Remodeling Multivariate Control Chart by Using Spatial Signed Rank for Detecting Mean Shift in Normal and Non-Normal Processes
Keywords:
Multivariate exponentially weighted moving average (MEWMA), statistical process control (SPC), average run length (ARL), detection of nonconforming product, correlation of quality characteristicsAbstract
This research aimed to modify the traditional multivariate control charts by using the multivariate spatial signed rank under the normal distribution, the t distribution, and the gamma distribution. The performance of the modern multivariate control charts is measured based on the average run length (ARL). The ARL is computed using a Monte Carlo simulation. The Monte Carlo approach is applied to simulate the circumstances via MATLAB software. The spatial signed-rank multivariate exponentially weighted moving average (SSRM) control chart is found to be the most appropriate approach to detect the small mean shifts and the large smoothing parameters
of all three distributions. Besides, SSRM is a robust tool for detecting waste and is suitable for most industrial processes.
References
Alkahtani S. Robustness of DEWMA versus EWMA control charts to non-normal. J Mod Appl Stat Methods. 2013; 12(1): 148-163.
Alkahtani S, Schaffer J. A double multivariate exponentially weighted moving average (dMEWMA) control chart for a process location monitoring. Commun Stat - Simul Comput. 2012; 41(2): 238-252.
Baxley RV. Discussion. Technometrics. 1990; 32(1): 13-16.
Chakraborty B, Chaudhuri P. On an adaptive transformation and retransformation estimate of multivariate location. J R Stat Soc Series B Stat Methodol. 1998; 60(1): 145-157.
Gan FF. An optimal design of EWMA control charts based on median run length. J Stat Comput Simul. 1993; 45(3-4): 169-184.
Graham MA, Chakraborti S, Human SW. A nonparametric exponentially weighted moving average signed-rank chart for monitoring location. Comput Stat Data Anal. 2011; 55(8): 2490-2503.
Graham MA, Chakraborti S, Mukherjee A. Design and implementation of CUSUM exceedance control charts for unknown location. Int J Prod Res. 2014; 52(18): 5546-5564.
Kvam PH, Vidakovic B. Nonparametric statistics with applications to science and engineering. New York: John Wiley & Sons; 2007.
Maravelakis PE, Panaretos J, Psarakis S. An examination of the robustness to non normality of the EWMA control charts for the dispersion. Commun Stat - Simul Comput. 2005; 34(4): 1069-1079.
Montgomery DC. Introduction to statistical quality control. New York: John Wiley & Sons; 2005.
Montgomery DC. Introduction to statistical quality control. New York: John Wiley & Sons; 2009.
Montgomery DC. Introduction to statistical quality control. New York: John Wiley & Sons; 2013.
NCSS. Control charts for variability (simulation): sample size. Operations Research. 2018 [cited 2018 Mar 15]. Available from: https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/PASS/Control_Charts_for_Variability-Simulation.pdf.
Nevalainen J, Larocque D, Oja H, Pörsti L. Nonparametric analysis of clustered multivariate data. J Am Stat Assoc. 2018; 105(490): 864-872.
Nordhausen K, Möttönen J, Oja H. Multivariate nonparametric methods: an approach based on spatial signs and ranks. The R package MNM. 2018 [cited 2018 Mar 15]. Available from: https://cran.r-project.org/web/packages/MNM/ MNM.pdf.
Shamma SE, Shamma AK. Development and evaluation of control charts using double exponentially weighted moving average. Int J Qual Reliab Manag. 1992; 9(6): 18-25.
Sirkia S, Miettinen J, Nordhausen K, Oja H, Taskinen S. Multivariate nonparametric methods based on spatial signs and ranks. The R package
SpatialNP. 2018 [cited 2018 Mar 15]. Available form: https://cran.r-project.org/web/ packages/SpatialNP/ SpatialNP.pdf.
Tiengket S, Sukparungsee S, Busababodhin P, Areepong Y. Construction of bivariate copulas on the hotelling’s T2 control chart. Thail Stat. 2020; 18(1): 1-15.
Tiengket S, Sukparungsee S, Busababodhin P, Areepong Y. The efficiency of constructed bivariate copulas for MEWMA and Hotelling’s T2 control charts. Commun Stat - Simul Comput. 2022; 51(4): 1837-1851.
Sukparungsee S, Kuvattana S, Busababodhin P, Areepong Y. Multivariate copulas on the MCUSUM control chart. Cogent math. 2017; 4(1): 1342318.
Sukparungsee S, Sasiwannapong S, Busababodhin P, Areepong Y. The effects of constructed bivariate copulas on multivariate control charts effectiveness. Qual Reliab Eng Int. 2021; 37(5): 2156-2168.
Haanchumpol T, Sudasna-na-Ayudthya P, Singhtaun C. Modified multivariate control chart using spatial signs and ranks for monitoring process mean: A case of t-distribution. IEOM 2019: Proceedings of the 9th International Conference on Industrial Engineering and Operations Management; 2019 Mar 5-7; Thailand. IEOM Society International; 2019. pp.1415-1427.
Haanchumpol T, Sudasna-na-Ayudthya P, Singhtaun C. Modern multivariate control chart using spatial signed rank for non-normal process. Eng Sci Technol Int J. 2020; 23(4): 859-869.
Thongrong N, Sukparungsee S, Areepong Y. Evaluation of average run length of nonparametric EWMA sign control chart by markov chain approach. J King Mongkut Univ tehnol north Bangk. 2016; 26(3): 487-497.
Teoh WL, Khoo MBC, Teh SY. Optimal designs of the median run length based double sampling X̄ chart for minimizing the average sample size. PLoS One. 2013; 8(7): e68580.
Zeinab JH. An affine invariant signed-rank multivariate exponentially weighted moving average control chart for process location monitoring. PhD [dissertation]. University of Northern Colorado; 2013.
Zou C, Tsung F. A multivariate sign EWMA control chart. Technometrics. 2011; 53(1): 84-97.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
