EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

Imad Khan; Muhammad Noor-ul-Amin; Narjes Turki Khalifa; Asma Arshad; Imad Khan; Muhammad Noor-ul-Amin; Narjes Turki Khalifa; Asma Arshad

doi:10.3934/math.20231036

AIMS Mathematics

2023, Volume 8, Issue 9: 20324-20350. doi: 10.3934/math.20231036

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EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

1.
Department of Statistics, Abdul Wali Khan University Mardan, Pakistan
2.
Department of Statistics, COMSATS University Islamabad, Lahore Campus, Pakistan
3.
Department of Mathematics, AL-Qunfudhah University college, Umm Al-Qura University, KSA
4.
Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan

Received: 22 March 2023 Revised: 29 April 2023 Accepted: 17 May 2023 Published: 20 June 2023
MSC : 62A86

Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.
- statistical process control,
- EWMA,
- Bayesian approach,
- loss function,
- average run length,
- PRSS
Citation: Imad Khan, Muhammad Noor-ul-Amin, Narjes Turki Khalifa, Asma Arshad. EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering[J]. AIMS Mathematics, 2023, 8(9): 20324-20350. doi: 10.3934/math.20231036

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Abstract

Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.

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