Browse > Article
http://dx.doi.org/10.12989/sem.2008.28.3.263

Cubic normal distribution and its significance in structural reliability  

Zhao, Yan-Gang (Department of Architecture and Civil Engineering, Nagoya Institute of Technology)
Lu, Zhao-Hui (Department of Architecture and Civil Engineering, Nagoya Institute of Technology)
Publication Information
Structural Engineering and Mechanics / v.28, no.3, 2008 , pp. 263-280 More about this Journal
Abstract
Information on the distribution of the basic random variable is essential for the accurate analysis of structural reliability. The usual method for determining the distributions is to fit a candidate distribution to the histogram of available statistical data of the variable and perform approximate goodness-of-fit tests. Generally, such candidate distribution would have parameters that may be evaluated from the statistical moments of the statistical data. In the present paper, a cubic normal distribution, whose parameters are determined using the first four moments of available sample data, is investigated. A parameter table based on the first four moments, which simplifies parameter estimation, is given. The simplicity, generality, flexibility and advantages of this distribution in statistical data analysis and its significance in structural reliability evaluation are discussed. Numerical examples are presented to demonstrate these advantages.
Keywords
structural reliability; probability distributions; statistical moments; data fitting, fourth-moment; reliability index;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 Ang, A.H.-S. and Tang, W.H. (1975), Probability Concepts in Engineering Planning and Design. Vol I: Basic Principles, John Wiley & Sons, New York
2 Ono, T., Idota, H. and Kawahara, H. (1986), "A statistical study on resistances of steel columns and beams using higher order moments", J. Struct. Constr. Eng., AIJ, Tokyo, 370, 19-37. (in Japanese)
3 Schueller, G.I. (2007), "On procedures for reliability assessment of mechanical systems and structures", Struct. Eng. Mech., 25(3), 275-289   DOI   ScienceOn
4 Johnson, N.L. and Kotz, S. (1970), Continuous Univariate Distributions-1, John Wiley & Sons, New York
5 Lind, N.C. and Chen, X. (1986), "Consistent distribution parameter estimation for reliability analysis", Struct. Saf., 4(2), 141-149   DOI   ScienceOn
6 Lind, N.C. and Nowak, A.S. (1988), "Pooling expert opinions on probability distribution", J. Engng. Mech., ASCE, 114(2), 328-341   DOI
7 MacGregor, J.G. (1988), Reinforced Concrete Mechanics and Design. Prentice-Hall, Englewood Cliffs, NJ
8 Nadarajah, S. and Kotz, S. (2006), "The beta exponential distribution", Reliab. Eng. Syst. Saf., 91(6), 689-697   DOI   ScienceOn
9 Der Kiureghian, A. (2001), "Analysis of structural reliability under model and statistical uncertainties: A Bayesian approach", Comput. Struct. Eng., 1(2), 81-87
10 Fleishman, A.L. (1978), "A method for simulating non-normal distributions", Psychometrika, 43(4), 521-532   DOI
11 Grigoriu, M. (1983), "Approximate analysis of complex reliability problems", Struct. Saf., 1(4), 277-288   DOI   ScienceOn
12 Hong, H.P. and Lind, N.C. (1996), "Approximation reliability analysis using normal polynomial and simulation results", Struct. Saf., 18(4), 329-339   DOI   ScienceOn
13 Zhao, Y.G., Ono, T. and Kiyoshi, I. (2002), "Monte Carlo simulation using moments of random variables", J. Asian Archi. Build. Eng., 1(1), 13-20   DOI
14 Zong, Z. and Lam, K.Y. (1998), "Estimation of complicated distributions using B-spline functions", Struct. Saf., 20(4), 341-355   DOI   ScienceOn
15 Chen, X. and Tung, Y.K. (2003), "Investigation of polynomial normal transformation", Struct. Saf., 25(4), 423-445   DOI   ScienceOn
16 Ramberg, J. and Schmeiser, B. (1974), "An approximate method for generating asymmetric random variables", Comm. ACM, 17(2), 78-82   DOI   ScienceOn
17 Stuart, A. and Ord, J.K. (1987), Kendall's Advanced Theory of Statistics, Vol.1, Charles Griffin & Company Ltd., London
18 Tichy, M. (1993), Applied Methods of Structural Reliability, Kluwer academic publishers, Dordrecht/Boston/ London
19 Wolfram, S. (1999), The Mathematica Book, 4th edition, Wolfram Media/Cambridge University Press
20 Xie, M., Tang, Y. and Goh, T.N. (2002) "A modified Weibull extension with bathtub-shaped failure rate function", Reliab. Eng. Syst. Saf., 76(3), 279-285   DOI   ScienceOn
21 Zhao, Y.G. and Ang, A.H.-S. (2002), "Three-Parameter Gamma distribution and its significance in structure", Comput. Struct. Eng., 2(1), 1-10
22 Zhao, Y.G. and Ono, T. (2000), "New point estimates for probability moments", J. Eng. Mech., ASCE, 126(4), 433-436   DOI   ScienceOn
23 Zhao, Y.G. and Ono, T. (2004), "On the problems of the fourth moment method", Struct. Saf., 26(3), 343-347   DOI   ScienceOn
24 Zhao, Y.G. and Lu, Z.H. (2007), "Fourth moment standardization for structural reliability assessment", J. Struct. Eng., ASCE, 133(7), 916-924   DOI   ScienceOn
25 Zong, Z. and Lam, K.Y. (2000), "Bayesian estimation of complicated distributions", Struct. Saf., 22(1), 81-95   DOI   ScienceOn
26 Zong, Z. and Lam, K.Y. (2001), "Bayesian estimation of 2-dimensional complicated distributions", Struct. Saf., 23(2), 105-121   DOI   ScienceOn