Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data
In this paper, we propose an optimization for the simple step stress accelerated life test for the Fr´echet distribution under type I censoring. The extreme value distribution has recently become increasingly important in engineering statistics as a suitable model to represent phenomena with extrem...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2017-01-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/201 |
| _version_ | 1818513163654529024 |
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| author | Nooshin Hakamipour Sadegh Rezaei |
| author_facet | Nooshin Hakamipour Sadegh Rezaei |
| author_sort | Nooshin Hakamipour |
| collection | DOAJ |
| description |
In this paper, we propose an optimization for the simple step stress accelerated life test for the Fr´echet distribution under type I censoring. The extreme value distribution has recently become increasingly important in engineering statistics as a suitable model to represent phenomena with extreme observations. One probability distribution, that is used to model the maximum extreme events, is the Fr´echet (extreme value type II) distribution. A log-linear relationship between the Fr´echet scale parameter and the stress are assumed. Furthermore, we model the effects of changing stress as a cumulative exposure function. The maximum likelihood estimators of the model parameters are derived. By minimizing the asymptotic variance of the desired life estimate and the reliability estimate, we obtain the optimal simple step stress accelerated life test. Finally, the simulation results are discussed to illustrate the effect of the initial estimates on the optimal values.
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| first_indexed | 2024-12-10T23:57:22Z |
| format | Article |
| id | doaj.art-aea0b9e4371b4fe490404e28c0837656 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-12-10T23:57:22Z |
| publishDate | 2017-01-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-aea0b9e4371b4fe490404e28c08376562022-12-22T01:28:34ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712017-01-0115110.57805/revstat.v15i1.201Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet DataNooshin Hakamipour0Sadegh Rezaei1Amirkabir University of TechnologyAmirkabir University of Technology In this paper, we propose an optimization for the simple step stress accelerated life test for the Fr´echet distribution under type I censoring. The extreme value distribution has recently become increasingly important in engineering statistics as a suitable model to represent phenomena with extreme observations. One probability distribution, that is used to model the maximum extreme events, is the Fr´echet (extreme value type II) distribution. A log-linear relationship between the Fr´echet scale parameter and the stress are assumed. Furthermore, we model the effects of changing stress as a cumulative exposure function. The maximum likelihood estimators of the model parameters are derived. By minimizing the asymptotic variance of the desired life estimate and the reliability estimate, we obtain the optimal simple step stress accelerated life test. Finally, the simulation results are discussed to illustrate the effect of the initial estimates on the optimal values. https://revstat.ine.pt/index.php/REVSTAT/article/view/201Fréchet distributionlog-linear relationshipmaximum likelihood estimatoroptimal designreliabilitystep stress accelerated life test |
| spellingShingle | Nooshin Hakamipour Sadegh Rezaei Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data Revstat Statistical Journal Fréchet distribution log-linear relationship maximum likelihood estimator optimal design reliability step stress accelerated life test |
| title | Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data |
| title_full | Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data |
| title_fullStr | Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data |
| title_full_unstemmed | Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data |
| title_short | Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data |
| title_sort | optimizing the simple step stress accelerated life test with type i censored frechet data |
| topic | Fréchet distribution log-linear relationship maximum likelihood estimator optimal design reliability step stress accelerated life test |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/201 |
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