A saddlepoint approximation based simulation method for uncertainty analysis

International Journal of Reliability and Safety

Volumn 1, Issue 1-2, 2006, Pages 206-224

  Huang, Beiqing ^a   Du, Xiaoping ^a   Lakshminarayana, Ramaprasad E ^a  

^a Architectural and Environmental Engineering   (United States)

Author keywords

cumulant generating function (cgf); Monte Carlo Simulation (MCS); reliability analysis; Saddlepoint Approximation (SPA); uncertainty analysis

Indexed keywords

EID: 84885432017     PISSN: 1479389X     EISSN: 14793903     Source Type: Journal    
DOI: 10.1504/ijrs.2006.010698     Document Type: Article

References (39)

1. Adhikari, S. and Langley, R.S. (2002) ‘Reduction of random variables in structural reliability analysis’, Third International Conference on Mathematical Methods in Reliability Methodology and Practice, Trondheim, Norway.
2. Breitung, K. (1984) ‘Asymptotic approximations for multinomial integrals’, Journal of Engineering Mechanics, Vol. 110, No. 3, pp.357–366.
3. Canty, A.J. and Davison, A.C. (1996) ‘Implementation of saddlepoint approximations to bootstrap distribution’, Proceedings of the 28th Symposium on the Interface, Computer Science and Statistics, pp.248–253.
4. Daniel, H.E. (1987) ‘Tail probability approximations’, International Statistical Review, Vol. 55, No. 1, pp.37–48.
5. Daniels, H.E. (1954) ‘Saddlepoint approximations in statistics’, Annals of Mathematical Statistics, Vol. 25, pp.631–650.
6. Dey, A. and Mahadevan, S. (1998) ‘Ductile structural system reliability analysis using adaptive importance sampling’, Structural Safety, Vol. 20, No. 2, pp.137–154.
7. Ding, K., Zhou, Z. and Liu, C. (1998) ‘Latin hypercube sampling used in the calculation of the fracture probability’, Reliability Engineering and System Safety, Vol. 59, No. 2, pp.239–242.
8. Du, X. and Chen, W. (2000) ‘Towards a better understanding of modeling feasibility robustness in engineering design’, ASME Journal of Mechanical Design, Vol. 122, No. 4, pp.385–394.
9. Du, X. and Chen, W. (2001) ‘A most probable point based method for uncertainty analysis’, Journal of Design and Manufacturing Automation, Vol. 4, No. 1, pp.47–66.
10. Du, X. and Sudjianto, A. (2004) ‘The first order saddlepoint approximation for reliability analysis’, AIAA Journal, Vol. 42, No. 6, pp.1199–1207.
11. Du, X., Sudjianto, A. and Chen, W. (2004) ‘An integrated framework for optimization under uncertainty using inverse reliability strategy’, ASME Journal of Mechanical Design, Vol. 126, No. 4, pp.562–570.
12. Fisher, R.A. (1928) ‘Moments and product moments of sampling distribution’, Proceeding of London Mathematical Society, Vol. 30, No. 2, pp.199–238.
13. Gatto, R. and Ronchetti, E. (1996) ‘General saddlepoint approximations of marginal densities and tail probabilities’, Journal of the American Statistical Association, Vol. 91, No. 433, pp.666–673.
14. Goutis, C. and Casella, G. (1999) ‘Explaining the saddlepoint approximation’, The American Statistician, Vol. 53, No. 3, pp.216–224.
15. Haldar, A. and Mahadevan, S. (2000) Probability, Reliability, and Statistical Methods in Engineering Design, John Wiley and Sons.
16. Helton, J.L. and Davis, F.J. (2003) ‘Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems’, Reliability Engineering and System Safety, Vol. 81, pp.23–69.
17. Hohenbichler, M., Gollwitzer, S., Kruse, W. and Rackwitz, R. (1987) ‘New light on first- and second-order reliability methods’, Structural Safety, Vol. 4, pp.267–284.
18. Huzurbazar, S. (1999) ‘Practical saddlepoint approximations’, The American Statistician, Vol. 53, No. 3, pp.225–232.
19. Isukapalli, S.S., Roy, A. and Georgopoulos, P.G. (1998) ‘Stochastic response surface methods (SRSMs) for uncertainty progagation: application to environmental and biological system’, Risk Analysis, Vol. 18, No. 3, pp.351–363.
20. Jensen, J.L. (1995) Saddlepoint Approximations, Oxford: Clarendon Press.
21. Jin, R., Du, X. and Chen, W. (2003) ‘The use of metamodeling techniques for design under uncertainty’, Structural and Multidisciplinary Optimization, Vol. 25, pp.99–116.
22. Kendall, M.G. and Stuart, A. (1958) The Advanced Theory of Statistics Volume 1: Distribution Theory, London: Charles Griffin and Company Ltd.
23. Kolassa, J.E. (1991) ‘Saddlepoint approximations in the case of intractable cumulant generating functions’, Selected Proceedings of the Sheffield Symposium on Applied Probability, Institute of Mathematical Statistics, Hayward, CA, pp.236–255.
24. Kuonen, D. (2001) ‘Computer-intensive statistical methods: saddlepoint approximations with applications in bootstrap and robust inference’, PhD Thesis, Swiss Federal Institute of Technology.
25. Lugannani, R. and Rice, S.O. (1980) ‘Saddlepoint approximation for the distribution of the sum of independent random variables’, Advances in Applied Probability, Vol. 12, pp.475–490.
26. Mckay, M.D., Conover, W.J. and Beckman, R.J. (1979) ‘A comparison of three methods for selecting values of input variables in the analysis of output from a computer code’, Technometrics, Vol. 21, No. 2, pp.239–245.
27. Moarefzadeh, M.R. and Melchers, R.E. (1999) ‘Directional importance sampling for ill-proportioned spaces’, Structural Safety, Vol. 21, No. 1, pp.1–22.
28. Mohanty, S. and Wu, Y-T. (2001) ‘CDF sensitivity analysis technique for ranking influential parameters in the performance assessment of the proposed high-level waste repository at Yucca Mountain, Nevada, USA’, Reliability Engineering and System Safety, Vol. 73, No. 2, pp.167–176.
29. Owen, A. (1997) ‘Monte Carlo variance of scrambled equidistribution quadrature’, SIAM Journal of Numerical Analysis, Vol. 34, No. 5, pp.1884–1910.
30. Rackwitz, R. and Fiessler, B. (1978) ‘Structural reliability under combined random load sequences’, Computer and Structures, Vol. 9, No. 5, pp.489–494.
31. Rubinstein, R.Y. (1981) Simulation and the Monte Carlo Method, New York: Wiley.
32. Seo, H.S. and Kwak, B.M. (2002) ‘Efficient statistical tolerance analysis for general distributions using three-point information’, International Journal of Production Research, Vol. 40, No. 4, pp.931–944.
33. Tvedt, L. (1988) ‘Second order reliability by an exact integral’, Reliability and Optimization of Structural System’88; Proceedings of the Second IFIP WG7.5 Conference, London, UK, pp.377–384.
34. Wang, S. (1992) ‘General saddlepoint approximations in the bootstrap’, Statistics and Probability Letters, Vol. 13, pp.61–66.
35. Wojtkiewicz, S.F., Spencer Jr., B.F. and Bergman, L.A. (1996) ‘On the Cumulant-neglect closure method in stochastic dynamics’, International Journal of Non-linear Mechanics, Vol. 31, No. 5, pp.657–684.
36. Wu, W.F. and Lin, Y.K. (1984) ‘Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations’, International Journal of Non-linear Mechanics, Vol. 19, No. 4, pp.349–362.
37. Wu, Y-T. (1998) ‘Methods for efficient probabilistic analysis of systems with large number of random variables’, Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, MO, USA: St. Louis.
38. Zhao, Y.G., Alfredo, H.S. and Ang, H.M. (2003) ‘System reliability assessment by method of moments’, ASCE Journal of Structural Engineering, Vol. 129, No. 10, pp.1341–1349.
39. Zou, Z., Mourelatos, Z., Mahadevan, S. and Tu, J. (2003) ‘An indicator response surface-based Monte Carlo method for efficient component and system reliability analysis’, Proceedings of ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, IL.