Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring
This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likeli...
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| Format: | Article |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1609 |
| _version_ | 1827672067246391296 |
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| author | Wenjie Zhang Wenhao Gui |
| author_facet | Wenjie Zhang Wenhao Gui |
| author_sort | Wenjie Zhang |
| collection | DOAJ |
| description | This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood estimates of the parameters are obtained. Then, the observed Fisher information matrix is derived and utilized to construct asymptotic confidence intervals. Meanwhile, the parametric bootstrap methods are provided for the interval estimation. In addition, the Bayes estimates under the squared error loss function are obtained by applying the Tierney and Kadane technique and Lindley’s approximation. As for the optimal design, D- and A-optimality criteria are considered to determine the optimal transformed stress level. Finally, the simulation is carried out to demonstrate the proposed estimation techniques and the optimal criteria, and a real data set is discussed. |
| first_indexed | 2024-03-10T03:55:33Z |
| format | Article |
| id | doaj.art-5ecd690a8ef8433f9d803880f737f068 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:55:33Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5ecd690a8ef8433f9d803880f737f0682023-11-23T08:46:52ZengMDPI AGMathematics2227-73902022-05-01109160910.3390/math10091609Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II CensoringWenjie Zhang0Wenhao Gui1School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaThis paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood estimates of the parameters are obtained. Then, the observed Fisher information matrix is derived and utilized to construct asymptotic confidence intervals. Meanwhile, the parametric bootstrap methods are provided for the interval estimation. In addition, the Bayes estimates under the squared error loss function are obtained by applying the Tierney and Kadane technique and Lindley’s approximation. As for the optimal design, D- and A-optimality criteria are considered to determine the optimal transformed stress level. Finally, the simulation is carried out to demonstrate the proposed estimation techniques and the optimal criteria, and a real data set is discussed.https://www.mdpi.com/2227-7390/10/9/1609accelerated life testingthe Chen distributionmaximum likelihood estimationparametric bootstrap methodsBayes estimationoptimal criteria |
| spellingShingle | Wenjie Zhang Wenhao Gui Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring Mathematics accelerated life testing the Chen distribution maximum likelihood estimation parametric bootstrap methods Bayes estimation optimal criteria |
| title | Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring |
| title_full | Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring |
| title_fullStr | Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring |
| title_full_unstemmed | Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring |
| title_short | Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring |
| title_sort | statistical inference and optimal design of accelerated life testing for the chen distribution under progressive type ii censoring |
| topic | accelerated life testing the Chen distribution maximum likelihood estimation parametric bootstrap methods Bayes estimation optimal criteria |
| url | https://www.mdpi.com/2227-7390/10/9/1609 |
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