Publisher : The Korea Academia-Industrial cooperation Society
DOI : 10.5762/KAIS.2016.17.5.645
Title & Authors
A Comparison Study on Statistical Modeling Methods Noh, Yoojeong;
The statistical modeling of input random variables is necessary in reliability analysis, reliability-based design optimization, and statistical validation and calibration of analysis models of mechanical systems. In statistical modeling methods, there are the Akaike Information Criterion (AIC), AIC correction (AICc), Bayesian Information Criterion, Maximum Likelihood Estimation (MLE), and Bayesian method. Those methods basically select the best fitted distribution among candidate models by calculating their likelihood function values from a given data set. The number of data or parameters in some methods are considered to identify the distribution types. On the other hand, the engineers in a real field have difficulties in selecting the statistical modeling method to obtain a statistical model of the experimental data because of a lack of knowledge of those methods. In this study, commonly used statistical modeling methods were compared using statistical simulation tests. Their advantages and disadvantages were then analyzed. In the simulation tests, various types of distribution were assumed as populations and the samples were generated randomly from them with different sample sizes. Real engineering data were used to verify each statistical modeling method.
Y. Noh, and S. Lee "Statistical Modeling of Joint Distribution Functions for Reliability Analysis", Journal of the Korean Academia-Industrial cooperation Society, Vol. 15, No. 5, 2014, pp. 2603-2609. DOI: http://dx.doi.org/10.5762/KAIS.2014.15.5.2603
Y. Noh, K. K. Choi, I. Lee, "Identification of Marginal and Joint CDFs Using the Bayesian Method for RBDO", Structural and Multidisciplinary Optimization, Vol. 40, No.1, 2010, pp.35-51. DOI: http://dx.doi.org/10.1007/s00158-009-0385-1
S.-Y. Baik, B.-G., Lee, "A Study on Reliability Design of Fracture Mechanics Method Using FEM", Journal of the Korea Academia-Industrial cooperation Society, Vol. 16, No. 7, pp.4398-4404, 2015.
H. Akaike, "A New Look at the Statistical Model Identification", IEEE Transactions on Automatic Control, Vol.19, No.6, pp. 716-723, 1974. DOI: http://dx.doi.org/10.1109/TAC.1974.1100705
N. Sugiura, Further Analysts of the Data by Akaike's Information Criterion and the Finite Corrections", Communications in Statistics-Theory and Methods, Vol. 7, No. 1, 1978, pp. 13-26. DOI: http://dx.doi.org/10.1080/03610927808827599
D. F. Findley, "Counter examples to Parsimony and BIC", Annals of the Institute of Statistical Mathematics, Vol. 43, No. 3, 1991, pp. 505-514. DOI: http://dx.doi.org/10.1007/BF00053369
J. P. Piper, The Fatigue Properties of Formable Hot Rolled Strip Steels, Ph.D. Thesis, Univ. of Woolongong, 1993.
P. Hess, D. Bruchman, I. Asskkaf, B. M. Ayyub, "Uncertainties in Material Strength, Geometric, and Load Variables", Naval Engineers Journal, Vol. 114, No. 2, 2002, pp. 139-166. DOI: http://dx.doi.org/10.1111/j.1559-3584.2002.tb00128.x