J. Prod. Res., 52 (2014), 445-461.  doi: 10.1080/00207543.2013.832001.  Google Scholar

[25]

W. LiangX. Pu and Y. Li, A new EWMA chart based on weighted loss function for monitoring the process mean and variance, Quality Reliability Engrg. Internat., 31 (2015), 905-916.  doi: 10.1002/qre.1647.  Google Scholar

[26]

T. LinghanM. Rui and Y. Dong, An improved control chart of multiple exponential weighted moving average, J.Shanghai Jiaotong Univ., 6 (2010), 868-872.   Google Scholar

[27]

T.-J. LiuZ.-G. Liu and Z.-W. Han, Application of adaptive fuzzy support vector machine proximity increment algorithm in transformer fault diagnosis, Power Syst. Protection Control, 38 (2010), 47-52.   Google Scholar

[28]

Y. LiuB. ZhangB. Chen and Y. Yang, Robust solutions to fuzzy one-class support vector machine, Pattern Recognition Lett., 71 (2016), 73-77.  doi: 10.1016/j.patrec.2015.12.014.  Google Scholar

[29]

H. Long, Research on Ae Signal Feature Extraction and Diagnosis Method of Wind Gearbox Bearing Fault, Doctoral dissertation. Google Scholar

[30]

C. A. LowryW. H. WoodallC. W. Champ and S. E. Rigdon, A multivariate exponentially weighted moving average control chart, Technometrics, 34 (1992), 46-53.  doi: 10.2307/1269551.  Google Scholar

[31]

V. MartynyukM. OrtigueiraM. Fedula and O. Savenko, Methodology of electrochemical capacitor quality control with fractional order model, AEU-Internat. J. Electron. Comm., 91 (2018), 118-124.  doi: 10.1016/j.aeue.2018.05.005.  Google Scholar

[32]

I. Masood and A. Hassan, Bivariate quality control using two-stage intelligent monitoring scheme, Expert Syst. Appl., 41 (2014), 7579-7595.  doi: 10.1016/j.eswa.2014.05.042.  Google Scholar

[33]

I. Masood and V. B. E. Shyen, Quality control in hard disc drive manufacturing using pattern recognition technique, in IOP Conference Series: Materials Science and Engineering, 160, IOP Publishing, 2016. doi: 10.1088/1757-899X/160/1/012008.  Google Scholar

[34]

K. NishimuraS. Matsuura and H. Suzuki, Multivariate EWMA control chart based on a variable selection using AIC for multivariate statistical process monitoring, Statist. Probab. Lett., 104 (2015), 7-13.  doi: 10.1016/j.spl.2015.05.003.  Google Scholar

[35]

J. Park and C.-H. Jun, A new multivariate EWMA control chart via multiple testing, J. Process Control, 26 (2015), 51-55.  doi: 10.1016/j.jprocont.2015.01.007.  Google Scholar

[36]

P. PhaladiganonS. B. KimV. C. P. ChenJ.-G. Baek and S.-K. Park, Bootstrap-based $T^2$ multivariate control charts, Comm. Statist. Simulation Comput., 40 (2011), 645-662.  doi: 10.1080/03610918.2010.549989.  Google Scholar

[37]

V. RanaeeA. Ebrahimzadeh and R. Ghaderi, Application of the PSO–SVM model for recognition of control chart patterns, ISA Transactions, 49 (2010), 577-586.  doi: 10.1016/j.isatra.2010.06.005.  Google Scholar

[38]

M. RaugeiA. Hutchinson and D. Morrey, Can electric vehicles significantly reduce our dependence on non-renewable energy? Scenarios of compact vehicles in the UK as a case in point, J. Cleaner Prod., 201 (2018), 1043-1051.  doi: 10.1016/j.jclepro.2018.08.107.  Google Scholar

[39]

M. SalehiA. Bahreininejad and I. Nakhai, On-line analysis of out-of-control signals in multivariate manufacturing processes using a hybrid learning-based model, Neurocomputing, 74 (2011), 2083-2095.  doi: 10.1016/j.neucom.2010.12.020.  Google Scholar

[40]

M. SalehiR. B. Kazemzadeh and A. Salmasnia, On line detection of mean and variance shift using neural networks and support vector machine in multivariate processes, Appl. Soft Comput., 12 (2012), 2973-2984.  doi: 10.1016/j.asoc.2012.04.024.  Google Scholar

[41]

G. Tuerhong and S. B. Kim, Gower distance-based multivariate control charts for a mixture of continuous and categorical variables, Expert Syst. Appl., 41 (2014), 1701-1707.  doi: 10.1016/j.eswa.2013.08.068.  Google Scholar

[42]

F.-K. WangB. Bizuneh and X.-B. Cheng, One-sided control chart based on support vector machines with differential evolution algorithm, Quality Reliability Engrg. Internat., 35 (2019), 1634-1645.  doi: 10.1002/qre.2465.  Google Scholar

[43]

Z. WangC. ZhaoJ. Yin and B. Zhang, Purchasing intentions of Chinese citizens on new energy vehicles: How should one respond to current preferential policy?, J. Cleaner Prod., 161 (2017), 1000-1010.  doi: 10.1016/j.jclepro.2017.05.154.  Google Scholar

[44]

C. Wu and L. Zhao, Control graph pattern recognition based on wavelet analysis and SVM, China Mechanical Engrg., 21 (2010), 1572-1576.   Google Scholar

[45]

Z.-Z. Wu, Research on monitoring the source of abnormal mean value of multivariable programming using neural network and support vector machine technology, Tao Yuan, Yuanzhi University. Google Scholar

[46]

X. Yan and Y.-Q. Zhang, Membership algorithm for FSVM remote sensing image classification using cloud model, Comput. Appl. Software, 30. Google Scholar

[47]

D.-X. YangL.-S. QiuJ.-J. YanZ.-Y. Chen and M. Jiang, The government regulation and market behavior of the new energy automotive industry, J. Cleaner Prod., 210 (2019), 1281-1288.  doi: 10.1016/j.jclepro.2018.11.124.  Google Scholar

[48]

S.-Y. Yang and H. Zhang, Pattern Recognition and Intelligent Computing, Publishing House of Electronic Industry, Beijing, 2015. Google Scholar

[49]

W.-A. Yang, Monitoring and diagnosing of mean shifts in multivariate manufacturing processes using two-level selective ensemble of learning vector quantization neural networks, J. Intell. Manufac., 26 (2015), 769-783.  doi: 10.1007/s10845-013-0833-z.  Google Scholar

[50]

X. ZhaS. Ni and P. Zhang, Fuzzy support vector machine method based on multi-region partition, J. Central South Univ. (Natural Sci. Ed.), 5 (2015), 1680-1687.  doi: 10.11817/j.issn.1672-7207.2015.05.016.  Google Scholar

[51]

Y.-M. ZhaoZ. He and S.-G. He, Support vector machine multiple control graph mean deviation diagnosis model based on PSO, J. Tianjin Univ. (Natural Sci. Engrg. Tech. Ed.), 46 (2013), 469-475.   Google Scholar

[52]

Y.-M. ZhaoZ. He and M. Zhang, Binary process mean vector and covariance monitoring based on joint control graph, Syst. Engrg., 30 (2012), 111-116.   Google Scholar

show all references

References:
[1]

S. Abe, Fuzzy support vector machines for multilabel classification, Pattern Recognition, 48 (2015), 2110-2117.  doi: 10.1016/j.patcog.2015.01.009.  Google Scholar

[2]

Z. Bo, Research on automatic processing quality control method based on support vector machine, Chongqing University. Google Scholar

[3]

H. M. BushP. ChongfuangprinyaV. C. ChenT. Sukchotrat and S. B. Kim, Nonparametric multivariate control charts based on a linkage ranking algorithm, Quality Reliability Engrg. Internat., 26 (2010), 663-675.  doi: 10.1002/qre.1129.  Google Scholar

[4]

J. CamachoA. Pérez-VillegasP. García Teodoro and G. Maciá Fernández, PCA-based multivariate statistical network monitoring for anomaly detection, Comput. & Security, 59 (2016), 118-137.  doi: 10.1016/j.cose.2016.02.008.  Google Scholar

[5]

G. Capizzi, Recent advances in process monitoring: Nonparametric and variable-selection methods for Phase I and Phase II, Quality Engrg., 27 (2015), 44-67.  doi: 10.1080/08982112.2015.968046.  Google Scholar

[6]

Z.-Y. Chang and J.-S. Sun, Adaptive EWMA control chart statistical economic design, Control Decision, 31 (2015), 1715-1719.   Google Scholar

[7]

C.-S. Cheng and H.-T. Lee, Diagnosing the variance shifts signal in multivariate process control using ensemble classifiers, J. Chinese Institute Engineers, 39 (2016), 64-73.  doi: 10.1080/02533839.2015.1073662.  Google Scholar

[8]

Z.-Q. ChengY.-Z. Ma and J. Bu, Variance shifts identification model of bivariate process based on LS-SVM pattern recognizer, Comm. Statist. Simulation Comput., 40 (2011), 274-284.  doi: 10.1080/03610918.2010.535625.  Google Scholar

[9]

X. Y. ChewM. B. C. KhooS. Y. Teh and P. Castagliola, The variable sampling interval run sum $\bar{X}$ control chart, Comput. & Industr. Engrg., 90 (2015), 25-38.  doi: 10.1016/j.cie.2015.08.015.  Google Scholar

[10]

P. ChinasI. LopezJ. A. VazquezR. Osorio and G. Lefranc, SVM and ANN application to multivariate pattern recognition using scatter data, IEEE Latin America Transactions, 13 (2015), 1633-1639.  doi: 10.1109/TLA.2015.7112025.  Google Scholar

[11]

P. ChongfuangprinyaS. B. KimS.-K. Park and T. Sukchotrat, Integration of support vector machines and control charts for multivariate process monitoring, J. Stat. Comput. Simul., 81 (2011), 1157-1173.  doi: 10.1080/00949651003789074.  Google Scholar

[12]

A. Dhini and I. Surjandari, Review on some multivariate statistical process control methods for process monitoring, in Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management in Kuala Lumpur, 2016,754–759. Google Scholar

[13]

S. DuD. Huang and J. Lv, Recognition of concurrent control chart patterns using wavelet transform decomposition and multiclass support vector machines, Comput. & Industr. Engrg., 66 (2013), 683-695.  doi: 10.1016/j.cie.2013.09.012.  Google Scholar

[14]

A. EbrahimzadehJ. Addeh and Z. Rahmani, Control chart pattern recognition using k-mica clustering and neural networks, ISA transactions, 51 (2012), 111-119.  doi: 10.1016/j.isatra.2011.08.005.  Google Scholar

[15]

Q. FanZ. WangD. LiD. Gao and H. Zha, Entropy-based fuzzy support vector machine for imbalanced datasets, Knowledge-Based Syst., 115 (2017), 87-99.  doi: 10.1016/j.knosys.2016.09.032.  Google Scholar

[16]

S. HeW. Jiang and H. Deng, A distance-based control chart for monitoring multivariate processes using support vector machines, Ann. Oper. Res., 263 (2018), 191-207.  doi: 10.1007/s10479-016-2186-4.  Google Scholar

[17]

S.-G. He and E.-S. Qi, Multivariate statistical process control and diagnosis model based on projection transformation, J. Tianjin Univ., 41 (2008), 1512-1517.   Google Scholar

[18]

H. Hotelling, Multivariate Quality Control. Techniques of Statistical Analysis, McGraw-Hill, New York. Google Scholar

[19]

C.-C. HsuM.-C. Chen and L.-S. Chen, Intelligent ICA–SVM fault detector for non-Gaussian multivariate process monitoring, Expert Syst. Appl., 37 (2010), 3264-3273.  doi: 10.1016/j.eswa.2009.09.053.  Google Scholar

[20]

J. Jiadong and F. Yuncheng, A new control diagram based on characteristic structure of covariance matrix, China Management Sci., 3 (2011), 123-133.   Google Scholar

[21]

M. B. C. KhooZ. WuP. Castagliola and H. C. Lee, A multivariate synthetic double sampling $T^2$ control chart, Comput. & Industr. Engrg., 64 (2013), 179-189.  doi: 10.1016/j.cie.2012.08.017.  Google Scholar

[22]

T.-F. Li, S. Hu, Z.-Y. Wei and Z.-Q. Liao, A framework for diagnosing the out-of-control signals in multivariate process using optimized support vector machines, Math. Probl. Engrg., 2013 (2013). doi: 10.1155/2013/494626.  Google Scholar

[23]

W. LiX. PuF. Tsung and D. Xiang, A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection, Comput. & Industr. Engrg., 103 (2017), 116-130.  doi: 10.1016/j.cie.2016.11.024.  Google Scholar

[24]

Y. LiY. LiuC. Zou and W. Jiang, A self-starting control chart for high-dimensional short-run processes, Internat. J. Prod. Res., 52 (2014), 445-461.  doi: 10.1080/00207543.2013.832001.  Google Scholar

[25]

W. LiangX. Pu and Y. Li, A new EWMA chart based on weighted loss function for monitoring the process mean and variance, Quality Reliability Engrg. Internat., 31 (2015), 905-916.  doi: 10.1002/qre.1647.  Google Scholar

[26]

T. LinghanM. Rui and Y. Dong, An improved control chart of multiple exponential weighted moving average, J.Shanghai Jiaotong Univ., 6 (2010), 868-872.   Google Scholar

[27]

T.-J. LiuZ.-G. Liu and Z.-W. Han, Application of adaptive fuzzy support vector machine proximity increment algorithm in transformer fault diagnosis, Power Syst. Protection Control, 38 (2010), 47-52.   Google Scholar

[28]

Y. LiuB. ZhangB. Chen and Y. Yang, Robust solutions to fuzzy one-class support vector machine, Pattern Recognition Lett., 71 (2016), 73-77.  doi: 10.1016/j.patrec.2015.12.014.  Google Scholar

[29]

H. Long, Research on Ae Signal Feature Extraction and Diagnosis Method of Wind Gearbox Bearing Fault, Doctoral dissertation. Google Scholar

[30]

C. A. LowryW. H. WoodallC. W. Champ and S. E. Rigdon, A multivariate exponentially weighted moving average control chart, Technometrics, 34 (1992), 46-53.  doi: 10.2307/1269551.  Google Scholar

[31]

V. MartynyukM. OrtigueiraM. Fedula and O. Savenko, Methodology of electrochemical capacitor quality control with fractional order model, AEU-Internat. J. Electron. Comm., 91 (2018), 118-124.  doi: 10.1016/j.aeue.2018.05.005.  Google Scholar

[32]

I. Masood and A. Hassan, Bivariate quality control using two-stage intelligent monitoring scheme, Expert Syst. Appl., 41 (2014), 7579-7595.  doi: 10.1016/j.eswa.2014.05.042.  Google Scholar

[33]

I. Masood and V. B. E. Shyen, Quality control in hard disc drive manufacturing using pattern recognition technique, in IOP Conference Series: Materials Science and Engineering, 160, IOP Publishing, 2016. doi: 10.1088/1757-899X/160/1/012008.  Google Scholar

[34]

K. NishimuraS. Matsuura and H. Suzuki, Multivariate EWMA control chart based on a variable selection using AIC for multivariate statistical process monitoring, Statist. Probab. Lett., 104 (2015), 7-13.  doi: 10.1016/j.spl.2015.05.003.  Google Scholar

[35]

J. Park and C.-H. Jun, A new multivariate EWMA control chart via multiple testing, J. Process Control, 26 (2015), 51-55.  doi: 10.1016/j.jprocont.2015.01.007.  Google Scholar

[36]

P. PhaladiganonS. B. KimV. C. P. ChenJ.-G. Baek and S.-K. Park, Bootstrap-based $T^2$ multivariate control charts, Comm. Statist. Simulation Comput., 40 (2011), 645-662.  doi: 10.1080/03610918.2010.549989.  Google Scholar

[37]

V. RanaeeA. Ebrahimzadeh and R. Ghaderi, Application of the PSO–SVM model for recognition of control chart patterns, ISA Transactions, 49 (2010), 577-586.  doi: 10.1016/j.isatra.2010.06.005.  Google Scholar

[38]

M. RaugeiA. Hutchinson and D. Morrey, Can electric vehicles significantly reduce our dependence on non-renewable energy? Scenarios of compact vehicles in the UK as a case in point, J. Cleaner Prod., 201 (2018), 1043-1051.  doi: 10.1016/j.jclepro.2018.08.107.  Google Scholar

[39]

M. SalehiA. Bahreininejad and I. Nakhai, On-line analysis of out-of-control signals in multivariate manufacturing processes using a hybrid learning-based model, Neurocomputing, 74 (2011), 2083-2095.  doi: 10.1016/j.neucom.2010.12.020.  Google Scholar

[40]

M. SalehiR. B. Kazemzadeh and A. Salmasnia, On line detection of mean and variance shift using neural networks and support vector machine in multivariate processes, Appl. Soft Comput., 12 (2012), 2973-2984.  doi: 10.1016/j.asoc.2012.04.024.  Google Scholar

[41]

G. Tuerhong and S. B. Kim, Gower distance-based multivariate control charts for a mixture of continuous and categorical variables, Expert Syst. Appl., 41 (2014), 1701-1707.  doi: 10.1016/j.eswa.2013.08.068.  Google Scholar

[42]

F.-K. WangB. Bizuneh and X.-B. Cheng, One-sided control chart based on support vector machines with differential evolution algorithm, Quality Reliability Engrg. Internat., 35 (2019), 1634-1645.  doi: 10.1002/qre.2465.  Google Scholar

[43]

Z. WangC. ZhaoJ. Yin and B. Zhang, Purchasing intentions of Chinese citizens on new energy vehicles: How should one respond to current preferential policy?, J. Cleaner Prod., 161 (2017), 1000-1010.  doi: 10.1016/j.jclepro.2017.05.154.  Google Scholar

[44]

C. Wu and L. Zhao, Control graph pattern recognition based on wavelet analysis and SVM, China Mechanical Engrg., 21 (2010), 1572-1576.   Google Scholar

[45]

Z.-Z. Wu, Research on monitoring the source of abnormal mean value of multivariable programming using neural network and support vector machine technology, Tao Yuan, Yuanzhi University. Google Scholar

[46]

X. Yan and Y.-Q. Zhang, Membership algorithm for FSVM remote sensing image classification using cloud model, Comput. Appl. Software, 30. Google Scholar

[47]

D.-X. YangL.-S. QiuJ.-J. YanZ.-Y. Chen and M. Jiang, The government regulation and market behavior of the new energy automotive industry, J. Cleaner Prod., 210 (2019), 1281-1288.  doi: 10.1016/j.jclepro.2018.11.124.  Google Scholar

[48]

S.-Y. Yang and H. Zhang, Pattern Recognition and Intelligent Computing, Publishing House of Electronic Industry, Beijing, 2015. Google Scholar

[49]

W.-A. Yang, Monitoring and diagnosing of mean shifts in multivariate manufacturing processes using two-level selective ensemble of learning vector quantization neural networks, J. Intell. Manufac., 26 (2015), 769-783.  doi: 10.1007/s10845-013-0833-z.  Google Scholar

[50]

X. ZhaS. Ni and P. Zhang, Fuzzy support vector machine method based on multi-region partition, J. Central South Univ. (Natural Sci. Ed.), 5 (2015), 1680-1687.  doi: 10.11817/j.issn.1672-7207.2015.05.016.  Google Scholar

[51]

Y.-M. ZhaoZ. He and S.-G. He, Support vector machine multiple control graph mean deviation diagnosis model based on PSO, J. Tianjin Univ. (Natural Sci. Engrg. Tech. Ed.), 46 (2013), 469-475.   Google Scholar

[52]

Y.-M. ZhaoZ. He and M. Zhang, Binary process mean vector and covariance monitoring based on joint control graph, Syst. Engrg., 30 (2012), 111-116.   Google Scholar

Figure 1.  The relevant literatures of multivariate quality control
Figure 2.  Cloud model of sample "standard" and its digital characteristics
Figure 3.  The flow diagram of cuckoo research algorithm
Figure 4.  Fractal visualization diagram of sample data and category labels
Figure 5.  Fractal visualization diagram of sample data and category labels
Figure 6.  Fitness curve of original sample parameter optimization by cuckoo search algorithm
Figure 7.  Fitness curve of optimization of sample parameters with degree of membership by cuckoo search algorithm
Figure 8.  Classification results of 7 types of abnormal test for mean deviation of variables $ D $, $ E $ and $ L $
Figure 9.  The degree of membership of quality characteristics of $ D $ and $ E $
Figure 10.  Classification results of 7 types of abnormal test of mean deviation for variables $ D $, $ E $ and $ L $ with degree of membership
Figure 11.  Comparison of actual classification and prediction classification of original sample test set
Figure 12.  Comparison of actual classification and prediction classification of sample test sets with degree of membership
Figure 13.  MEWMA control chart for chip diameter (d) and height (h)
Figure 14.  The optimization results for parameters $ C $ and $ g $
Figure 15.  Comparison between actual classification and prediction classification of sample test set
Table 1.  The abnormal pattern of $ P = 3 $
Number of abnormal variables Production process status Combination patterns Output value
No abnormity (0, 0, 0)
One Mean-shift of first variable (1, 0, 0) 1
Mean-shift of Second variable (0, 1, 0) 2
Mean-shift of Third variable (0, 0, 1) 3
Two Mean-shift of first and second variable (1, 1, 0) 4
Mean-shift of first and third variable (1, 0, 1) 5
Mean-shift of second and third variable (0, 1, 1) 6
Three Mean-shift of three variables (1, 1, 1) 7
Number of abnormal variables Production process status Combination patterns Output value
No abnormity (0, 0, 0)
One Mean-shift of first variable (1, 0, 0) 1
Mean-shift of Second variable (0, 1, 0) 2
Mean-shift of Third variable (0, 0, 1) 3
Two Mean-shift of first and second variable (1, 1, 0) 4
Mean-shift of first and third variable (1, 0, 1) 5
Mean-shift of second and third variable (0, 1, 1) 6
Three Mean-shift of three variables (1, 1, 1) 7
Table 2.  Comparison of abnormity diagnostic effect
Type Mean offset Diagnostic accuracy
CS-FSVM CS-SVM FSVM SVM
(1, 0, 0) $ (3\sigma, 0, 0) $ 96.74% 86.44% 88.28% 78.86%
(0, 1, 0) $ (0, 3\sigma, 0) $ 98.15% 88.5% 90.36% 86.34%
(0, 0, 1) $ (0, 0, 3\sigma) $ 97.24% 89.33% 92.54% 88.52%
(1, 1, 0) $ (3\sigma, 3\sigma, 0) $ 96.65% 90.65% 89.25% 84.3%
(1, 0, 1) $ (3\sigma, 0, 3\sigma) $ 98.5% 87.5% 89.37% 82.65%
(0, 1, 1) $ (0, 3\sigma, 3\sigma) $ 97.26% 88.26% 88.42% 79.64%
(1, 1, 1) $ (3\sigma, 3\sigma, 3\sigma) $ 97.71% 80.71% 82.77% 80.22%
Average diagnostic accuracy 97.42% 87.34% 88.71% 82.93%
Type Mean offset Diagnostic accuracy
CS-FSVM CS-SVM FSVM SVM
(1, 0, 0) $ (3\sigma, 0, 0) $ 96.74% 86.44% 88.28% 78.86%
(0, 1, 0) $ (0, 3\sigma, 0) $ 98.15% 88.5% 90.36% 86.34%
(0, 0, 1) $ (0, 0, 3\sigma) $ 97.24% 89.33% 92.54% 88.52%
(1, 1, 0) $ (3\sigma, 3\sigma, 0) $ 96.65% 90.65% 89.25% 84.3%
(1, 0, 1) $ (3\sigma, 0, 3\sigma) $ 98.5% 87.5% 89.37% 82.65%
(0, 1, 1) $ (0, 3\sigma, 3\sigma) $ 97.26% 88.26% 88.42% 79.64%
(1, 1, 1) $ (3\sigma, 3\sigma, 3\sigma) $ 97.71% 80.71% 82.77% 80.22%
Average diagnostic accuracy 97.42% 87.34% 88.71% 82.93%
Table 3.  Diagnosis results of application example for model
Abnormal variable Combination pattern Diagnosis accuracy Average accuracy
(d) (1, 0) 95.42% 95.60%
(h) (0, 1) 96.08%
(d) & (h) (1, 1) 95.31%
Abnormal variable Combination pattern Diagnosis accuracy Average accuracy
(d) (1, 0) 95.42% 95.60%
(h) (0, 1) 96.08%
(d) & (h) (1, 1) 95.31%
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