Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula
Abstract In this paper, we investigate the inferential procedures for dependent stress-strength reliability within a series-parallel system, utilizing the Clayton copula to characterize the dependence structure between stress and strength variables, which follow proportional reversed hazard rate mod...
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Nature Portfolio
2025-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-13878-4 |
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| author | Li Zhang Rongfang Yan Junrui Wang |
| author_facet | Li Zhang Rongfang Yan Junrui Wang |
| author_sort | Li Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the inferential procedures for dependent stress-strength reliability within a series-parallel system, utilizing the Clayton copula to characterize the dependence structure between stress and strength variables, which follow proportional reversed hazard rate model. We establish maximum likelihood estimations for model parameters and system reliability, along with improved approximate confidence intervals based on Fisher information. Bayesian estimations are performed using the highly flexible Gamma-Beta prior distribution under different loss functions, and the highest posterior density interval is obtained via the Metropolis-Hastings algorithm. To assess the performance of the proposed methods, Monte Carlo simulations are conducted. Finally, an original data set, the general dam occupancy rate of Istanbul, is analyzed for illustrative purposes. |
| format | Article |
| id | doaj-art-c64deaaf22724eaea11af0788eece9ee |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c64deaaf22724eaea11af0788eece9ee2025-08-20T03:46:00ZengNature PortfolioScientific Reports2045-23222025-08-0115111710.1038/s41598-025-13878-4Bayesian inference for dependent stress–strength reliability of series–parallel system based on copulaLi Zhang0Rongfang Yan1Junrui Wang2College of Mathematics and Statistics, Northwest Normal UniversityCollege of Mathematics and Statistics, Northwest Normal UniversityCollege of Mathematics and Statistics, Northwest Normal UniversityAbstract In this paper, we investigate the inferential procedures for dependent stress-strength reliability within a series-parallel system, utilizing the Clayton copula to characterize the dependence structure between stress and strength variables, which follow proportional reversed hazard rate model. We establish maximum likelihood estimations for model parameters and system reliability, along with improved approximate confidence intervals based on Fisher information. Bayesian estimations are performed using the highly flexible Gamma-Beta prior distribution under different loss functions, and the highest posterior density interval is obtained via the Metropolis-Hastings algorithm. To assess the performance of the proposed methods, Monte Carlo simulations are conducted. Finally, an original data set, the general dam occupancy rate of Istanbul, is analyzed for illustrative purposes.https://doi.org/10.1038/s41598-025-13878-4Dependent stress-strength reliabilitySeries-parallel systemClayton copulaMaximum likelihood estimationBayesian estimation |
| spellingShingle | Li Zhang Rongfang Yan Junrui Wang Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula Scientific Reports Dependent stress-strength reliability Series-parallel system Clayton copula Maximum likelihood estimation Bayesian estimation |
| title | Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula |
| title_full | Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula |
| title_fullStr | Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula |
| title_full_unstemmed | Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula |
| title_short | Bayesian inference for dependent stress–strength reliability of series–parallel system based on copula |
| title_sort | bayesian inference for dependent stress strength reliability of series parallel system based on copula |
| topic | Dependent stress-strength reliability Series-parallel system Clayton copula Maximum likelihood estimation Bayesian estimation |
| url | https://doi.org/10.1038/s41598-025-13878-4 |
| work_keys_str_mv | AT lizhang bayesianinferencefordependentstressstrengthreliabilityofseriesparallelsystembasedoncopula AT rongfangyan bayesianinferencefordependentstressstrengthreliabilityofseriesparallelsystembasedoncopula AT junruiwang bayesianinferencefordependentstressstrengthreliabilityofseriesparallelsystembasedoncopula |