A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution
In lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data q...
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2025-06-01
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| author | Mervat K. Abd Elaal Hebatalla H. Mohammad Zakiah I. Kalantan Abeer A. EL-Helbawy Gannat R. AL-Dayian Sara M. Behairy Reda M. Refaey |
| author_facet | Mervat K. Abd Elaal Hebatalla H. Mohammad Zakiah I. Kalantan Abeer A. EL-Helbawy Gannat R. AL-Dayian Sara M. Behairy Reda M. Refaey |
| author_sort | Mervat K. Abd Elaal |
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| description | In lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data quality. This paper develops a Bayesian model based on Type II censored data, assuming that item lifetimes follow the Topp–Leone inverted Kumaraswamy distribution, a flexible alternative to classical lifetime models due to its ability to capture various hazard rate shapes and to model bounded and skewed lifetime data more effectively than traditional models observed in real-world reliability data. Bayes estimators of the model parameters and acceleration factor are derived under both symmetric (balanced squared error) and asymmetric (balanced linear exponential) loss functions using informative priors. The novelty of this work lies in the integration of the Topp–Leone inverted Kumaraswamy distribution within the Bayesian step-stress partially accelerated life testing framework, which has not been explored previously, offering improved modeling capability for complex lifetime data. The proposed method is validated through comprehensive simulation studies under various censoring schemes, demonstrating robustness and superior estimation performance compared to traditional models. A real-data application involving COVID-19 mortality data further illustrates the practical relevance and improved fit of the model. Overall, the results highlight the flexibility, efficiency, and applicability of the proposed Bayesian approach in reliability analysis. |
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| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-f559c11de49c4b41bffba6875bc12f9c2025-06-25T13:28:31ZengMDPI AGAxioms2075-16802025-06-0114647610.3390/axioms14060476A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime DistributionMervat K. Abd Elaal0Hebatalla H. Mohammad1Zakiah I. Kalantan2Abeer A. EL-Helbawy3Gannat R. AL-Dayian4Sara M. Behairy5Reda M. Refaey6Department of Statistics, Faculty of Commerce, Al-Azhar University, (Girls’ Branch), Cairo 11751, EgyptDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Statistics, Faculty of Commerce, Al-Azhar University, (Girls’ Branch), Cairo 11751, EgyptDepartment of Statistics, Faculty of Commerce, Al-Azhar University, (Girls’ Branch), Cairo 11751, EgyptDepartment of Statistics, Faculty of Commerce, Al-Azhar University, (Girls’ Branch), Cairo 11751, EgyptDepartment of Statistics, Faculty of Commerce, Al-Azhar University, (Girls’ Branch), Cairo 11751, EgyptIn lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data quality. This paper develops a Bayesian model based on Type II censored data, assuming that item lifetimes follow the Topp–Leone inverted Kumaraswamy distribution, a flexible alternative to classical lifetime models due to its ability to capture various hazard rate shapes and to model bounded and skewed lifetime data more effectively than traditional models observed in real-world reliability data. Bayes estimators of the model parameters and acceleration factor are derived under both symmetric (balanced squared error) and asymmetric (balanced linear exponential) loss functions using informative priors. The novelty of this work lies in the integration of the Topp–Leone inverted Kumaraswamy distribution within the Bayesian step-stress partially accelerated life testing framework, which has not been explored previously, offering improved modeling capability for complex lifetime data. The proposed method is validated through comprehensive simulation studies under various censoring schemes, demonstrating robustness and superior estimation performance compared to traditional models. A real-data application involving COVID-19 mortality data further illustrates the practical relevance and improved fit of the model. Overall, the results highlight the flexibility, efficiency, and applicability of the proposed Bayesian approach in reliability analysis.https://www.mdpi.com/2075-1680/14/6/476accelerated life teststep stress-partiallyTopp–Leone-inverted Kumaraswamy distributionType II censored samplesbalancedsquare error |
| spellingShingle | Mervat K. Abd Elaal Hebatalla H. Mohammad Zakiah I. Kalantan Abeer A. EL-Helbawy Gannat R. AL-Dayian Sara M. Behairy Reda M. Refaey A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution Axioms accelerated life test step stress-partially Topp–Leone-inverted Kumaraswamy distribution Type II censored samples balanced square error |
| title | A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution |
| title_full | A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution |
| title_fullStr | A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution |
| title_full_unstemmed | A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution |
| title_short | A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution |
| title_sort | bayesian approach to step stress partially accelerated life testing for a novel lifetime distribution |
| topic | accelerated life test step stress-partially Topp–Leone-inverted Kumaraswamy distribution Type II censored samples balanced square error |
| url | https://www.mdpi.com/2075-1680/14/6/476 |
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