Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application
This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach,...
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| פורמט: | Article |
| שפה: | English |
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MDPI AG
2024-09-01
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| סדרה: | Mathematics |
| נושאים: | |
| גישה מקוונת: | https://www.mdpi.com/2227-7390/12/17/2747 |
| _version_ | 1827115915972444160 |
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| author | Hassan S. Bakouch Fernando A. Moala Shuhrah Alghamdi Olayan Albalawi |
| author_facet | Hassan S. Bakouch Fernando A. Moala Shuhrah Alghamdi Olayan Albalawi |
| author_sort | Hassan S. Bakouch |
| collection | DOAJ |
| description | This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach’s performance and one-sample lifetime data are presented to illustrate the proposed methodology. |
| first_indexed | 2025-03-20T12:25:22Z |
| format | Article |
| id | doaj.art-411f64d0f6dd4039aab5a5b8da99da68 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2025-03-20T12:25:22Z |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-411f64d0f6dd4039aab5a5b8da99da682024-09-13T12:40:34ZengMDPI AGMathematics2227-73902024-09-011217274710.3390/math12172747Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data ApplicationHassan S. Bakouch0Fernando A. Moala1Shuhrah Alghamdi2Olayan Albalawi3Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Statistics, State University of Sao Paulo, Sao Paulo 19060-900, BrazilDepartment of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi ArabiaDepartment of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi ArabiaThis paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach’s performance and one-sample lifetime data are presented to illustrate the proposed methodology.https://www.mdpi.com/2227-7390/12/17/2747step-stress accelerated lifetime testingBayesian analysistype II censoringreparametrizationgamma distributionSimulation |
| spellingShingle | Hassan S. Bakouch Fernando A. Moala Shuhrah Alghamdi Olayan Albalawi Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application Mathematics step-stress accelerated lifetime testing Bayesian analysis type II censoring reparametrization gamma distribution Simulation |
| title | Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application |
| title_full | Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application |
| title_fullStr | Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application |
| title_full_unstemmed | Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application |
| title_short | Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application |
| title_sort | bayesian methods for step stress accelerated test under gamma distribution with a useful reparametrization and an industrial data application |
| topic | step-stress accelerated lifetime testing Bayesian analysis type II censoring reparametrization gamma distribution Simulation |
| url | https://www.mdpi.com/2227-7390/12/17/2747 |
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