A new control chart based on discriminant analysis for simple linear profiles monitoring
الموضوعات :
Mona Ayoubi
1
(Industrial Engineering Department, West Tehran Branch- Islamic Azad University-shahid Azari Street- Ashrafi Esfahani Highway -Tehran-Iran)
Negin Khaksari
2
(Industrial Engineering Department, West Tehran Branch- Islamic Azad University-shahid Azari Street- Ashrafi Esfahani Highway -Tehran-Iran)
الکلمات المفتاحية: Statistical Process Control, discriminant analysis, Profile monitoring, simple linear profiles, Phase II,
ملخص المقالة :
In many processes, quality characteristic is identified by the regression relationship between one or more dependent variables and one or more independent variables called profile. In this paper, a control chart based on discriminant analysis (DA) is proposed to monitor simple linear profiles in Phase II. A chi-square control chart joined with DA chart is also used to improve detecting variance shifts. Performance of the proposed method is evaluated in terms of average run length using Monte-Carlo simulations. Performance of the proposed control chart is compared to the basic methods in simple linear profile monitoring. Results present the desirable performance of the proposed method. The real case in shoes leather industry is also investigated to show the effectiveness of the proposed method. results also confirm an acceptable performance of the real case, because the average run length of the proposed control chart is less than the average run length of the comparable method.
[2] Amiri, A., Zand, A., & Soudbakhsh, D. (2011, January). Monitoring simple linear profiles in the leather industry (a case study). In Proceedings of the 2nd International Conference on Industrial Engineering and Operations Management, Kuala Lumpur, Malaysia (pp. 22-24).
[3] Deng, X., Tian, X., Chen, S., & Harris, C. J. (2017). Fault discriminant enhanced kernel principal component analysis incorporating prior fault information for monitoring nonlinear processes. Chemometrics and Intelligent Laboratory Systems, 162, 21-34.
[4] Galiaskarov, M. R., Kurkina, V. V., & Rusinov, L. A. (2017). Online diagnostics of timevarying nonlinear chemical processes using moving window kernel principal component analysis and Fisher discriminant analysis. Journal of Chemometrics, 31(8), e2866.
[5] Gupta, S., Montgomery, D. C., & Woodall, W. H. (2006). Performance evaluation of two methods for online monitoring of linear calibration profiles. International Journal of Production Research, 44(10), 1927-1942.
[6] Haq, A., Bibi, M., & Shah, B. A. (2020). A novel approach to monitor simple linear profiles using individual observations. Communications in Statistics-Simulation and Computation, DOI:
10.1080/03610918.2020.1799229.
[7] Hosseinifard, S. Z., Abdollahian, M., & Zeephongsekul, P. (2011). Application of artificial neural networks in linear profile monitoring. Expert Systems with Applications, 38(5), 4920-4928.
[8] HU, Y. X., & LI, X. B. (2012). Bayes discriminant analysis method to identify risky of complicated goaf in mines and its application. Transactions of Nonferrous Metals Society of China, 22(2), 425-431.
[10] Kalaei, M., Soleimani, P., Niaki, S. T. A., & Atashgar, K. (2018). Phase-I monitoring of standard deviations in multistage linear profiles. Journal of Industrial Engineering International, 14(1), 133-142.
[11] Kang, L., & Albin, S. L. (2000). On-line monitoring when the process yields a linear profile. Journal of quality Technology, 32(4), 418-426.
[12] Kim, K., Mahmoud, M. A., & Woodall, W. H. (2003). On the monitoring of linear profiles. Journal of Quality Technology, 35(3), 317-328.
[13] Li, Z., & Wang, Z. (2010). An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles. Computers & Industrial Engineering, 59(4), 630-637.
[14] Lim, Y. F., Yahaya, S. S. S., & Ali, H. (2018). Robust Linear Discriminant Analysis with Highest Breakdown Point Estimator. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 10(1-11), 7-12.
[15] Mahmoud, M. A., Morgan, J. P., & Woodall, W. H. (2010). The monitoring of simple linear regression profiles with two observations persample. Journal of Applied Statistics, 37(8), 1249-1263.
[16] Maleki, M. R. (2015). Online monitoring and fault diagnosis of multivariate-attribute process mean using neural networks and discriminant analysis technique. International Journal of Engineering, 28(11), 1634-1643.
[18] Máquina, A. D. V., Souza, L. M. D., Gontijo, L. C., Santos, D. Q., & Borges Neto, W. (2017). Characterization of Biodiesel by Infrared Spectroscopy with Partial Least Square Discriminant Analysis. Analytical Letters, 50(13), 2117-2128.
[19] Moheghi, H. R., Noorossana, R., & Ahmadi, O. (2020). GLM profile monitoring using robust estimators. Quality and Reliability Engineering International. DOI: 10.1002/qre.2755.
[20] Narvand, A., Soleimani, P., & Raissi, S. (2013). Phase II monitoring of auto-correlated linear profiles using linear mixed model. Journal of Industrial Engineering International, 9(1), 12.
[22] Noorossana, R., & Ayoubi, M. (2012). Profile monitoring using nonparametric bootstrap T 2 control chart. Communications in Statistics- Simulation and Computation, 41(3), 302-315.
[23] Noorossana, R., Eyvazian, M., & Vaghefi, A. (2010). Phase II monitoring of multivariate simple linear profiles. Computers & Industrial Engineering, 58(4), 563-570.
[24] Nor, N. M., Hussain, M. A., & Hassan, C. R. C. (2015). Process monitoring and fault detection in non-linear chemical process based on multi-scale kernel Fisher discriminant analysis. In Computer Aided Chemical Engineering (Vol. 37, pp. 1823-1828). Elsevier.
[25] Nor, N. M., Hussain, M. A., & Hassan, C. R. C. (2017). Fault diagnosis and classification framework using multi-scale classification based on kernel Fisher discriminant analysis for chemical process system. Applied Soft Computing, 61, 959-972.
[26] Pei, X., Yamashita, Y., Yoshida, M., & Matsumoto, S. (2006). Discriminant analysis and control chart for the fault detection and identification. In Computer Aided Chemical Engineering (Vol. 21, pp.1281-1286). Elsevier.
[27] Rahimi, S. B., Amiri, A., & Ghashghaei, R. (2019). Simultaneous monitoring of mean vector and covariance matrix of multivariate simple linear profiles in the presence of within profile autocorrelation. Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2019.1588314.
[28] Ren, R., Han, K., Zhao, P., Shi, J., Zhao, L., Gao, D., ... & Yang, Z. (2019). Identification of asphalt fingerprints based on ATR-FTIR spectroscopy and principal component-linear discriminant
analysis. Construction and Building Materials, 198, 662-668.
[29] Theophilou, G., Lima, K. M., Martin-Hirsch, P. L., Stringfellow, H. F., & Martin, F. L. (2016). ATR-FTIR spectroscopy coupled with chemometric analysis discriminates normal, borderline and malignant ovarian tissue: classifying subtypes of human cancer. Analyst, 141(2), 585-594.
[30] Wang, Y., Zhou, J., Wei, G., Dong, Z., & Chen, H. (2016). Stator winding single-phase grounding faults protective scheme based on discriminant analysis for Powerformers with selectivity. International Journal of Electrical Power & Energy Systems, 77, 145-150.
[31] Yan, B., Fang, Z., Shen, L., & Qu, H. (2015). Root Cause Analysis of Quality Defects Using HPLC–MS Fingerprint Knowledgebase for Batch tobatch Quality Control of Herbal Drugs. Phytochemical analysis, 26(4), 261-268.
[32] Yazdi, A. A., Hamadani, A. Z., & Amiri, A. (2019). Phase II monitoring of multivariate simple linear profiles with estimated parameters. Journal of Industrial Engineering International, 15(4), 557-570.
[33] Zhang, J., Li, Z., & Wang, Z. (2009). Control chart based on likelihood ratio for monitoring linear profiles. Computational statistics & data analysis, 53(4), 1440-1448.
[34] Zhang, G., Sun, H., Ji, Z., Xia, G., Feng, L., & Sun, Q. (2016). Kernel dictionary learning based discriminant analysis. Journal of Visual Communication and Image Representation, 40, 470-484.
[35] Zhao, C., & Gao, F. (2015). A nested-loop Fisher discriminant analysis algorithm. Chemometrics and Intelligent Laboratory Systems, 146,396-406.
[36] Zhao, C., Wang, W., & Gao, F. (2016). Probabilistic fault diagnosis based on Monte Carlo and nested-loop fisher discriminant analysis for industrial processes. Industrial & Engineering Chemistry Research, 55(50), 12896-12908.
[37] Zheng, J., Wang, H., Song, Z., & Ge, Z. (2019). Ensemble semi- supervised Fisher discriminant analysis model for fault classification in industrial processes. ISA transactions, 92, 109-117.
[38] Zhu, J., & Lin, D. K. (2009). Monitoring the slopes of linear profiles. Quality Engineering, 22(1), 1-12.
[41] Zou, C., Zhou, C., Wang, Z., & Tsung, F. (2007). A self-starting control chart for linear profiles. Journal of Quality Technology, 39(4), 364-375.
