Efficient control chart-based monitoring of scale parameter for a process with heavy-tailed non-normal distribution

Mediha Maqsood; Aamir Sanaullah; Yasar Mahmood; Afrah Yahya Al-Rezami; Manal Z. M. Abdalla; Mediha Maqsood; Aamir Sanaullah; Yasar Mahmood; Afrah Yahya Al-Rezami; Manal Z. M. Abdalla

doi:10.3934/math.20231538

AIMS Mathematics

2023, Volume 8, Issue 12: 30075-30101. doi: 10.3934/math.20231538

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Efficient control chart-based monitoring of scale parameter for a process with heavy-tailed non-normal distribution

1.
Department of Statistics, COMSATS University Islamabad, Lahore Campus, Pakistan
2.
Department of Statistics, Government College University, Lahore, Pakistan
3.
Mathematics Department, College of Humanities and Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia
4.
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia

Received: 04 August 2023 Revised: 28 September 2023 Accepted: 15 October 2023 Published: 06 November 2023
MSC : 62P30, 62F25

Statistical process control is a procedure of quality control that is widely used in industrial processes to enable monitoring by using statistical techniques. All production processes are faced with natural and unnatural variations. To maintain the stability of the production process and reduce variation, different tools are used. Control charts are significant tools to monitor a production process. In this article, we design an extended exponentially weighted moving average (EEWMA) chart under the assumption of inverse Maxwell (IM) distribution, an IM EEWMA (IMEEWMA) control chart. We have estimated the performance of the proposed chart in terms of various run-length (RL) properties, including the average RL, standard deviation of the RL and median RL. We have also carried out a comparative analysis of the proposed chart with the existing Shewhart-type chart for IM distribution (VIM chart) and IM exponential weighted moving average (IMEWMA) chart. We observed that the proposed IMEEWMA chart performed better than the VIM chart and IMEWMA chart in terms of the ability to detect small and moderate shifts. To demonstrate its practical application, we have applied the IMEEWMA chart, along with existing control charts, to monitor the lifetime of car brake pad data. This real-world example illustrates the superiority of the IMEEWMA chart over its counterparts in industrial scenarios.
Citation: Mediha Maqsood, Aamir Sanaullah, Yasar Mahmood, Afrah Yahya Al-Rezami, Manal Z. M. Abdalla. Efficient control chart-based monitoring of scale parameter for a process with heavy-tailed non-normal distribution[J]. AIMS Mathematics, 2023, 8(12): 30075-30101. doi: 10.3934/math.20231538

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Abstract

Statistical process control is a procedure of quality control that is widely used in industrial processes to enable monitoring by using statistical techniques. All production processes are faced with natural and unnatural variations. To maintain the stability of the production process and reduce variation, different tools are used. Control charts are significant tools to monitor a production process. In this article, we design an extended exponentially weighted moving average (EEWMA) chart under the assumption of inverse Maxwell (IM) distribution, an IM EEWMA (IMEEWMA) control chart. We have estimated the performance of the proposed chart in terms of various run-length (RL) properties, including the average RL, standard deviation of the RL and median RL. We have also carried out a comparative analysis of the proposed chart with the existing Shewhart-type chart for IM distribution (VIM chart) and IM exponential weighted moving average (IMEWMA) chart. We observed that the proposed IMEEWMA chart performed better than the VIM chart and IMEWMA chart in terms of the ability to detect small and moderate shifts. To demonstrate its practical application, we have applied the IMEEWMA chart, along with existing control charts, to monitor the lifetime of car brake pad data. This real-world example illustrates the superiority of the IMEEWMA chart over its counterparts in industrial scenarios.

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