Employing the Inverse Weibull Failure Time Model to Estimate Some of the Reliability Metrics of k‐Out‐of‐n Systems.
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| Title: | Employing the Inverse Weibull Failure Time Model to Estimate Some of the Reliability Metrics of k‐Out‐of‐n Systems. |
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| Authors: | Hameed, Fatimah Saad1 (AUTHOR) fatimas.hajjami@student.uokufa.edu.iq, Asker, Hussein K.1 (AUTHOR), Su, Lei1 (AUTHOR) ahutsulei@ahut.edu.cn |
| Source: | Journal of Applied Mathematics. 6/19/2026, Vol. 2026, p1-22. 22p. |
| Subjects: | Statistical reliability, Reliability in engineering, Maximum likelihood statistics, Mechanical failures, Markov chain Monte Carlo, Weibull distribution, Monte Carlo method, Mean time between failure |
| Abstract: | This paper presents a new approach to determine the mean time to system failure (MTSF) and reliability function of k‐out‐of‐n systems with independent and identically distributed components following the inverse Weibull (IW) distribution. The system remains operational when at least k of its n components function properly. We derive tractable expressions for system reliability metrics and develop estimation procedures using maximum likelihood estimation (MLE), least squares (LS) methods, and a rigorous Bayesian MCMC approach. Asymptotic confidence intervals for the reliability function are established using Fisher information matrix. Through extensive Monte Carlo simulations, we evaluate the effectiveness of our proposed methods across various sample sizes and parameter combinations. The practical applicability of our approach is demonstrated using real‐world wind turbine gearbox failure data. Our results indicate that the Bayesian MCMC method achieves the lowest mean squared error (MSE), demonstrating superior efficiency. For the specific scenario of k = 3 components, the MLE method outperformed the LS method. The general superiority of the LS method over MLE is observed only for scenarios with higher redundancy (e.g., k > 3). The proposed MTSF expression and large‐sample confidence intervals are tractable and attain empirical coverage, within ±1% of the nominal 95%. Wind‐turbine gearbox data confirm the practical utility of the approach. This research fills a significant gap in reliability engineering by providing the first tractable MTSF and asymptotic confidence intervals for general k‐out‐of‐n systems under the IW failure model. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194722560 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Employing the Inverse Weibull Failure Time Model to Estimate Some of the Reliability Metrics of k‐Out‐of‐n Systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hameed%2C+Fatimah+Saad%22">Hameed, Fatimah Saad</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fatimas.hajjami@student.uokufa.edu.iq</i><br /><searchLink fieldCode="AR" term="%22Asker%2C+Hussein+K%2E%22">Asker, Hussein K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Su%2C+Lei%22">Su, Lei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ahutsulei@ahut.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 6/19/2026, Vol. 2026, p1-22. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Statistical+reliability%22">Statistical reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Reliability+in+engineering%22">Reliability in engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+failures%22">Mechanical failures</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+chain+Monte+Carlo%22">Markov chain Monte Carlo</searchLink><br /><searchLink fieldCode="DE" term="%22Weibull+distribution%22">Weibull distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Mean+time+between+failure%22">Mean time between failure</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a new approach to determine the mean time to system failure (MTSF) and reliability function of k‐out‐of‐n systems with independent and identically distributed components following the inverse Weibull (IW) distribution. The system remains operational when at least k of its n components function properly. We derive tractable expressions for system reliability metrics and develop estimation procedures using maximum likelihood estimation (MLE), least squares (LS) methods, and a rigorous Bayesian MCMC approach. Asymptotic confidence intervals for the reliability function are established using Fisher information matrix. Through extensive Monte Carlo simulations, we evaluate the effectiveness of our proposed methods across various sample sizes and parameter combinations. The practical applicability of our approach is demonstrated using real‐world wind turbine gearbox failure data. Our results indicate that the Bayesian MCMC method achieves the lowest mean squared error (MSE), demonstrating superior efficiency. For the specific scenario of k = 3 components, the MLE method outperformed the LS method. The general superiority of the LS method over MLE is observed only for scenarios with higher redundancy (e.g., k > 3). The proposed MTSF expression and large‐sample confidence intervals are tractable and attain empirical coverage, within ±1% of the nominal 95%. Wind‐turbine gearbox data confirm the practical utility of the approach. This research fills a significant gap in reliability engineering by providing the first tractable MTSF and asymptotic confidence intervals for general k‐out‐of‐n systems under the IW failure model. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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: Identifiers: – Type: doi Value: 10.1155/jama/2802965 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 1 Subjects: – SubjectFull: Statistical reliability Type: general – SubjectFull: Reliability in engineering Type: general – SubjectFull: Maximum likelihood statistics Type: general – SubjectFull: Mechanical failures Type: general – SubjectFull: Markov chain Monte Carlo Type: general – SubjectFull: Weibull distribution Type: general – SubjectFull: Monte Carlo method Type: general – SubjectFull: Mean time between failure Type: general Titles: – TitleFull: Employing the Inverse Weibull Failure Time Model to Estimate Some of the Reliability Metrics of k‐Out‐of‐n Systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hameed, Fatimah Saad – PersonEntity: Name: NameFull: Asker, Hussein K. – PersonEntity: Name: NameFull: Su, Lei IsPartOfRelationships: – BibEntity: Dates: – D: 19 M: 06 Text: 6/19/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
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