Improved Non-Parametric Double Homogenously Weighted Moving Average Control Chart for Monitoring Changes in Process Location
Keywords:
Average run length, control chart, signed rank test, non-parametric, wilcoxon signed rank
Abstract
Parametric control charts' statistical performance often raises concerns when dealing with processes that lack a predefined probability distribution. In such cases, non-parametric control charts emerge as a viable alternative. Additionally, the adoption of ranked set sampling, with its ability to reduce process parameter variability and enhance control chart performance, proves to be advantageous over traditional simple random sampling techniques. In the field of statistical process control (SPC), control charts are essential tools used to monitor and improve process performance. Among various control charts, the double homogeneously weighted moving average (DHWMA) control chart is recognized for its capability to detect small shifts in process parameters. The study focusses on enhancing the sensitivity and robustness of the NPDHWARSS for detection of shift in process mean and make it more reliable across diverse applications. This study aims to improve the non-parametric double homogeneously weighted moving average control chart, employing the Wilcoxon signed rank test and leveraging the ranked set sampling method, referred to as NPIDHWMA-WSR in this paper. To evaluate the efficiency of the proposed control chart, a comparison was conducted against non-parametric double exponentially weighted moving average using signed rank test (NPRDEWMA-SR) and non-parametric double homogeneously weighted moving average (NPDHWMA) control charts. The comparative analysis highlights the superior performance of the proposed NPIDHWMA-WSR control chart, especially in scenarios involving minimal to moderate changes in process location, as evidenced by metrics such as average run length (ARL), standard deviation run length (SDRL), and median deviation run length (MDRL). Additionally, the study presents a practical application, providing skilled practitioners with tangible evidence of the chart's effectiveness in maintaining both product and process quality. Moreover, the NPIRDHWMA-WSR control chart identified an out-of-control (OOC) condition by the 18th sample, whereas the competing NPDHWMA-RSS control chart didn't signal OOC until the 22nd sample.References
References
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[28] Tsai, C. F., Lu, S. L., & Huang, C. J. (2015). “Design of an Extended Nonparametric EWMA Sign Chart.” International Journal of Industrial Engineering, 22(6). https://doi.org/10.23055/ijietap.2015.22.6.1172
[29] Yang S.-F, Lin J.-S, and Cheng S. W. (2011). “A new nonparametric EWMA sign control chart,” Expert Systems with Applications, 38(5), 6239 – 6243.
[1] Abbas N. (2018). “Homogeneously weighted moving average control chart with an application in the substrate manufacturing process,” Computers & Industrial Engineering, 120, 460 – 470.
[2] Abbas Z, Nazir H. Z, M. Abid, N. Akhtar, and Riaz M. (2020). “Enhanced nonparametric control charts under simple and ranked set sampling schemes,” Transactions of the Institute of Measurement and Control, 42(14), 2744 – 2759.
[3] Abid M, Shabbir A, Nazir H. Z., Sherwani R. A. K., and Riaz M. (2020). “A double homogeneously weighted moving average control chart for monitoring of the process mean,” Quality and Reliability Engineering International, 36(5), 1513 - 1527.
[4] Abid M, Nazir H. Z, Riaz M, and Lin Z. (2017). “An efficient nonparametric EWMA Wilcoxon signed-rank chart for monitoring location,” Quality and Reliability Engineering International, 33(3), 669 – 685.
[5] Adegoke N. A, Smith A. N. H, Anderson M. J, Sanusi R. A, and Pawley M. D. M. (2019). “Efficient homogeneously weighted moving average chart for monitoring process mean using an auxiliary variable,” IEEE Access, 7, 94021 – 94032.
[6] Amin R. W. and Searcy A. J. (1991). “A nonparametric exponentially weighted moving average control scheme,” Communications in Statistics - Simulation and Computation, 20(4), 1049 – 1072.
[7] Anwar S. M., Aslam M., Zaman B., and Riaz M. (2021). “An enhanced double homogeneously weighted moving average control chart to monitor process location with application in automobile field,” Quality and Reliability Engineering International, 38(1), 174 - 194.
[8] Anwar S. M., Aslam M., Zaman B., and Riaz M. (2021). “Mixed memory control chart based on auxiliary information for simultaneously monitoring of process parameters: an application in glass field,” Computers & Industrial Engineering, 156, ttps://doi.org/10.1016/j.cie.2021.107284
[9] Bakir S. T. (2004). A distribution-free Shewhart quality control chart based on signed ranks. Quality Engineering 16(4): 613 – 623.
[10] Chakraborty N, Chakraborti S, Human S. W, and Balakrishnan N. (2016). “A generally weighted moving average signed-rank control chart,” Quality and Reliability Engineering International, 32(8), 2835 - 2845.
[11] Chakraborti, S., Human, S. W., & Graham, M. A. (2008). Phase I statistical process control charts: an overview and some results. Quality Engineering, 21(1), 52 – 62.
[12] Chakraborti S, Graham M. A. (2019). Nonparametric Statistical Process Control. John Wiley and Sons pp. 23 – 52.
[13] Chakraborti S and Graham M. (2019). “Nonparametric (distribution-free) control charts: an updated overview and some results,” Quality Engineering, 31, 1– 22.
[14] Cortez P., Cerdeira A., Almeida F., Matos T., Reis J. (2009). “Modeling wine preferences by data mining from physicochemical properties”, 47(4), 547-553
[15] Graham M., Chakraborti S, and Human S. (2011). “A nonparametric EWMA sign chart for location based on individual measurements,” Quality Engineering, 23, 227 – 241.
[16] Graham M., Chakraborti S., and Human S. (2011). “A nonparametric exponentially weighted moving average signed-rank chart for monitoring location,” Computational Statistics & Data Analysis, 55, 2490 – 2503.
[17] Hag A, J. Brown, E. Moltchanova, and Al-Omari A. I. (2015). “Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes,” Journal of Statistical Computation and Simulation, 85(6), 1224 – 1246.
[18] Kim D. H. and Kim Y. C. (1996). “Wilcoxon signed rank test using ranked-set sample,” Korean Journal of Computational & Applied Mathematics, 3(2), pp. 235 – 243.
[19] Lu S.-L. (2015). “An extended nonparametric exponentially weighted moving average sign control chart,” Quality and Reliability Engineering International, 31(1), 3 – 13.
[20] Lu S.-L. (2018). “Nonparametric double generally weighted moving average sign charts based on process proportion,” Communications in Statistics - Theory and Methods, 47(11), 2684 – 2700.
[21] Mahmood T and Xie M. (2019). “Models and monitoring of zero-inflated processes: the past and current trends,” Quality and Reliability Engineering International, 35(8), 2540 –2557.
[22] Mahmood T. (2020). “Generalized linear model based monitoring methods for high-yield processes,” Quality and Reliability Engineering International, 36(5), 1570 – 1591.
[23] Malela-Majika, J.-C.; Human, S.W.; Chatterjee, K. (2024). Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions. Mathematics, 12, 637. https:// doi.org/10.3390/math12050637.
[24] Rasheed Z, Khan M, Nafiu L. Abiodun, Syed M. Anwar, Khalaf G. and Saddam A. Abbasi. (2022). “Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling,” Mathematical Problems in Engineering, 2022, 1 – 15.
[25] Rasheed Z, Zhang H, Anwar S. M., and Zaman B. (2021). “Homogeneously mixed memory charts with application in the substrate production process,” Mathematical Problems in Engineering, 2021, Article ID 2582210, 15 pages
[26] Rasheed Z, Zhang H, Arslan M., et al. (2021). “An efficient robust nonparametric triple EWMA Wilcoxon signed-rank control chart for process location,” Mathematical Problems in Engineering, 2021, Article ID 2570198.
[27] Ridwan A. S, Muhammad R, Nurudeen A. A, and Min X. (2017). “An EWMA monitoring scheme with a single auxiliary variable for industrial processes,” Computers & Industrial Engineering, 114, 1 – 10.
[28] Tsai, C. F., Lu, S. L., & Huang, C. J. (2015). “Design of an Extended Nonparametric EWMA Sign Chart.” International Journal of Industrial Engineering, 22(6). https://doi.org/10.23055/ijietap.2015.22.6.1172
[29] Yang S.-F, Lin J.-S, and Cheng S. W. (2011). “A new nonparametric EWMA sign control chart,” Expert Systems with Applications, 38(5), 6239 – 6243.
Published
2025-08-19
How to Cite
Oladipupo, O. O., Adekeye, K. S., Olaomi, J. O., & Alayande, S. A. (2025). Improved Non-Parametric Double Homogenously Weighted Moving Average Control Chart for Monitoring Changes in Process Location. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2244
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Section
Research Articles
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