Performance of Cluster-Based Logistic Profile Monitoring Under Existence of Different Linkage Functions

Subject Areas : Statistical Quality Control

Davood Saremian ¹ , Rasool Noorossana ^{2 *} , Sadigh Raissi ³ , Paria Soleimani ⁴

1 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Information Systems and Operations Management Department, College of Business, University of Central Oklahoma, Edmond, OK, 73034, United States
3 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
4 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2023-10-03 Accepted : 2024-09-04 Published : 2024-09-05

Keywords: Binary logistic profiles, Linkage functions, Phase I analysis, Hotelling T^2, Cluster-based control chart,

Abstract :

In monitoring the quality of a product or process, in some cases, the description of the relationship between a response variable and one or more descriptive variables is used, which is called as a profile. But the perceptible challenge in this issue is the reliable estimation of profile parameters that can be very deviated under the influence of outliers. The current study investigates the effect of using different linkage functions, including complete, average, single, weighted, centroid, median, and ward linkage on the performance of cluster-based control charts to monitor logistic profiles. The results of performance comparison based on simulation runs showed that the Hotelling T^2 control chart based on clustering method has better performance than non-clustering method. Also, the performance of using various linkage functions such as average, centroid, and ward linkage outperforms than a complete linkage, and a more accurate estimate of the parameters of control charts is obtained.

References:

[1] Kang, L., & Albin, S.L. (2000). On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 32(4): 418-426. DOI: 10.1080/00224065.2000.11980027
[2] Soleimani, P., Noorossana, R. & Amiri, A. (2009). Simple linear profiles monitoring in the presence of within profile autocorrelation. Computers and Industrial Engineering, 57(3):1015-1021. DOI: 10.1016/j.cie.2009.04.005
[3] Chen, S., & Nembhard, H. B. (2010). A high-dimensional control chart for profile monitoring. Quality and Reliability Engineering International, 27(4), 451–464. DOI:10.1002/qre.1140
[4] Noorossana, R., Aminmadani, M., & Saghaei, A. (2016). Effect of phase I estimation error on the monitoring of simple linear profiles in Phase II. IntJ Adv Manuf Technol, 84:873-884. DOI:10.1007/s00170-015-7078-2
[5] Mahmood, T., Abbasi, S.A., Riaz, M., & Abbas, N.(2019). An efficient Phase I analysis of linear profiles with application in photo-voltaic system. Arab J Sci Eng. 2019;44(3):2699-2716. DOI:10.1007/s13369-018-3426-5
[6] Moheghi, H.R., Noorossana, R., Ahmadi, O. (2020) Phase I and Phase II analysis of linear profile monitoring using robust estimators. Commun Stat Theory Methods. 49:1-18. DOI:10.1080/03610926.2020.1758724
[7] Ghasemi, Z., Zeinal Hamadani, A., & Ahmadi Yazdi, A. (2023). New methods for phase II monitoring of multivariate simple linear profiles. Communications in Statistics-Simulation and Computation, 1-25. DOI:10.1080/03610918.2023.2249268
[8] Pakzad, A., Adibfar, S., Razavi, H., & Noorossana, R. (2023). Process capability analysis for simple linear profiles. Qual Quan. DOI: 10.1007/s11135-023-01726-4
[9] Adibfar, S., Noorossana, R., & Ahmadi, O. (2023). Process capability analysis for multivariate simple linear profiles in a multistage process. Journal of Industrial and Systems Engineering, 14(4), 158-173. DOI:10.18187/pjsor.v20i1.4410
[10] Williams, J.D., Woodall, W.H., Birch, J.B., & Sullivan, J.H. (2006). Distribution of Hotelling’s T2 Statistic Based on the Successive Differences Estimator. Journal of Quality Technology. 38(3), 217–229. DOI:10.1080/00224065.2006.11918611
[11] Steiner, S., Jensen, W.A., Grimshaw, S.D., & Espen, B.(2016). Nonlinear profile monitoring for oven-temperature data. J Qual Technol. 48(1):84-97. DOI:10.1080/00224065.2016.11918153
[12] Pan, J.N., Li ,C.I., Lu, M.Z. (2019). Detecting the process changes for multivariate nonlinear profile data. Qual Reliab Eng Int.35:1890-1910. DOI:10.1002/qre.2482.
[13] Noorossana, R., Saghaei, A., Amiri, A.(2012). Statistical Analysis of Profile Monitoring. Hoboken, NJ: John Wiley & Sons.
[14] Maleki, M.R., Amiri, A., Castagliola, P. (2018) An overview on recent profile monitoring papers based on conceptual classification scheme. Comput Ind Eng. 126:705-728. DOI:10.1016/j.cie.2018.10.008
[15] Cheng, C. S., Chen, P. W., & Wu, Y. T. (2023). Phase I Analysis of Nonlinear Profiles Using Anomaly Detection Techniques. Applied Sciences, 13(4), 2147. DOI:10.3390/app13042147
[16] Montgomery, D.C., Peck, E.A, and Vining, G,G.(2008). Introduction to Linear Regression Analysis, fourth edition, Wiley, Hoboken, NJ .
[17] Yeh, A.B., Huwang, L., & Li, Y.M. (2009). Profile monitoring for a binary response. IIE Transactions. 41(11):931-941. DOI: 10.1080/07408170902735400
[18] Shang, Y., Tsung, F., & Zou, C. (2011). Profile Monitoring with Binary Data and Random Predictors. Journal of Quality Technology. 43(3), 196–208. DOI:10.1080/00224065.2011.11917857
[19] Koosha, M., & Amiri, A. (2012). Generalized linear mixed model for monitoring autocorrelated logistic regression profiles. International Journal of Advanced Manufacturing Technology. 64(1-4):487-495.DOI: 10.1007/s00170-012-4018-2
[20] Paynabar, K., Jin, J., & Yeh, A.B. (2012). Phase I Risk-Adjusted Control Charts for Monitoring Surgical Performance by Considering Categorical Covariates. Journal of Quality Technology. 44(1), 39 53. DOI:10.1080/00224065.2012.11917880
[21] Amiri, A., Koosha, M., Azhdari, A. & Wang, G. (2014). Phase I monitoring of generalized linear model-based regression profiles. Journal of Statistical Computation and Simulation. 85(14), 2839-2859. DOI: 10.1080/00949655.2014.942864
[22] Shadman, A., Mahlooji, H., Yeh, A.B., & Zou, C. (2015). A change-point method for monitoring generalized linear profiles in Phase I. Quality and Reliability Engineering International. 31(8):1367-1381. DOI: 10.1002/qre.1671
[23] Shadman, A., Mahlooji, H., & Yeh, A.B. (2014). A Change Point Method for Phase II Monitoring of Generalized Linear Profiles. Communications in Statistics - Simulation and Computation. 46(1): 559–578. DOI:10.1080/03610918.2014.970698
[24] Noorossana, R., Niaki, S., Izadbakhsh, H. (2015). Statistical monitoring of nominal logistic profiles in phase II. Commun Stat Theory Methods. 44(13):2689-2704. DOI:10.1080/03610926.2013.788712
[25] Shang, Y., Wand, Z., He, Z., & He, S. (2017). Nonparametric change-point detection for profiles with binary data. J Qual Technol. 49(2):123-135. DOI:10.1080/00224065.2017.11917984
[26] Izadbakhsh, H., Noorossana, R., & Niaki, S. T. A. (2018). Monitoring multinomial logistic profiles in Phase I using log-linear models. International Journal of Quality & Reliability Management. 35(3), 678–689. DOI:10.1108/ijqrm-04-2017-0068
[27] Bandara, K., Abdel-Salam, A.S. G., & Birch, J. B. (2020). Model robust profile monitoring for the generalized linear mixed model for Phase I analysis. Applied Stochastic Models in Business and Industry. 36(6), 1037-1059. DOI:10.1002/asmb.2587
[28] Hakimi, A., Amiri, A., & Kamranrad, R. (2017). Robust approaches for monitoring logistic regression profiles under outliers. International Journal of Quality & Reliability Management. 34(4), 494–507. DOI:10.1108/ijqrm-04-2015-0053
[29] Hakimi, A., Amiri, A., & Kamranrad, R. (2018). Robust Method for Logistic Profiles Monitoring in Phase I. Production and Operations Management. 9(16). DOI: 10.22108/JPOM.2018.92335.0
[30] Moheghi, H.R., Noorossana, R., & Ahmadi, O. (2020). GLM profile monitoring using robust estimators. Quality and Reliability Engineering International. 1– 17. DOI:10.1002/qre.2755
[31] Cantoni, E., Ronchetti, E. (2001). Robust inference for generalized linear models. J Am Statist Assoc. 96(455):1022-1030. DOI: 10.1198/016214501753209004
[32] Saremian, D., Noorossana, R., Raissi, S., & Soleimani, P. (2021). Robust Cluster-Based method for monitoring generalized linear profiles in phase I. Journal of Industrial Engineering, International. 17(1), 88-97. DOI: 2021.1920761.1085
[33] Chen, Y., Birch, J.B., & Woodall, WH. (2015). Cluster-Based Profile Analysis in Phase I. Journal of Quality Technology 2015. 47(1):14–29. DOI:10.1080/00224065.2015.11918103
[34] Saremian, D., Noorossana, R., Raissi, S., Soleimani, P. (2022). Monitoring logistic profiles in phase I using robust cluster-based method. Qual Reliab Eng Int. 38: 1977– 1993. DOI:10.1002/qre.3054
[35] McCullagh, P., Nelder, J.A. (1989) Generalized Linear Models (2nd edn), Chapman & Hall, London, UK.
[36] Dobson, A.J., Barnett,A.G. (2008). An Introduction to Generalized Linear Models, Third Edition, CRC Press,Taylor & Francis Group.