Efficient control charting methodology based on Distance Weighted Mean for normal distribution

Bisma Zaman; Syed Muhammad Muslim Raza; Javed  Iqbal; Naima Shehzadi; Muhammad Moeen Butt; Muhammad Riaz

doi:10.47264/idea.nasij/4.1.1

Authors

Bisma Zaman Department of Economics and Statistics, Dr. Hasan Murad School of Management (HSM), University of Management and Technology, Lahore, Pakistan. https://orcid.org/0000-0003-2675-0312
Syed Muhammad Muslim Raza Department of Economics and Statistics, Dr. Hasan Murad School of Management (HSM), University of Management and Technology, Lahore, Pakistan. https://orcid.org/0000-0002-3637-195X
Javed Iqbal Department of Statistics, Virtual University, Pakistan.
Naima Shehzadi Department of Economics and Statistics, Dr. Hasan Murad School of Management (HSM), University of Management and Technology, Lahore, Pakistan. https://orcid.org/0009-0003-6390-2968
Muhammad Moeen Butt Department of Economics and Statistics, Dr. Hasan Murad School of Management (HSM), University of Management and Technology, Lahore, Pakistan. https://orcid.org/0000-0003-1736-8998
Muhammad Riaz Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

DOI:

https://doi.org/10.47264/idea.nasij/4.1.1

Keywords:

Average Run Length (ARL), Simple Random Sampling (SRS), Distance Weighted Mean (DWM), Monte Carlo Simulation, Shewhart

Abstract

This research suggests a Distance Weighted Mean (DWM) based control chart under normal distribution implementing Simple Random Sampling (SRS). The control limits are calculated using the quantile point method. The control chart's performance is assessed using the Average Run Length (ARL) statistic. The numerical findings are illustrated using samples of sizes 3 and 5. The ARL1 values are determined using Monte Carlo Simulation for increasing and decreasing shifts in the location parameter ranging from 5% to 30%. Using the ARL₁ measurement, the proposed DWM control charts are compared to the existing Shewhart control charts. According to the comparison analysis, the suggested DWM control chart surpasses the competing Shewhart control chart. The real-life application of the proposed DWM control chart is also shown by using the lifetime of the light bulb (in hours). The results suggest that the proposed DWM control chart can be a useful tool for monitoring process mean shifts, especially when the sample size is large, and the magnitude of the shift is significant.

References

Abbas, N., Riaz, M., & Does, R. J. M. M. (2012). CS-EWMA chart for monitoring process dispersion. Quality and Reliability Engineering International, 29(5), 653–663. https://doi.org/10.1002/qre.1414 DOI: https://doi.org/10.1002/qre.1414

Aczel, A. D. (1989). Complete business statistics. Irwin.

Ali, S., Ahmed, N., Shah, I., Lone, S. A., & Alsubie, A. (2021). Absolute deviation-based control charts for monitoring mean of Weibull distribution with type-I censoring. IEEE Access, 9, 107519-107547. https://ieeexplore.ieee.org/abstract/document/9500210/ DOI: https://doi.org/10.1109/ACCESS.2021.3100845

Butt, M. M., & Raza, S. M. M. (2017). The optimization of design of EWMA control chart using Box-Behnken method under type I censoring. Journal of Statistics, 24(1), 133-149. https://www.gcu.edu.pk/pages/gcupress/statJournal/volumes/Vol-24-2017/10.pdf

Castagliola, P., Amdouni, A., Taleb, H., & Celano, G. (2015). One-sided Shewhart-type charts for monitoring the coefficient of variation in short production runs. Quality Technology & Quantitative Management, 12(1), 53-67. https://doi.org/10.1080/16843703.2015.11673366 DOI: https://doi.org/10.1080/16843703.2015.11673366

Chen, G., S. W. Cheng, and H. Xie. (2004). A new EWMA control chart for monitoring both location and dispersion. Quality Technology Quantity Management, 1(2), 217–31. https://doi.org/10.1080/16843703.2004.11673074 DOI: https://doi.org/10.1080/16843703.2004.11673074

Dodonov, Y. S., & Dodonova, Y. A. (2011). Robust measures of central tendency: weighting as a possible alternative to trimming in response-time data analysis. Psikhologicheskie Issledovaniya, 5(19), 1-11.

Grant, E. L., & Leavenworth, R. S. (1980). Statistical quality control (Vol. 7). McGraw-Hill.

Gupta, C. B., & Gupta, V. (2009). Introduction to statistical methods. Vikas Publishing.

Hyder, M., Mahmood, T., Butt, M. M., Raza, S. M. M., & Abbas, N. (2022). On the location?based memory type control charts under modified successive sampling scheme. Quality and Reliability Engineering International, 38(4), 2200-2217. DOI: https://doi.org/10.1002/qre.3049

Montgomery, D. C. (2009). Statistical quality control (Vol. 7). Wiley.

Raji, I. A., Abbas, N., & Riaz, M. (2018). On designing a robust double exponentially weighted moving average control chart for process monitoring. Transactions of the Institute of Measurement and Control, 40(15), 4253-4265. https://doi.org/10.1177/0142331217744614 DOI: https://doi.org/10.1177/0142331217744614

Riaz, M. (2008). A dispersion control chart. Communications in Statistics—Simulation and Computation®, 37(6), 1239-1261. https://doi.org/10.1080/03610910802049623 DOI: https://doi.org/10.1080/03610910802049623

Roberts, S. W. (2000). Control chart tests based on geometric moving averages. Technometrics, 42(1), 97-101. DOI: https://doi.org/10.1080/00401706.2000.10485986

Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), 43-87. https://doi.org/10.1002/j.1538-7305.1924.tb01347.x DOI: https://doi.org/10.1002/j.1538-7305.1924.tb01347.x

Woodall, W. H. (2006). The use of control charts in health-care and public-health surveillance. Journal of Quality Technology, 38(2), 89-104. https://doi.org/10.1080/00224065.2006.11918593 DOI: https://doi.org/10.1080/00224065.2006.11918593