CUSUM Control Chart for Symlets Wavelet to Monitor Production Process Quality.

Section: Research Paper
Issue
Vol. 21 No. 2 (2024): Volume 21 Issue 2
Published
Jun 25, 2025
Pages
52-61

Abstract

In this paper, it was proposed to create a new chart that represents the Symlets wavelet chart with orders of (1, 2, and 3) to obtain discrete wavelet transformation maximum overall coefficients, through which the threshold parameter is estimated using the universal method and then applied hard threshold rule to obtain de-noise data which will be relied upon in constructing the Cumulative Sum Chart using the Tabular method. The efficiency of the proposed chart was measured and compared to the classical chart by simulating several cases and real data and calculating the difference between the control limits (Difference), the standard deviation and the number of points outside the control limits to determine the sensitivity of the chart to minor changes that may occur in the production process, using an algorithm in the MATLAB program it was designed for this purpose. The research results revealed that the proposed charts are more efficient and sensitive to minor changes (that may event) in the production process than the classical charts.

References

  1. Ali, Taha Hussein & Mardin Samir Ali. "Analysis of Some Linear Dynamic Systems with Bivariate Wavelets" Iraqi Journal of Statistical Sciences 16.3 (2019): 85-109.
  2. Ali, Taha Hussein and Jwana Rostam Qadir. "Using Wavelet Shrinkage in the Cox Proportional Hazards Regression model (simulation study)", Iraqi Journal of Statistical Sciences, 19, 1, 2022, 17-29.
  3. Ali, Taha Hussein, and Saleh, Dlshad Mahmood, "Proposed Hybrid Method for Wavelet Shrinkage with Robust Multiple Linear Regression Model: With Simulation Study" QALAAI ZANIST JOURNAL 7.1 (2022): 920-937
  4. Ali, Taha Hussein, and Saleh, Dlshad Mahmood, "Proposed Hybrid Method for Wavelet Shrinkage with Robust Multiple Linear Regression Model: With Simulation Study" QALAAI ZANIST JOURNAL 7.1 (2022): 920-937.
  5. Ali, Taha Hussein, and Saleh, Dlshad Mahmood. "Comparison Between Wavelet Bayesian and Bayesian Estimators to Remedy Contamination in Linear Regression Model" PalArch's Journal of Archaeology of Egypt/Egyptology 18.10 (2021): 3388-3409.
  6. Ali, Taha Hussein, Nasradeen Haj Salih Albarwari, and Diyar Lazgeen Ramadhan. "Using the hybrid proposed method for Quantile Regression and Multivariate Wavelet in estimating the linear model parameters." Iraqi Journal of Statistical Sciences 20.1 (2023): 9-24.
  7. Ali, Taha Hussein, Rahim, Alan Ghafur, and Saleh Dlshad Mahmood, "Construction of Bivariate F-Control Chart with Application" Eurasian Journal of Science & Engineering, 4.2 (2018): 116-133.
  8. Ali, Taha Hussien, and Nazeera Sedeek Kareem. "Awaz shahab mohammad, (2021), Data de-noise for Discriminant Analysis by using Multivariate Wavelets (Simulation with practical application)." Journal of Arab Statisticians Union (JASU) 5: 78-87.
  9. Cabana, E. and Lillo, R. E. (2021). Robust multivariate control chart based on shrinkage
  10. Centofanti, F., Colosimo, B. M., Grasso, M. L., Menafoglio, A., Palumbo, B., and Vantini,S. (2021a). Robust functional ANOVA with application to additive manufacturing.
  11. Chenouri, S., Steiner, S. H., and Variyath, A. M. (2009). A multivariate robust control chart for individual observations. Journal of Quality Technology, 41(3):259271.
  12. Donoho, David L., and Iain M. Johnstone. Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika, vol. 81, no. 3, 1994, pp. 42555. JSTOR, https://doi.org/10.2307/2337118. Accessed 18 Mar. 2024.
  13. Grasso, M., Menafoglio, A., Colosimo, B. M., and Secchi, P. (2016). Using curve-registration information for profile monitoring. Journal of Quality Technology, 48(2):99127.
  14. Hagiwara, Kenta, Satoshi Horikoshi, and Nick Serpone. "Photoluminescent carbon quantum dots: synthetic approaches and photophysical properties." ChemistryA European Journal 27.37 (2021): 9466-9481.
  15. Johnson, R. A., Wichern, D. W., et al. (2014). Applied multivariate statistical analysis, volume 6. Pearson London, UK.
  16. Kareem, Nazeera Sedeek and Mohammad, Awaz Shahab, and Ali, Taha Hussein, "Construction robust simple linear regression profile Monitoring" Journal of Kirkuk University for Administrative and Economic Sciences, 9.1. (2019): 242-257.
  17. Koshti, V. V. (2011). Cumulative Sum Control Chart, International Journal of Physics and Mathematical 32.
  18. Montgomery, D. C. (2012). Introduction to statistical quality control. John Wiley & Sons. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-EHEP002023.html.
  19. Mustafa, Qais, and Ali, Taha Hussein. "Comparing the Box Jenkins models before and after the wavelet filtering in terms of reducing the orders with application." Journal of Concrete and Applicable Mathematics 11 (2013): 190-198.
  20. Omer, A. W., Sedeeq, B. S., & Ali, T. H. (2024). A proposed hybrid method for Multivariate Linear Regression Model and Multivariate Wavelets (Simulation study). Polytechnic Journal of Humanities and Social Sciences, 5(1), 112-124.
  21. P. Quesenberry, The multivariate short-run snapshot Q chart, Quality Engineering, vol. 13, no. 4, pp. 679683, 2001.
  22. R. Moheghi, R. Noorossana & O. Ahmadi (2022) Phase I and phase II analysis of linear profile monitoring using robust estimators, Communications in Statistics - Theory and Methods, 51:5, 1252-1269, DOI: 10.1080/03610926.2020.1758724.
  23. Sakar Ali Jalal; Dlshad Mahmood Saleh; Bekhal Samad Sedeeq; Taha Hussein Ali. "Construction of the Daubechies Wavelet Chart for Quality Control of the Single Value". IRAQI JOURNAL OF STATISTICAL SCIENCES, 21, 1, 2024, 160-169. doi: 10.33899/iqjoss.2024.183257
  24. Samad Sedeeq, B., Muhammad, Z. A., Ali, I. M., & Ali, T. H. (2024). Construction Robust -Chart and Compare it with Hotellings T2-Chart. Zanco Journal of Human Sciences, 28(1), 140157. https://doi.org/10.21271/zjhs.28.1.11.
  25. Umble, Elisabeth J. Cumulative Sum Charts and Charting for Quality Improvement. Technometrics 43 (2001): 107 - 107.

Authors

Taha.H Ali

Department of Informatics & Statistic, College of Administration and Economics, Salahaddin University, Erbil,, Iraq

ORCID
Duaa Faiz Abdullah Faiz Abdullah

1 ,4 Department of Statistics and Informatics, College of Administration and Economics, University of Salahaddin, Erbil, Kurdistan Region, Iraq

ORCID
Jwana Rostom Qadir

Raparin University- Ranya, Kurdistan Region, Iraq, College of Science, Department of Medical Laboratory.

ORCID
Diyar Lazgeen Ramadhan

Duhok University, College of Health Sciences, Department of Medical Laboratory Sciences, Duhok, Iraq

ORCID

Identifiers

Download this PDF file
PDF

Statistics

How to Cite

Ali, T., طه, Faiz Abdullah Faiz Abdullah, D., دعاء, Rostom Qadir, J., جوانا, Lazgeen Ramadhan, D., & ديار. (2025). CUSUM Control Chart for Symlets Wavelet to Monitor Production Process Quality. IRAQI JOURNAL OF STATISTICAL SCIENCES, 21(2), 52–61. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/21010