Enhanced fault detection models with real-life applications

Showkat Ahmad Lone; Zahid Rasheed; Sadia Anwar; Majid Khan; Syed Masroor Anwar; Sana Shahab; Showkat Ahmad Lone; Zahid Rasheed; Sadia Anwar; Majid Khan; Syed Masroor Anwar; Sana Shahab

doi:10.3934/math.20231000

AIMS Mathematics

2023, Volume 8, Issue 8: 19595-19636. doi: 10.3934/math.20231000

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Enhanced fault detection models with real-life applications

1.
Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, 11673, KSA
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, 710049, China
3.
Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, AJ&K, 12500, Pakistan
4.
Department of Mathematics, College of Arts & Sciences (Wadi Addawasir), Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia
5.
Government Akhtar Nawaz Khan (Shaheed) Degree College, KTS, Haripur, KPK, 22800, Pakistan
6.
Department of Statistics, University of Azad Jammu and Kashmir, Muzaffarabad, 13100, Pakistan
7.
Department of Business Administration, College of Business Administration, Princes Nourah Bint Abdulrahman University P.O Box 84428, Riyadh, 11671, Saudi Arabia

Received: 23 February 2023 Revised: 09 May 2023 Accepted: 22 May 2023 Published: 12 June 2023
MSC : 62P30

Nonconforming events are rare in high-quality processes, and the time between events (TBE) may follow a skewed distribution, such as the gamma distribution. This study proposes one- and two-sided triple homogeneously weighted moving average charts for monitoring TBE data modeled by the gamma distribution. These charts are labeled as the THWMA TBE charts. Monte Carlo simulations are performed to approximate the run length distribution of the one- and two-sided THWMA TBE charts. The THWMA TBE charts are compared to competing charts like the DHWMA TBE, HWMA TBE, THWMA TBE, DEWMA TBE, and EWMA TBE charts at a single shift and over a range of shifts. For the single shift comparison, the average run length (ARL) and standard deviation run length (SDRL) measures are used, whereas the extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are employed for a range of shifts comparison. The comparison reveals that the THWMA TBE charts outperform the competing charts at a single shift as well as at a certain range of shifts. Finally, two real-life data applications are presented to evaluate the applicability of the THWMA TBE charts in practical situations, one with boring machine failure data and the other with hospital stay time for traumatic brain injury patients.
- average run length,
- extra quadratic loss,
- fault detection,
- high-quality process,
- process monitoring
Citation: Showkat Ahmad Lone, Zahid Rasheed, Sadia Anwar, Majid Khan, Syed Masroor Anwar, Sana Shahab. Enhanced fault detection models with real-life applications[J]. AIMS Mathematics, 2023, 8(8): 19595-19636. doi: 10.3934/math.20231000

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Abstract

Nonconforming events are rare in high-quality processes, and the time between events (TBE) may follow a skewed distribution, such as the gamma distribution. This study proposes one- and two-sided triple homogeneously weighted moving average charts for monitoring TBE data modeled by the gamma distribution. These charts are labeled as the THWMA TBE charts. Monte Carlo simulations are performed to approximate the run length distribution of the one- and two-sided THWMA TBE charts. The THWMA TBE charts are compared to competing charts like the DHWMA TBE, HWMA TBE, THWMA TBE, DEWMA TBE, and EWMA TBE charts at a single shift and over a range of shifts. For the single shift comparison, the average run length (ARL) and standard deviation run length (SDRL) measures are used, whereas the extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are employed for a range of shifts comparison. The comparison reveals that the THWMA TBE charts outperform the competing charts at a single shift as well as at a certain range of shifts. Finally, two real-life data applications are presented to evaluate the applicability of the THWMA TBE charts in practical situations, one with boring machine failure data and the other with hospital stay time for traumatic brain injury patients.

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