DOI QR코드

DOI QR Code

Statistical Modeling of Joint Distribution Functions for Reliability Analysis

신뢰성 해석을 위한 결합분포함수의 통계모델링

  • Received : 2014.04.02
  • Accepted : 2014.05.08
  • Published : 2014.05.31

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

References

  1. C. Genest, A.C. Favre, "Everything you always wanted to know about copula modeling but were afraid to ask". Journal of Hydrologic Engineering, Vol. 12, No.4, pp. 347-368, 2007. DOI: http://dx.doi.org/10.1061/(ASCE)1084-0699(2007) 12:4(347) https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347)
  2. D. Huard, G. Evin, A.C. Favre, "Bayesian Copula Selection", Computational Statistics & Data Analysis, Vol. 51, pp. 809-822, 2006. DOI: http://dx.doi.org/10.1016/j.csda.2005.08.010 https://doi.org/10.1016/j.csda.2005.08.010
  3. Y. Noh, I. Lee, K.K. Choi, "Identification of Marginal and Joint CDFs Using Bayesian Method for RBDO", Structural Multidisciplinary Optimization, Vol.40, p. 35-51, 2010. DOI: http://dx.doi.org/10.1007/s00158-009-0385-1 https://doi.org/10.1007/s00158-009-0385-1
  4. R.B. Nelseon, An Introduction to Copulas, Springer, New York, 1999. DOI: http://dx.doi.org/10.1007/978-1-4757-3076-0 https://doi.org/10.1007/978-1-4757-3076-0
  5. I. Lee, K.K. Choi, L. Du, D. Gorsich, "Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems" Computational Methods Applied Mechanical Engineering, Vol. 198, pp. 14-27, 2008. DOI: http://dx.doi.org/10.1016/j.cma.2008.03.004 https://doi.org/10.1016/j.cma.2008.03.004
  6. D. Socie, Probabilistic Statistical Simulations Technical Background, eFatigue LLC, 2008, https://www.efatigue.com/probabilistic/background/statsi m.html#Cor, April, 2014.
  7. G. Nam, B. Lee, "Evaluation of Chassis Component Reliability Considering Variation of Fatigue Data", Journal of Korean Society for Precision Engineering, Vol. 24, No. 2, pp.110-117, 2007.

Acknowledgement

Supported by : 한국연구재단