Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process
In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hy...
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MDPI AG
2022-09-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/9/455 |
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| author | Manal M. Yousef Amal S. Hassan Huda M. Alshanbari Abdal-Aziz H. El-Bagoury Ehab M. Almetwally |
| author_facet | Manal M. Yousef Amal S. Hassan Huda M. Alshanbari Abdal-Aziz H. El-Bagoury Ehab M. Almetwally |
| author_sort | Manal M. Yousef |
| collection | DOAJ |
| description | In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss the inference of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>=</mo><mi>P</mi><mo>(</mo><mi>X</mi><mo><</mo><mi>Y</mi><mo><</mo><mi>Z</mi><mo>)</mo></mrow></semantics></math></inline-formula> for a component when it is exposed to two stresses, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>,</mo><mi>Z</mi></mrow></semantics></math></inline-formula>, and it has one strength <i>X</i> that is regarded. We assume that both the stresses and strength variables follow an exponentiated exponential distribution with a common scale parameter. We obtain <i>R</i>’s maximum likelihood estimator and approximate confidence intervals. In addition, the Bayesian estimators for symmetric, such as squared error, and asymmetric loss functions, such as linear exponential, are developed. Credible intervals with the highest posterior densities are established. Monte Carlo simulations are used to evaluate and compare the effectiveness of the many proposed estimators. The process is then precisely described using an analysis of real data. |
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| last_indexed | 2024-03-10T00:44:27Z |
| publishDate | 2022-09-01 |
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| spelling | doaj.art-c0a40d4d8cce4b30aa0fc8abb5f902b52023-11-23T15:02:19ZengMDPI AGAxioms2075-16802022-09-0111945510.3390/axioms11090455Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring ProcessManal M. Yousef0Amal S. Hassan1Huda M. Alshanbari2Abdal-Aziz H. El-Bagoury3Ehab M. Almetwally4Department of Mathematics, Faculty of Science, New Valley University, El-Khargah 72511, EgyptFaculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaBasic Science Department, Higher Institute of Engineering and Technology, El-Mahala El-Kobra 6734723, EgyptFaculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, EgyptIn many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss the inference of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>=</mo><mi>P</mi><mo>(</mo><mi>X</mi><mo><</mo><mi>Y</mi><mo><</mo><mi>Z</mi><mo>)</mo></mrow></semantics></math></inline-formula> for a component when it is exposed to two stresses, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>,</mo><mi>Z</mi></mrow></semantics></math></inline-formula>, and it has one strength <i>X</i> that is regarded. We assume that both the stresses and strength variables follow an exponentiated exponential distribution with a common scale parameter. We obtain <i>R</i>’s maximum likelihood estimator and approximate confidence intervals. In addition, the Bayesian estimators for symmetric, such as squared error, and asymmetric loss functions, such as linear exponential, are developed. Credible intervals with the highest posterior densities are established. Monte Carlo simulations are used to evaluate and compare the effectiveness of the many proposed estimators. The process is then precisely described using an analysis of real data.https://www.mdpi.com/2075-1680/11/9/455stress–strength modelexponentiated exponentialgeneralized progressive hybrid censoringmaximum likelihood methodBayesian inference |
| spellingShingle | Manal M. Yousef Amal S. Hassan Huda M. Alshanbari Abdal-Aziz H. El-Bagoury Ehab M. Almetwally Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process Axioms stress–strength model exponentiated exponential generalized progressive hybrid censoring maximum likelihood method Bayesian inference |
| title | Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process |
| title_full | Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process |
| title_fullStr | Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process |
| title_full_unstemmed | Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process |
| title_short | Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process |
| title_sort | bayesian and non bayesian analysis of exponentiated exponential stress strength model based on generalized progressive hybrid censoring process |
| topic | stress–strength model exponentiated exponential generalized progressive hybrid censoring maximum likelihood method Bayesian inference |
| url | https://www.mdpi.com/2075-1680/11/9/455 |
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