Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions
The stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as...
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University of Baghdad, College of Science for Women
2021-06-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3011 |
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| author | Awatif Rezoky Mazaal Nada Sabah Karam Ghada Sabah Karam |
| author_facet | Awatif Rezoky Mazaal Nada Sabah Karam Ghada Sabah Karam |
| author_sort | Awatif Rezoky Mazaal |
| collection | DOAJ |
| description | The stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as a measure of the component performance. In this paper, a Bayesian analysis has been considered for R when the two variables X and Y are independent Weibull random variables with common parameter α in order to study the effect of each of the two different scale parameters β and λ; respectively, using three different [weighted, quadratic and entropy] loss functions under two different prior functions [Gamma and extension of Jeffery] and also an empirical Bayes estimator Using Gamma Prior, for singly type II censored sample. An empirical study has been used to make a comparison between the three estimators of the reliability for stress – strength Weibull model, by mean squared error MSE criteria, taking different sample sizes (small, moderate and large) for the two random variables in eight experiments of different values of their parameters. It has been found that the weighted loss function was the best for small sample size, and the entropy and Quadratic were the best for moderate and large sample sizes under the two prior distributions and for empirical Bayes estimation. |
| format | Article |
| id | doaj-art-6d0c08789fc5401d91add705caee41cb |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2021-06-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-6d0c08789fc5401d91add705caee41cb2025-08-20T03:33:39ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862021-06-0118210.21123/bsj.2021.18.2.0306Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss FunctionsAwatif Rezoky Mazaal0Nada Sabah Karam1Ghada Sabah Karam2Al-Mustansiriyah UniversityAl-Mustansiriyah UniversityAl-Mustansiriyah UniversityThe stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as a measure of the component performance. In this paper, a Bayesian analysis has been considered for R when the two variables X and Y are independent Weibull random variables with common parameter α in order to study the effect of each of the two different scale parameters β and λ; respectively, using three different [weighted, quadratic and entropy] loss functions under two different prior functions [Gamma and extension of Jeffery] and also an empirical Bayes estimator Using Gamma Prior, for singly type II censored sample. An empirical study has been used to make a comparison between the three estimators of the reliability for stress – strength Weibull model, by mean squared error MSE criteria, taking different sample sizes (small, moderate and large) for the two random variables in eight experiments of different values of their parameters. It has been found that the weighted loss function was the best for small sample size, and the entropy and Quadratic were the best for moderate and large sample sizes under the two prior distributions and for empirical Bayes estimation.https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3011Weibull Distribution, Stress-Strength Model, Reliability, Bayesian, Estimation |
| spellingShingle | Awatif Rezoky Mazaal Nada Sabah Karam Ghada Sabah Karam Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions مجلة بغداد للعلوم Weibull Distribution, Stress-Strength Model, Reliability, Bayesian, Estimation |
| title | Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions |
| title_full | Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions |
| title_fullStr | Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions |
| title_full_unstemmed | Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions |
| title_short | Comparing Weibull Stress – Strength Reliability Bayesian Estimators for Singly Type II Censored Data under Different loss Functions |
| title_sort | comparing weibull stress strength reliability bayesian estimators for singly type ii censored data under different loss functions |
| topic | Weibull Distribution, Stress-Strength Model, Reliability, Bayesian, Estimation |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3011 |
| work_keys_str_mv | AT awatifrezokymazaal comparingweibullstressstrengthreliabilitybayesianestimatorsforsinglytypeiicensoreddataunderdifferentlossfunctions AT nadasabahkaram comparingweibullstressstrengthreliabilitybayesianestimatorsforsinglytypeiicensoreddataunderdifferentlossfunctions AT ghadasabahkaram comparingweibullstressstrengthreliabilitybayesianestimatorsforsinglytypeiicensoreddataunderdifferentlossfunctions |