Simulation modeling with memory-type control charts for monitoring the process variability
Keywords:
average run-length, exponentially weighted moving average, dispersion control chart, Monte-Carlo simulations, standard deviation of run-lengthAbstract
Memory-type control charts, renowned for their effectiveness in identifying small deviations in the process variance, are commonly used to monitor the process variability. In this article, we introduce a new tool, the Quadruple Exponentially Weighted Moving Average (QEWMA) chart, which is designed for the specific purpose of monitoring changes in the process variability. We refer to this chart as the -QEWMA chart. The performance of the -QEWMA chart is assessed through an extensive series of Monte-Carlo simulations, carefully considering the run-length distribution. Comparing it with other well-known memory-type charts, it becomes evident that the -QEWMA chart excels in its ability to effectively detect small shifts in the process dispersion. To illustrate the practical application of this chart, we provide an example.
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References
E.S. Page, “Continuous inspection schemes,” Biometrika. vol. 41, pp. 100–115,
E.S. Page, “Controlling the standard deviation by CUSUMs and warning lines,”
Technometrics. vol. 5, pp 307–315, 1963.
S.W. Roberts, “Control chart tests based on geometric moving averages,” Technometrics. vol. 1, pp. 239−250, 1959.
S.E. Shamma, and A.K. Shamma, “Development and evaluation of control charts
using double exponentially weighted moving averages,” Int. J. Qual. Reliab.
Manag. vol. 9, pp. 18–26, 1992.
L. Zhang, and G. Chen, “An extended EWMA mean chart,” Qual. Technol. Quant.
Manag. vol. 2, pp. 39– 52, 2005.
S.H. Sheu, and T.C. Lin, “The generally weighted moving average control chart
for detecting small shifts in the process mean,” Qual. Eng. vol. 16, pp. 209−231,
A. Haq, “A new hybrid exponentially weighted moving average control chart for
monitoring process mean,” Qual. Reliab. Eng. Int. vol. 29, pp. 1015−1025, 2013.
A. Haq, “A new hybrid exponentially weighted moving average control chart
for monitoring process mean: Discussion,” Qual. Reliab. Eng. Int. vol. 33, pp.
−1631, 2017a.
V. Alevizakos, K. Chatterjee, and C. Koukouvinos, “The triple exponentially
weighted moving average control chart,” Qual. Technol. Quant. Manag. vol. 18,
pp. 326−354, 2021.
V. Alevizakos, K. Chatterjee, and C. Koukouvinos, “The quadruple exponentially
weighted moving average control chart,” Qual. Technol. Quant. Manag. vol. 19,
pp. 50−73, 2022.
P. Castagliola, “A New S2-EWMA Control Chart for Monitoring Process Variance,” Qual. Reliab. Eng. Int. vol. 21, pp. 781−794, 2005.
P. Castagliola, G. Celano, and S. Fichera, “A New CUSUM-S2 Control Chart for
Monitoring the Process Variance,” J. Qual. Maint. Eng. vol. 15, pp. 344−357,
N. Abbas, M. Riaz, and R.J.M.M. Does, “CS-EWMA Chart for Monitoring Process Dispersion, Qual. Reliab. Eng. Int. vol. 29, pp. 653−663, 2013.
S. Tariq, M. Noor-ul-Amin, M. Aslam, and M. Hanif, “Design of hybrid EWMlnS2
control chart,” J. Ind. Prod. Eng. vol. 36, pp. 554−562, 2019.
K. Chatterjee, C. Koukouvinos, and A. Lappa, “A new S2-TEWMA control chart
for monitoring process dispersion,” Qual. Reliab. Eng. Int. vol. 37, pp. 1334−1354,2021.
V. Alevizakos, K. Chatterjee, C. Koukouvinos, and A. Lappa, “A double generally
weighted moving average control chart for monitoring the process variability,” J.
Appl. Stat. vol. 50, pp. 2079−2107, 2023.
V. Alevizakos, K. Chatterjee, C. Koukouvinos, and A. Lappa, “A S2-GWMA control chart for monitoring the process variability,” Qual. Eng. vol. 33, pp. 533−551,2021.
M.R. Reynolds, and Z.G. Stoumbos, “Comparisons of some exponentially weighted
moving average control charts for monitoring the process mean and variance,”
Technometrics. vol. 48, pp. 550−567, 2006.
P. Castagliola, G. Celano, S. Fichera, and F. Giuffrida, “A variable sampling
interval S2-EWMA control chart for monitoring the process variance,” Int. J.Tech. Manag. vol. 37, pp. 125−146, 2007.
P. Castagliola, G. Celano, and S. Fichera, “A Johnson’ s Type Transformation
EWMA-S2 Control Chart,” Int. J. Qual. Eng. Technol. vol. 1, pp. 253−275, 2010.
L. Shu, and W. Jiang, “A new EWMA chart for monitoring process dispersion,”
J. Qual. Technol. vol. 40, pp. 319−331, 2008.
S.A. Abbasi, M. Riaz, A. Miller, S. Ahmad, and H.Z. Nazir, “EWMA dispersion
control charts for normal and non-normal processes,” Qual. Reliab. Eng. Int. vol.
, pp. 1691−1704, 2015.
B. Zaman, N. Abbas, M. Riaz, and M.H. Lee, “Mixed CUSUM-EWMA chart
for monitoring process dispersion,” Int. J. Adv. Manuf. Technol. vol. 86, pp.3025−3039, 2016.
M. Zhou, Q. Zhou, and W. Geng, “A new nonparametric control chart for monitoring variability,” Qual. Reliab. Eng. Int. vol. 32, pp. 2471−2479, 2016.
R.A. Sanusi, M. Riaz, N. Abbas, and M.R. Abujiya, “Using FIR to Improve
CUSUM Charts for Monitoring Process Dispersion,” Qual. Reliab. Eng. Int. vol.
, pp. 1045−1056, 2017.
R. Ali, and A. Haq, “New memory-type dispersion control charts,” Qual. Reliab.
Eng. Int. vol. 33, pp. 2131−2149, 2017.
R. Ali, and A. Haq, “New GWMA-CUSUM control chart for monitoring the process dispersion, ” Qual. Reliab. Eng. Int. vol. 34, pp. 997−1028, 2018.
A. Haq, “New EWMA control charts for monitoring process dispersion using auxiliary information,” Qual. Reliab. Eng. Int. vol. 33, pp. 2597−2614, 2017b.
A. Haq, “A new adaptive EWMA control chart for monitoring the process dispersion,” Qual. Reliab. Eng. Int. vol. 34, pp. 846−857, 2018.
T. Abbas, B. Zaman, A. Atir, M. Riaz, and S. Akbar Abbasi, “On improved
dispersion control charts under ranked set schemes for normal and non-normal
processes,” Qual. Reliab. Eng. Int. vol. 35, pp. 1313−1341, 2019.
C.J. Huang, S.L. Lu, and J.H. Chen, “Enhanced generally weighted moving average variance charts for monitoring process variance with individual observations,”
Qual. Reliab. Eng. Int. vol. 36, pp. 285–302, 2020.
M. Riaz, S.A. Abbasi, M. Abid, and A.K. Hamzat, “A New HWMA Dispersion
Control Chart with an Application to Wind Farm Data,” Mathematics. vol. 8,
, 2020.
S.B. Mahadik, D.G. Godase, and W.L. Teoh, “A two-sided SPRT control chart
for process dispersion,” J. Stat. Comput. Simul. vol. 91, pp. 3603−3614, 2021.
A. Arshad, M. Noor-ul-Amin, and M. Hanif, “Function-based adaptive exponentially weighted moving average dispersion control chart,” Qual. Reliab. Eng. Int.vol. 37, pp. 2685–2698, 2021.
A. Haq, and F. Razzaq, “New weighted adaptive CUSUM dispersion charts,” Qual.
Reliab. Eng. Int. vol. 38, pp. 110–133, 2022.
D.G. Godase, A.C. Rakitzis, S.B. Mahadik, and M.B.C. Khoo, “Deciles-based
EWMA-type sign charts for process dispersion,” Qual. Reliab. Eng. Int. vol. 38,
pp. 3726–3740, 2022.
G. A. Ajibade, J. O. Ajadi, O. J. Kuboye, and E. Alih, “Generalized new exponentially weighted moving average control charts (NEWMA) for monitoring process
dispersion,” Int. J. Qual. Reliab. Manag. (2023) https://doi.org/10.1108/IJQRM08-2022-0257.
S.F. Yang, L.P. Chen, and C.K. Lin, “Adjustment of Measurement Error Effects on
Dispersion Control Chart with Distribution-Free Quality Variable,” Sustainability.
vol. 15, 4337, 2023.
M. Jafari, M.R. Maleki, and A. Salmasnia, “A high-dimensional control chart for
monitoring process variability under gauge imprecision effect,” Prod. Eng. Res.
Devel. vol. 17, pp. 547–564, 2023.
N.L. Johnson, “Systems of frequency curves generated by methods of translation,”
Biometrika. vol. 36, pp. 149–176, 1949.
N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions.
Wiley: New York, 1994.
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