Development of Clustering Technique and Genetic Algorithm to Monitor Multivariate Descriptive Processes based on Large-scale Nominal Contingency Tables (Case Study: Renewable Energy Process )

Subject Areas : Control Chart

Yaser  Vahedi Geshniani ¹ (Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
Bijan  Rahmani ² (Department of Industrial Engineering, Faculty of Technology and Engineering, Central Tehran Branch, Tehran, Iran.)
Reza  Kamranrad ³ (Department of industrial engineering, faculty of engineering, Semnan university, Semnan, Iran)

Received: 2022-02-15 Accepted : 2023-01-02 Published : 2022-06-01

Keywords: Genetic Algorithm, large-scale contingency table, log-linear model, correspondence analysis, Statistical process monitoring,

Abstract :

Many real-world issues are based on multivariate processes with descriptive characteristics that are represented by contingency tables. A contingency table is a tool for showing the simultaneous relationship of two or more descriptive variables that is modeled by the log-linear communication function and monitored over time. In some statistical process monitoring (SPM) applications, we are faced with the multiplicity of variables and, of course, the number of nominal classifications of the response variable. To model them, a log-linear model based on large-scale contingency tables is used that are called nominal large-scale descriptive multivariate processes. In monitoring this type of process, we face the negative impact of large dimensions of contingency tables on the performance of control charts. For this purpose, a new approach based on the clustering approach in correspondence analysis have been developed to reduce the effect of large dimensions and improvement performance of the control charts in diagnosing out of control status. The performance of control charts has been evaluated using simulated studies and the results indicate the appropriate efficiency of the proposed approach in reducing the impact of the contingency table dimensions on the performance of the control charts. In addition, to demonstrate the performance efficiency of the proposed methods, a real case study in the field of renewable energy has been used, the results of which indicate the proper performance of the proposed control charts in diagnosing out of control status.

References:

[1] Amiri, A., Hakimi, A., Farughi, H., & Arkat, J. (2022). Phase I Monitoring of Multivariate Ordinal based Processes: The MR and LRT Approaches (A real case study in drug dissolution process). International Journal of Industrial Engineering and Production Research, 33(1).

[2] Farahani, A., Tohidi, H., Shoja, A. (2019). An integrated optimization of quality control chart parameters and preventive maintenance using Markov chain. Advances in Production Engineering & Management. 14(1), pp 5–14. https://doi.org/10.14743/apem2019.1.307

[3] Farahani, A., Tohidi, H., Shoja, A. (2020). Optimization of Overall Equipment Effectiveness with Integrated Modeling of Maintenance and Quality. Engineering Letters, 28(2),

[4] Greenacre ،M. (2007). Correspondence analysis in practice. CRC press.

[5] Hakimi, A., Farughi, H., Amiri, A., & Arkat, J. (2019). New phase II control chart for monitoring ordinal contingency table based processes. Journal of Industrial and Systems Engineering, 12(Statistical Processes and Statistical Modeling).

[6] Hakimi, A., Farughi, H., Amiri, A., & Arkat, J. (2021). Phase II Monitoring of the Ordinal Multivariate Categorical Processes. Advances in Industrial Engineering, 55(3), 249-267.

[7] Kamranrad, R., & Bashiri, M. (2015). A novel approach in multi response optimization for correlated categorical data., scientia Iranica, 1117-1129.
[8] Kamranrad, R., Amiri, A., & Niaki, S.T.A. (2017a). New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II. Quality and Reliability Engineering International, 33(5), 1105-1129.
[9] Kamranrad, R., Amiri, A., & Niaki, S.T.A. (2017b). Phase II monitoring and diagnosing of multivariate categorical processes using generalized linear testbased control charts, Communications in Statistics-Simulation and Computation, 46(8), 5951-5980.
[10] Kamranrad, R., Amiri, A., Niaki, S.T.A. (2019). “Phase‐I monitoring of log‐linear model‐based processes (a case study in health care: Kidney patients),” Quality and Reliability Engineering International. 35(6), 1766-1788.
[11] Li J., Tsung F., Zou C. (2012). Directional control schemes for multivariate categorical processes. Journal of Quality Technology. 44: 136-155.
[12] Li J., Zou C., Wang Z., Huwang L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of Quality Technology. 45: 149-165.
[13] Li, J., Tsung, F., & Zou, C. (2014a). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), 526-542.
[14] Li, J., Tsung, F., & Zou, C. (2014b). A simple categorical chart for detecting location shifts with ordinal information. International Journal of Production Research, 52(2), 550-562.
[15] Tsung F., Zou C. (2013). Statistical process control for multistage processes with binary outputs. IIE Transactions. 45: 1008- 1023.
[16] Wang, Y., Snee, R.D., Keyvan, G., Muzzio, F.J. (2016). “Statistical comparison of dissolution profiles,” Drug Development and Industrial Pharmacy. 42(5), pp. 796–807.
[17] Yamamoto, K., Murakami, H. Model based on skew normal distribution for square contingency tables with ordinal categories. Comput Stat Data Anal. (2014).
[18] Yashchin E. (2012). On detection of changes in categorical data. Quality Technology & Quantitative Management. 9: 79-96.
[19] Yeh A.B., Huwang L. and Li Y.M. (2009). Profile monitoring for a binary response. IIE Transactions, 41: 931-941.
[20] Zafar, S. (2017). Non-iterative Estimation Methods for Ordinal Log-linear Models. Doctoral dissertation, The University of Newcastle.