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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Main Authors: Li Zhang, Rongfang Yan, Junrui Wang
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Scientific Reports
Subjects:
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.
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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