COMPARISON OF CONTROL CHART X ̅ BASED ON MEDIAN ABSOLUTE DEVIATION WITH S

  • Mayashari Mayashari Department of Statistics, Faculty of Mathematics and Natural Science, Hasanuddin University, Indonesia
  • Erna Tri Herdiani Department of Statistics, Faculty of Mathematics and Natural Science, Hasanuddin University, Indonesia https://orcid.org/0000-0003-2342-4247
  • Anisa Anisa Department of Statistics, Faculty of Mathematics and Natural Science, Hasanuddin University, Indonesia
Keywords: ARL, MAD, Quality Control, Control Chart X ̅

Abstract

A stable and controlled process will produce products of good quality following predetermined specifications. A control chart is one of the statistical tools that can be used to measure the stability of a product process in a controlled state. Control charts commonly used to evaluate the statistical control process are Shewhart control charts ( and ). The control chart is used to control the process, as seen from the average and variability of the process. If the data used is not normally distributed or there are outliers, then an alternative control chart, namely the Median Absolute Deviation (MAD), can be used. MAD is used to monitor the process mean and process standard deviation because it has properties that are robust or resistant to deviations. This research aims to form a control chart  based on MAD, apply it to data on fat content in animal feed products, and compare control charts  based on  with the control chart based on  control chart based on MAD. The limitations in this study are the quality characteristics used consist of only one variable and the data is not normally distributed, only limited to the mean process, and the data used in this study are observation data on the fat content contained in animal feed products at PT Japfa Comfeed Indonesia Tbk Makassar Unit from December 2021 to January 2022. The results of this study show that the control chart  based on MAD detects more out-of-control points than the control  based on . The performance of the control chart  based on MAD is better at detecting changes in the process than the control chart   based on  because it has a relatively smaller ARL value.

Downloads

Download data is not yet available.

References

R. Chaerunnisa, “SQC (Statistical Quality Control) Method Analysis of Quality Control in the Clothes Production Process,” in International Conference on Economics, Management and Accounting (ICEMAC 2022), 2023, pp. 179–187.

M. Mashuri et al., “Pengendalian Kualitas Statistika Dasar Bagi Staf Quality Assurance PT Semen Indonesia (Persero) Tbk,” Sewagati, vol. 6, no. 2, pp. 147–158, 2022.

A. Widiawati, F. Arina, and P. F. Ferdinant, “Perbandingan Bagan Kendali X ̅-R Dan EWMA Dengan Pendekatan P-Value Untuk Mendeteksi Pergeseran Rata-Rata Proses Di PT. XYZ,” Jurnal Teknik Industri Untirta, vol. 3, no. 3, 2015.

L. L. Boaventura, P. H. Ferreira, and R. L. Fiaccone, “On flexible Statistical Process Control with Artificial Intelligence: Classification control charts,” Expert Syst Appl, vol. 194, p. 116492, 2022, doi: https://doi.org/10.1016/j.eswa.2021.116492.

I. D. Czabak-Górska, D. Fraczek, A. Kucińska-Landwójtowicz, M. Lorenc, M. Rzasa, and M. Czabak, “Monitoring of location and dispersion parameters of production processes using hybrid control charts,” Comput Ind Eng, vol. 162, p. 107707, 2021.

D. T. Wijayanti, H. Helmi, and N. Imro’ah, “Perbandingan Kinerja Bagan Kendali Cumulative Sum Dan Bagan Kendali Exponentially Weighted Moving Average,” Bimaster: Buletin Ilmiah Matematika, Statistika dan Terapannya, vol. 9, no. 4, 2020.

P. Marlina, “Peta Kendali Berdasarkan Median dan Median Absolute Deviation,” Depok: Universitas Indonesia, 2012.

J. A. Adewara, K. S. Adekeye, and O. L. Aako, “On Performance of Two-Parameter Gompertz-Based X Control Charts,” J Probab Stat, vol. 2020, pp. 1–9, 2020.

B. John and S. M. Subhani, “A modified control chart for monitoring non-normal characteristics,” International Journal of Productivity and Quality Management, vol. 29, no. 3, pp. 309–328, 2020.

R. Mehmood, K. Mpungu, I. Ali, B. Zaman, F. H. Qureshi, and N. Khan, “A new approach for designing the Shewhart-type control charts with generalized sensitizing rules,” Comput Ind Eng, vol. 182, p. 109379, 2023.

F. Z. Okwonu, “Application of Shewhart Control Chart to Analyze the Effect of Income on Body Mass Index and Blood Pressure,” Applied Mathematics and Computational Intelligence (AMCI), vol. 10, pp. 140–153, 2021.

M. Alsaid, R. M. Kamal, and M. M. Rashwan, “The performance of control charts with economic-statistical design when parameters are estimated,” Review of Economics and Political Science, vol. 6, no. 2, pp. 142–160, 2021.

M. A. Abdullah, “Aplikasi peta kendali statistik dalam mengontrol hasil produksi suatu perusahaan,” Saintifik, vol. 1, no. 1, pp. 5–13, 2015.

N. E. Sahra, H. Yozza, and Y. Asdi, “Pengendalian Mutu Berat Produksi Pt. Semen Padang Menggunakan Bagan Kendali Median Absolute Deviation (Mad) Pada Data Tidak Normal,” Jurnal Matematika UNAND, vol. 3, no. 1, pp. 123–131, 2014.

Y. Norasia, “Diagram Kendali MAD pada Harga Cabai Rawit di Jawa Tengah,” Jurnal Matematika, vol. 11, no. 1, p. 34, 2021.

M. O. A. Abu-Shawiesh, “A simple robust control chart based on MAD,” J Math Stat, vol. 4, no. 2, p. 102, 2008.

K. S. Adekeye, “Modified simple robust control chart based on median absolute deviation,” Int J Stat Probab, vol. 1, no. 2, p. p91, 2012.

Ainun, “Performa Bagan Kendali Nonparametrik Exponentially Weighted Moving Average Sign Pada Produksi Pakan Ternak,” Makassar: Universitas Hasanuddin, 2022.

M. R. Sindhumol, M. R. Srinivasan, M. Gallo, and others, “Robust control charts based on modified trimmed standard deviation and Gini’s mean difference,” Journal of Applied Quantitative Methods, vol. 11, no. 3, pp. 18–30, 2016.

P. J. Rousseeuw and C. Croux, “Alternatives to the median absolute deviation,” J Am Stat Assoc, vol. 88, no. 424, pp. 1273–1283, 1993.

A. Sahab, Buku Ajar Analisis Kuantitatif Ilmu Politik dengan SPSS. Penerbit: Airlangga University Press, 2019.

E. R. van den Heuvel, S. A. W. van Driel, and Z. Zhan, “A bivariate zero-inflated Poisson control chart: Comments and corrections on earlier results,” Communications in Statistics-Theory and Methods, vol. 51, no. 10, pp. 3438–3445, 2022.

L. M. J. Afgani, E. T. Herdiani, and N. Sanusi, “Accuracy of Zero Inflated Generalized Poisson Exponentially Moving Average Control Chart,” Jurnal Matematik, Statistika dan Komputasi (JMSK), vol. 18, no. 1, pp. 121–129, 2021.

Published
2024-05-25
How to Cite
[1]
M. Mayashari, E. Herdiani, and A. Anisa, “COMPARISON OF CONTROL CHART X ̅ BASED ON MEDIAN ABSOLUTE DEVIATION WITH S”, BAREKENG: J. Math. & App., vol. 18, no. 2, pp. 0737-0750, May 2024.