Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions
Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4652 |
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| author | Refah Alotaibi Ehab M. Almetwally Qiuchen Hai Hoda Rezk |
| author_facet | Refah Alotaibi Ehab M. Almetwally Qiuchen Hai Hoda Rezk |
| author_sort | Refah Alotaibi |
| collection | DOAJ |
| description | Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknown parameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique. |
| first_indexed | 2024-03-09T16:07:42Z |
| format | Article |
| id | doaj.art-0179bb9433c242df81b3d596d69e3677 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:42Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0179bb9433c242df81b3d596d69e36772023-11-24T16:27:22ZengMDPI AGMathematics2227-73902022-12-011024465210.3390/math10244652Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss FunctionsRefah Alotaibi0Ehab M. Almetwally1Qiuchen Hai2Hoda Rezk3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 12613, EgyptDepartment of Mathematical, Physical, and Engineering Sciences, Texas A&M University-San Antonio, San Antonio, TX 78224, USADepartment of Statistics, Al-Azhar University, Cairo 4434003, EgyptAccelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknown parameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique.https://www.mdpi.com/2227-7390/10/24/4652the alpha power inverse Weibull distributionstep stress partially accelerated life testingadaptive progressive hybrid censored dataloss functions |
| spellingShingle | Refah Alotaibi Ehab M. Almetwally Qiuchen Hai Hoda Rezk Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions Mathematics the alpha power inverse Weibull distribution step stress partially accelerated life testing adaptive progressive hybrid censored data loss functions |
| title | Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions |
| title_full | Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions |
| title_fullStr | Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions |
| title_full_unstemmed | Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions |
| title_short | Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions |
| title_sort | optimal test plan of step stress partially accelerated life testing for alpha power inverse weibull distribution under adaptive progressive hybrid censored data and different loss functions |
| topic | the alpha power inverse Weibull distribution step stress partially accelerated life testing adaptive progressive hybrid censored data loss functions |
| url | https://www.mdpi.com/2227-7390/10/24/4652 |
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