Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring
As an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of...
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2901 |
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| author | Refah Alotaibi Mazen Nassar Hoda Rezk Ahmed Elshahhat |
| author_facet | Refah Alotaibi Mazen Nassar Hoda Rezk Ahmed Elshahhat |
| author_sort | Refah Alotaibi |
| collection | DOAJ |
| description | As an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of its reliability characteristics using progressively Type-II censored data. To get estimates of unknown parameters, reliability, and hazard rate functions, the maximum likelihood, and Bayesian estimation approaches are studied. To acquire estimated confidence intervals for unknown parameters and reliability characteristics, the maximum likelihood asymptotic properties are used. The Markov chain Monte Carlo approach is used in Bayesian estimation to provide Bayesian estimates under squared error and LINEX loss functions. Furthermore, the highest posterior density credible intervals of the parameters and reliability characteristics are determined. A Monte Carlo simulation study is used to investigate the accuracy of various point and interval estimators. In addition, various optimality criteria are used to choose the best progressive censoring schemes. Two real data from the engineering field are analyzed to demonstrate the applicability and significance of the proposed approaches. Based on numerical results, the Bayesian procedure for estimating the parameters and reliability characteristics of alpha power Weibull distribution is recommended. The analysis of two real data sets showed that the alpha power Weibull distribution is a good model to investigate engineering data in the presence of progressive Type-II censoring. |
| first_indexed | 2024-03-09T09:53:14Z |
| format | Article |
| id | doaj.art-c7ff946c788144d699090c4d663397ec |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:53:14Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-c7ff946c788144d699090c4d663397ec2023-12-01T23:57:31ZengMDPI AGMathematics2227-73902022-08-011016290110.3390/math10162901Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II CensoringRefah Alotaibi0Mazen Nassar1Hoda Rezk2Ahmed Elshahhat3Department 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, Al-Azhar University, Cairo 11751, EgyptFaculty of Technology and Development, Zagazig University, Zagazig 44519, EgyptAs an extension of the standard Weibull distribution, a new crucial distribution termed alpha power Weibull distribution has been presented. It can model decreasing, increasing, bathtub, and upside-down bathtub failure rates. This research investigates the estimation of model parameters and some of its reliability characteristics using progressively Type-II censored data. To get estimates of unknown parameters, reliability, and hazard rate functions, the maximum likelihood, and Bayesian estimation approaches are studied. To acquire estimated confidence intervals for unknown parameters and reliability characteristics, the maximum likelihood asymptotic properties are used. The Markov chain Monte Carlo approach is used in Bayesian estimation to provide Bayesian estimates under squared error and LINEX loss functions. Furthermore, the highest posterior density credible intervals of the parameters and reliability characteristics are determined. A Monte Carlo simulation study is used to investigate the accuracy of various point and interval estimators. In addition, various optimality criteria are used to choose the best progressive censoring schemes. Two real data from the engineering field are analyzed to demonstrate the applicability and significance of the proposed approaches. Based on numerical results, the Bayesian procedure for estimating the parameters and reliability characteristics of alpha power Weibull distribution is recommended. The analysis of two real data sets showed that the alpha power Weibull distribution is a good model to investigate engineering data in the presence of progressive Type-II censoring.https://www.mdpi.com/2227-7390/10/16/2901alpha power weibull distributionprogressive Type-II censoringmaximum likelihoodBayesian paradigmreliability measuresMCMC techniques |
| spellingShingle | Refah Alotaibi Mazen Nassar Hoda Rezk Ahmed Elshahhat Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring Mathematics alpha power weibull distribution progressive Type-II censoring maximum likelihood Bayesian paradigm reliability measures MCMC techniques |
| title | Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring |
| title_full | Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring |
| title_fullStr | Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring |
| title_full_unstemmed | Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring |
| title_short | Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring |
| title_sort | inferences and engineering applications of alpha power weibull distribution using progressive type ii censoring |
| topic | alpha power weibull distribution progressive Type-II censoring maximum likelihood Bayesian paradigm reliability measures MCMC techniques |
| url | https://www.mdpi.com/2227-7390/10/16/2901 |
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