# 신뢰성 해석을 위한 결합분포함수의 통계모델링

• Noh, Yoojeong (Department of Mechanical and Automotive Engineering, Keimyung University) ;
• Lee, Sangjin (Department of Mechanical and Automotive Engineering, Keimyung University)
• 노유정 (계명대학교 기계자동차공학과) ;
• 이상진 (계명대학교 기계자동차공학과)
• Accepted : 2014.05.08
• Published : 2014.05.31
• 77 17

#### Abstract

Reliability analysis of mechanical systems requires statistical modeling of input random variables such as distribution function types and statistical parameters that affect the performance of the mechanical systems. Some random variables are correlated, but considered as independent variables or wrong assumptions on input random variables have been used. In this paper, joint distributions were modeled using copulas and Bayesian method from limited number of data. To verify the proposed method, statistical simulation tests were carried out for various number of samples and correlation coefficients. As a result, the Bayesian method selected the most probable copula types among candidate copulas even though the candidate copula shapes are similar for low correlations or the number of data is limited. The most probable copulas also yielded similar reliabilities with the true reliability obtained from a true copula, so that it can be concluded that the Bayesian method provides accurate statistical modeling for the reliability analysis.

#### Keywords

Bayesian method;Copula;Joint cumulative distribution function;Reliability analysis;Statistical modeling

#### Acknowledgement

Supported by : 한국연구재단

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