Analysis and Application of Mechanical System Reliability Model Based on Copula Function

An, Honglei; Yin, Hang; Feng, He

doi:10.1515/pomr-2016-0064

Cited by 9 publications

(6 citation statements)

References 3 publications

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“…Equations ( 36) and (37) suggest that the failure probability distribution function solved by the multidimensional T-S DFTA with failure correlation is consistent with that solved using the reliability model of the failure correlation series system [14]. As a result, the correctness of the model in solving the reliability problem of the failure correlation series system is verified.…”

Section: Verification Of Multi-dimensional T-s Dfta With Failure Corr...supporting

confidence: 58%

Multi-dimensional T-S dynamic fault tree analysis method involving failure correlation

Chen,

Liu,

Yao

et al. 2023

IFS

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The lack of effective failure correlation analysis is one main reason for the gap between the reliability models and the actual complex systems with mixed static and dynamic characteristics. Takagi and Sugeno (T-S) dynamic fault tree is one powerful tool to analyze the static and dynamic failure logic relationship but it assumes the failure probability of the event is independent. Therefore, this paper proposes a multi-dimensional T-S dynamic fault tree analysis method involving failure correlation. The method integrates the failure probability distribution function of basic events with multi-factors and the multi-dimensional copula function, and the important measure of this method is also deduced. The reliability model expression for systems with failure correlations, both in series and in parallel, is discussed and verified. Compare the proposed method with the assumption that the probability of a failure event is independent. This method solves the problem of a large error when ignoring the failure correlation between parts and the degree of the correlation between variables can be characterized. The reliability analysis can be conducted on complex systems affected both by multi-factors and failure correlations. The proposed method is applied to the reliability analysis of a hydraulic height adjustment system and the correctness and superiority of the method are verified.

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Section: Verification Of Multi-dimensional T-s Dfta With Failure Corr...supporting

confidence: 58%

Multi-dimensional T-S dynamic fault tree analysis method involving failure correlation

Chen,

Liu,

Yao

et al. 2023

IFS

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show abstract

“…Copula Function 2.1. eory of Copula Function. After Sklar [14] proposed copula function in 1959, it was successfully applied in fields of statistical economics and finance [15], hydrology [16][17][18], and structural engineering [19][20][21][22][23][24], and a lot of research papers were published. e advantage of copula function is that it can directly construct joint distribution function for many related random variables or decouple a joint distribution function into multiple marginal distribution functions and a unique copula function [25].…”

Section: Load Effect Combination Methods Based Onmentioning

confidence: 99%

“…According to Table 1, the Kendall's rank correlation coefficient and copula function parameters can be transformed. e weight coefficient ω i is estimated by the maximum likelihood estimation method [24]. Based on the M-Copula load correlation analysis model, the specific process is divided into the following steps:…”

Section: Multivariate Sequence Correlation Analysismentioning

confidence: 99%

Based on M-Copula Reliability Analysis of Random Load Correlation

Huang

Mingdong

Liu

et al. 2020

Mathematical Problems in Engineering

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Load is one of the main causes of structural failure, and the correlation among loads would affect the evaluation results of structural performance. The purpose of this paper is to analyze the influence of the correlation among multiple loads on the structural reliability. In this paper, the nonparametric kernel density estimation (NKDE) method is used to estimate the probability density function (PDF) of related loads. In addition, the mixed copula (M-Copula) model is proposed, which combines Gumbel copula, Frank copula, Clayton copula, and weight coefficient, and the model parameters are fitted by MATLAB software to get the correlation of related loads. The reliability based on the related load combination is calculated according to the constructed model. After analyzing three numerical cases, the results show that the probability characteristics of NKDE estimation are very close to the actual conditions, and the reliability calculated by the M-Copula model is larger than those calculated by JCSS, Turkstra, and Gong methods. Using the M-Copula model for load correlation would avoid underestimating the reliability of the structure, which is conducive to structural economic development.

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“…, when each unit of a system is in parallel, the life time of the system is the largest in all the units, that is T= max(T 1 , T 2 ,…,T n ), then the reliability of a parallel system can be expressed as (Hai et al, 2016):…”

Section: Original Systemmentioning

confidence: 99%

Reliability Equivalence Factors of a Parallel System Subject to Weibull Distribution Using Multivariate FGM Copula

Temraz¹

2018

American Journal of Applied Sciences

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This paper analyze a parallel system consisted of n dependent components with lifetimes follow Weibull distribution. FGM Copula in multivariate case is used to generate the reliability function of the original system. Reduction method is introduced to improve system reliability. Other methods of hot, cold and warm duplication are established to improve system reliability. An application using real time data is introduced to show the results and compare between different improvement methods.

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Analysis and Application of Mechanical System Reliability Model Based on Copula Function

Cited by 9 publications

References 3 publications

Multi-dimensional T-S dynamic fault tree analysis method involving failure correlation

Multi-dimensional T-S dynamic fault tree analysis method involving failure correlation

Based on M-Copula Reliability Analysis of Random Load Correlation

Reliability Equivalence Factors of a Parallel System Subject to Weibull Distribution Using Multivariate FGM Copula

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