Stress-strength reliability estimation for bivariate copula function with rayleigh marginals

James, A.; Chandra, Navin; Sebastian, Nicy

doi:10.1007/s13198-022-01836-6

Cited by 7 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Domma & Giordano [47] FGM, Generalized FGM, Frank Burr III, Dagum, Singh-Maddala Gao et al [48] Mixed (Clayton, Gumbel, Frank) Empirical de Andrade et al [49] Clayton, Gumbel, Frank, Gauss, Plackett Weibull, Gamma, Log-normal, Dagum Rathie et al [50] Frank Dagum, Log-Dagum James et al [51] FGM Rayleigh Shang & Yan [52] Clayton Weibull, Kumaraswamy Lima et al [53] Clayton, Frank, Gumbel-Houggard Generalized extreme value, Weibull, gamma…”

Section: Copula Marginal Distributionmentioning

confidence: 99%

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

Nakazono,

Lin,

Liao

et al. 2024

Mathematics

View full text Add to dashboard Cite

The Mann–Whitney effect is a measure for comparing survival distributions between two groups. The Mann–Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann–Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent of each other, the traditional formula of the Mann–Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann–Whitney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands . Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.

show abstract

Section: Copula Marginal Distributionmentioning

confidence: 99%

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

Nakazono,

Lin,

Liao

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…In structural reliability engineering, correlation features primarily arise from stress and strength components, stress-strength [5,6], multiple failure mechanisms [7][8][9], and multiple parts [2,10]. Accurately quantifying and characterizing these correlation features is crucial for constructing a reliable structural analysis and calculation model.…”

Section: Introductionmentioning

confidence: 99%

“…The Copula function is a widely used method for portraying and characterizing correlation features [2,5,6,19]. It is preferred over other methods because it does not require edge distribution and can quantify correlation with higher accuracy.…”

Section: Introductionmentioning

confidence: 99%

A Structural Reliability Analysis Method Considering Multiple Correlation Features

Bai,

Li,

Zhang

et al. 2024

Machines

View full text Add to dashboard Cite

The paper analyzes the correlation features between stress strength, multiple failure mechanisms, and multiple components. It investigates the effects of different correlation features on reliability and proposes a method for structural reliability analysis that considers the joint effects of multiple correlation features. To portray the stress–strength correlation structure, the Copula function is utilized and the influence of the correlation degree parameter on reliability is clarified. The text describes the introduction of time-varying characteristics of structural strength and correlation parameters. A time-varying Copula is then constructed to calculate the structural reliability under the stress–strength correlation characteristics. Additionally, a time-varying hybrid Copula is constructed to characterize the intricate and correlation features of multiple failure mechanisms and components. The article proposes the variational adaptive sparrow search algorithm (VASSA) to obtain optimal parameters for the time-varying hybrid Copula. The effectiveness and accuracy of the proposed method are verified through actual cases. The results indicate that multiple correlation features significantly influence structural reliability. Incorporating multiple correlation features into the solution of structural reliability yields safer results that align with engineering practice.

show abstract

“…Domma and Giordano [18], based on stress and strength following different parameters of the Dagum distribution, utilized the Frank copula to characterize the dependence and studied the reliability of stress-strength models. Recently, James et al [19] assumed that the dependence between stress and strength is characterized by the FGM copula, with marginal distributions being different parameter Rayleigh distributions. They employed maximum likelihood estimation, marginal inference methods, and semi-parametric methods to conduct statistical analysis on the reliability of single-component stress-strength models.…”

Section: Introductionmentioning

confidence: 99%

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

Wang,

Yan

2024

Symmetry

View full text Add to dashboard Cite

This study investigates the dependence between stress and component strength in a stress–strength model with bivariate stresses by incorporating a specialized Archimedean copula, specifically the 3-dimensional Clayton copula. Diverging from prior research, we consider a scenario where two stresses simultaneously influence the component strength, enhancing the realism of our model. Initially, dependent parameter estimates were obtained through moment estimation. Subsequently, maximum likelihood estimation and Bayesian estimation were employed to acquire point and interval estimates for the model parameters. Finally, numerical simulations and real-world data analysis were conducted to validate the accuracy and practicality of our proposed model. This research establishes a foundation for further exploration of general dependence structures and multi-component stress–strength correlation issues.

show abstract

Stress-strength reliability estimation for bivariate copula function with rayleigh marginals

Cited by 7 publications

References 40 publications

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

A Structural Reliability Analysis Method Considering Multiple Correlation Features

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

Contact Info

Product

Resources

About