Performance Index for Weibull Distribution With the Progressive First‐Failure‐Censored Sampling.
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| Title: | Performance Index for Weibull Distribution With the Progressive First‐Failure‐Censored Sampling. |
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| Authors: | Jafari, A. A.1 (AUTHOR) aajafari@yazd.ac.ir, Karimi, M.1 (AUTHOR), Sen, Smritijit1 (AUTHOR) smsen@wiley.com |
| Source: | Journal of Probability & Statistics. 7/29/2026, Vol. 2026, p1-20. 20p. |
| Subjects: | Weibull distribution, Bayesian analysis, Monte Carlo method, Process capability, Confidence intervals, Maximum likelihood statistics, Markov chain Monte Carlo |
| Abstract: | Process capability indices are essential tools for assessing product quality, offering insights into how well a product meets specified standards and customer expectations. This paper explores the lifetime performance index under the assumption that product lifetimes follow a Weibull distribution. We first develop six generalized approaches using the concept of a generalized pivotal quantity and incorporate properties of progressively first‐failure‐censored samples, as well as maximum likelihood and weighted least squares estimation for the Weibull distribution. Additionally, we introduce a Bayesian approach for inference on the lifetime performance parameter and employ Markov chain Monte Carlo simulations to compute posterior estimates and construct credible intervals. Furthermore, we extend another Bayesian approach that uses a different strategy for specifying the prior distribution of parameters—a transition from progressive Type II censoring to progressive first‐failure censoring. We analyze the properties of confidence intervals for the performance index through Monte Carlo simulations, comparing the results of a large‐sample method based on maximum likelihood estimation and the extended Bayesian approach with the seven novel approaches. The behavior of the confidence intervals for the parameter is illustrated through two examples. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Probability & Statistics 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: 195791999 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Performance Index for Weibull Distribution With the Progressive First‐Failure‐Censored Sampling. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jafari%2C+A%2E+A%2E%22">Jafari, A. A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aajafari@yazd.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Karimi%2C+M%2E%22">Karimi, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sen%2C+Smritijit%22">Sen, Smritijit</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> smsen@wiley.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Probability+%26+Statistics%22">Journal of Probability & Statistics</searchLink>. 7/29/2026, Vol. 2026, p1-20. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Weibull+distribution%22">Weibull distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Process+capability%22">Process capability</searchLink><br /><searchLink fieldCode="DE" term="%22Confidence+intervals%22">Confidence intervals</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+chain+Monte+Carlo%22">Markov chain Monte Carlo</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Process capability indices are essential tools for assessing product quality, offering insights into how well a product meets specified standards and customer expectations. This paper explores the lifetime performance index under the assumption that product lifetimes follow a Weibull distribution. We first develop six generalized approaches using the concept of a generalized pivotal quantity and incorporate properties of progressively first‐failure‐censored samples, as well as maximum likelihood and weighted least squares estimation for the Weibull distribution. Additionally, we introduce a Bayesian approach for inference on the lifetime performance parameter and employ Markov chain Monte Carlo simulations to compute posterior estimates and construct credible intervals. Furthermore, we extend another Bayesian approach that uses a different strategy for specifying the prior distribution of parameters—a transition from progressive Type II censoring to progressive first‐failure censoring. We analyze the properties of confidence intervals for the performance index through Monte Carlo simulations, comparing the results of a large‐sample method based on maximum likelihood estimation and the extended Bayesian approach with the seven novel approaches. The behavior of the confidence intervals for the parameter is illustrated through two examples. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Probability & Statistics 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=195791999 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/jpas/5460987 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 1 Subjects: – SubjectFull: Weibull distribution Type: general – SubjectFull: Bayesian analysis Type: general – SubjectFull: Monte Carlo method Type: general – SubjectFull: Process capability Type: general – SubjectFull: Confidence intervals Type: general – SubjectFull: Maximum likelihood statistics Type: general – SubjectFull: Markov chain Monte Carlo Type: general Titles: – TitleFull: Performance Index for Weibull Distribution With the Progressive First‐Failure‐Censored Sampling. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jafari, A. A. – PersonEntity: Name: NameFull: Karimi, M. – PersonEntity: Name: NameFull: Sen, Smritijit IsPartOfRelationships: – BibEntity: Dates: – D: 29 M: 07 Text: 7/29/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1687952X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Probability & Statistics Type: main |
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