A proposed non-parametric triple generally weighted moving average sign chart

Dongmei Cui; Michael B. C. Khoo; Huay Woon You; Sajal Saha; Zhi Lin Chong; Dongmei Cui; Michael B. C. Khoo; Huay Woon You; Sajal Saha; Zhi Lin Chong

doi:10.3934/math.2025271

AIMS Mathematics

2025, Volume 10, Issue 3: 5928-5959. doi: 10.3934/math.2025271

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Research article

A proposed non-parametric triple generally weighted moving average sign chart

1.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2.
School of Business, Hunan International Economics University, 822 Fenglin Road, Yuelu District, Changsha City, Hunan Province, China
3.
Pusat GENIUS@Pintar Negara, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia
4.
Department of Mathematics, International University of Business Agriculture and Technology, Dhaka, Bangladesh
5.
Department of Electronic Engineering, Faculty of Engineering and Green Technology, Universiti Tunku Abdul Rahman, 31900 Kampar, Malaysia

Received: 11 November 2024 Revised: 01 February 2025 Accepted: 07 February 2025 Published: 18 March 2025
MSC : 62P30, 90B25

In practical applications of statistical process control (SPC), the distribution in which the sample data follow often remains unknown. Non-parametric control charts are necessary in process monitoring in such cases. A triple generally weighted moving average (TGWMA) sign chart is proposed in this study for monitoring the process when the underlying distribution is unknown. Simulation is used to compare the performance of the TGWMA sign chart with the existing double generally weighted moving average (DGWMA) sign chart, for both steady state (SS) and zero state (ZS) cases. From the comparison, the TGWMA sign chart shows superior sensitivity in identifying small shifts in the process proportion for both ZS and SS cases. Lastly, we demonstrate the application of the TGWMA sign chart through a practical example and compare it to the DGWMA sign chart in detecting process shifts, further showing the effectiveness of using the TGWMA sign chart.
- average run length,
- average sign chart,
- non-parametric control charts,
- steady state,
- triple generally weighted moving,
- zero state
Citation: Dongmei Cui, Michael B. C. Khoo, Huay Woon You, Sajal Saha, Zhi Lin Chong. A proposed non-parametric triple generally weighted moving average sign chart[J]. AIMS Mathematics, 2025, 10(3): 5928-5959. doi: 10.3934/math.2025271

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Abstract

In practical applications of statistical process control (SPC), the distribution in which the sample data follow often remains unknown. Non-parametric control charts are necessary in process monitoring in such cases. A triple generally weighted moving average (TGWMA) sign chart is proposed in this study for monitoring the process when the underlying distribution is unknown. Simulation is used to compare the performance of the TGWMA sign chart with the existing double generally weighted moving average (DGWMA) sign chart, for both steady state (SS) and zero state (ZS) cases. From the comparison, the TGWMA sign chart shows superior sensitivity in identifying small shifts in the process proportion for both ZS and SS cases. Lastly, we demonstrate the application of the TGWMA sign chart through a practical example and compare it to the DGWMA sign chart in detecting process shifts, further showing the effectiveness of using the TGWMA sign chart.

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