Explicit ARL Derivation of Extended EWMA Control Chart to Detect Changes in the First-Order SAR with Quadratic Trend and Its Application.
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| Title: | Explicit ARL Derivation of Extended EWMA Control Chart to Detect Changes in the First-Order SAR with Quadratic Trend and Its Application. |
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| Authors: | Areepong, Yupaporn1 yupaporn.a@sci.kmutnb.ac.th, Karoon, Kotchaporn2 kotchapornk@nu.ac.th |
| Source: | IAENG International Journal of Applied Mathematics. May2026, Vol. 56 Issue 5, p1924-1935. 12p. |
| Subjects: | Quality control charts, Autoregressive models, Fredholm equations, Numerical solutions to integral equations, Market volatility, Fixed point theory |
| Abstract: | The performance of control charts to detect shifts may be evaluated using the basic performance metric of Average Run Length (ARL). This study compares ARL estimates achieved using numerical integral equation (NIE) approaches, such as the Midpoint, Trapezoidal, Simpson's 1/3, Simpson's 3/8, and Boole's rules, with explicit ARL formulations derived for the Extended Exponentially Weighted Moving Average (extended EWMA) control chart. The suggested approach is based on an exponential white noise driven first-order seasonal autoregressive model with a quadratic trend, SAR(1)L model. By means of the Fredholm integral equation, the explicit ARL expressions are obtained, and the solution's uniqueness is rigorously shown by means of Banach's Fixed Point Theorem. The numerical findings show that when compared to NIE-based methods, the explicit ARL formulae significantly reduce computing cost and provide calculations that are almost immediate. The explicit ARL derivation of the extended EWMA had been extended to compare its performance with that of the traditional EWMA chart, and the results showed better performance. Finally, Monthly stock price series of Nike, characterized by substantial volatility driven by market dynamics, are employed to evaluate and confirm the superior performance of the proposed Extended EWMA control chart compared with the conventional EWMA chart. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193517549 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Explicit ARL Derivation of Extended EWMA Control Chart to Detect Changes in the First-Order SAR with Quadratic Trend and Its Application. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Areepong%2C+Yupaporn%22">Areepong, Yupaporn</searchLink><relatesTo>1</relatesTo><i> yupaporn.a@sci.kmutnb.ac.th</i><br /><searchLink fieldCode="AR" term="%22Karoon%2C+Kotchaporn%22">Karoon, Kotchaporn</searchLink><relatesTo>2</relatesTo><i> kotchapornk@nu.ac.th</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. May2026, Vol. 56 Issue 5, p1924-1935. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quality+control+charts%22">Quality control charts</searchLink><br /><searchLink fieldCode="DE" term="%22Autoregressive+models%22">Autoregressive models</searchLink><br /><searchLink fieldCode="DE" term="%22Fredholm+equations%22">Fredholm equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+integral+equations%22">Numerical solutions to integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Market+volatility%22">Market volatility</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The performance of control charts to detect shifts may be evaluated using the basic performance metric of Average Run Length (ARL). This study compares ARL estimates achieved using numerical integral equation (NIE) approaches, such as the Midpoint, Trapezoidal, Simpson's 1/3, Simpson's 3/8, and Boole's rules, with explicit ARL formulations derived for the Extended Exponentially Weighted Moving Average (extended EWMA) control chart. The suggested approach is based on an exponential white noise driven first-order seasonal autoregressive model with a quadratic trend, SAR(1)L model. By means of the Fredholm integral equation, the explicit ARL expressions are obtained, and the solution's uniqueness is rigorously shown by means of Banach's Fixed Point Theorem. The numerical findings show that when compared to NIE-based methods, the explicit ARL formulae significantly reduce computing cost and provide calculations that are almost immediate. The explicit ARL derivation of the extended EWMA had been extended to compare its performance with that of the traditional EWMA chart, and the results showed better performance. Finally, Monthly stock price series of Nike, characterized by substantial volatility driven by market dynamics, are employed to evaluate and confirm the superior performance of the proposed Extended EWMA control chart compared with the conventional EWMA chart. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1924 Subjects: – SubjectFull: Quality control charts Type: general – SubjectFull: Autoregressive models Type: general – SubjectFull: Fredholm equations Type: general – SubjectFull: Numerical solutions to integral equations Type: general – SubjectFull: Market volatility Type: general – SubjectFull: Fixed point theory Type: general Titles: – TitleFull: Explicit ARL Derivation of Extended EWMA Control Chart to Detect Changes in the First-Order SAR with Quadratic Trend and Its Application. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Areepong, Yupaporn – PersonEntity: Name: NameFull: Karoon, Kotchaporn IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 5 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
| ResultId | 1 |
