Maximum likelihood estimation for the poly-Weibull distribution.
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| Title: | Maximum likelihood estimation for the poly-Weibull distribution. |
|---|---|
| Authors: | Freels, Jason K.1 (AUTHOR), Timme, Daniel A.2 (AUTHOR) daniel.a.timme@gmail.com, Pignatiello, Joseph J.3 (AUTHOR), Warr, Richard L.4 (AUTHOR), Hill, Raymond R.5 (AUTHOR) |
| Source: | Quality Engineering. 2019, Vol. 31 Issue 4, p545-552. 8p. |
| Subjects: | Weibull distribution, Generalized method of moments, Maximum likelihood statistics, Failure mode & effects analysis |
| Abstract: | The Weibull distribution has long been a popular choice for modeling lifetime data of various mechanical and biological phenomena when the associated hazard rate function is constant or monotone increasing or decreasing. However, nonmonotone hazard functions are common in reliability and survivability contexts where a system may undergo an initial "burn-in" prior to periods of useful life and eventual wear out. In these scenarios, the Weibull can only model a portion of the "bathtub" curve but is incapable of adequately modeling the entire failure process. Several modifications to the standard two-parameter Weibull distribution have therefore been introduced in the literature to effectively model and analyze lifetime data where the hazard rate function is bathtub-shaped. The performance of each modified distribution is typically assessed by its ability to fit a reference data set that is known to have a bathtub-shaped hazard rate function. The current article compares the performance of two recent contributions in this area to that of the poly-Weibull distribution with respect to several goodness-of-fit measures. In addition, numerical and analytical procedures are developed for obtaining the maximum likelihood parameter estimates, standard errors, and an equation to determine the moments for the generalized poly-Weibull distribution with arbitrary number of terms. Our results show that both the bi-Weibull and tri-Weibull distributions fit the reference data set better than the current best-fit models. [ABSTRACT FROM AUTHOR] |
| Copyright of Quality Engineering is the property of Taylor & Francis Ltd 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: 138615481 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Maximum likelihood estimation for the poly-Weibull distribution. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Freels%2C+Jason+K%2E%22">Freels, Jason K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Timme%2C+Daniel+A%2E%22">Timme, Daniel A.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> daniel.a.timme@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Pignatiello%2C+Joseph+J%2E%22">Pignatiello, Joseph J.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Warr%2C+Richard+L%2E%22">Warr, Richard L.</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hill%2C+Raymond+R%2E%22">Hill, Raymond R.</searchLink><relatesTo>5</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Quality+Engineering%22">Quality Engineering</searchLink>. 2019, Vol. 31 Issue 4, p545-552. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Weibull+distribution%22">Weibull distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Generalized+method+of+moments%22">Generalized method of moments</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Failure+mode+%26+effects+analysis%22">Failure mode & effects analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The Weibull distribution has long been a popular choice for modeling lifetime data of various mechanical and biological phenomena when the associated hazard rate function is constant or monotone increasing or decreasing. However, nonmonotone hazard functions are common in reliability and survivability contexts where a system may undergo an initial "burn-in" prior to periods of useful life and eventual wear out. In these scenarios, the Weibull can only model a portion of the "bathtub" curve but is incapable of adequately modeling the entire failure process. Several modifications to the standard two-parameter Weibull distribution have therefore been introduced in the literature to effectively model and analyze lifetime data where the hazard rate function is bathtub-shaped. The performance of each modified distribution is typically assessed by its ability to fit a reference data set that is known to have a bathtub-shaped hazard rate function. The current article compares the performance of two recent contributions in this area to that of the poly-Weibull distribution with respect to several goodness-of-fit measures. In addition, numerical and analytical procedures are developed for obtaining the maximum likelihood parameter estimates, standard errors, and an equation to determine the moments for the generalized poly-Weibull distribution with arbitrary number of terms. Our results show that both the bi-Weibull and tri-Weibull distributions fit the reference data set better than the current best-fit models. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Quality Engineering is the property of Taylor & Francis Ltd 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: 10.1080/08982112.2018.1557685 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 545 Subjects: – SubjectFull: Weibull distribution Type: general – SubjectFull: Generalized method of moments Type: general – SubjectFull: Maximum likelihood statistics Type: general – SubjectFull: Failure mode & effects analysis Type: general Titles: – TitleFull: Maximum likelihood estimation for the poly-Weibull distribution. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Freels, Jason K. – PersonEntity: Name: NameFull: Timme, Daniel A. – PersonEntity: Name: NameFull: Pignatiello, Joseph J. – PersonEntity: Name: NameFull: Warr, Richard L. – PersonEntity: Name: NameFull: Hill, Raymond R. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: 2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 08982112 Numbering: – Type: volume Value: 31 – Type: issue Value: 4 Titles: – TitleFull: Quality Engineering Type: main |
| ResultId | 1 |
