Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation

Reliability Engineering and System Safety

Volumn 93, Issue 2, 2008, Pages 325-336

  Huang, Beiqing ^a   Du, Xiaoping ^a  

^a University of Missouri Rolla   (United States)

Author keywords

Cumulant generating function; Saddlepoint Approximation; Uncertainty analysis

Indexed keywords

APPROXIMATION THEORY; DISTRIBUTION FUNCTIONS; ITERATIVE METHODS; PROBABILISTIC LOGICS; RANDOM VARIABLES;

CUMULANT GENERATING FUNCTION; ITERATIVE SEARCH PROCESS; SADDLEPOINT APPROXIMATION; TAYLOR EXPANSION;

UNCERTAINTY ANALYSIS;

EID: 34848840902     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2006.10.021     Document Type: Article

References (51)

1. Apostolakis G. The concept of probability in safety assessments of technological systems. Science 250 4986 (1990) 1359-1364
2. Haldar A., and Mahadevan S. Probability, reliability, and statistical methods in engineering design (2001), Wiley
3. Du X., and Chen W. Towards a better understanding of modeling feasibility robustness in engineering design. ASME J Mech Design 122 4 (2000) 385-394
4. Mailhot A., and Villeneuve J.-P. Mean-value second-order uncertainty analysis method: application to water quality modeling. Adv Water Resour 26 5 (2003) 491-499
5. Seo H.S., and Kwak B.M. Efficient statistical tolerance analysis for general distributions using three-point information. Int J Prod Res 40 4 (2002) 931-944
6. Putko M.M., Newman P.A., Taylor AC I.I.I., and Green L.L. Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives. ASME J Fluids Eng 124 1 (2002) 60-69
7. Nikolaidis E., Chen S., Cudney H., Hatftka R.T., and Rosca R. Comparison of probability and possibility for design against catastrophic failure under uncertainty. ASME J Mech Design 126 3 (2004) 386-394
8. Youn B.D., and Choi K.K. An investigation of nonlinearity of reliability-based design optimization approaches. ASME J Mech Design 126 3 (2004) 403-411
9. Wu Y-T, Shin Y, Sues R, Cesare M. Safety-factor based approach for probabilistic-based design optimization. In: 42nd AIAA/ASME/ASCE/AHS/ASC Structures, structural dynamics and material conference and exhibit. Seattle, Washington, 2001.
10. Du X., Sudjianto A., and Chen W. An integrated framework for optimization under uncertainty using inverse reliability strategy. ASME J Mech Design 124 4 (2004) 562-570
11. Taguchi G. Taguchi on robust technology development: bringing quality engineering upstream (1993), ASME, New York
12. Du X., and Chen W. Sequential optimization and reliability assessment for probabilistic design. ASME J Mech Design 126 2 (2004) 225-233
13. Creveling C.M., Slutsky J.L., and Antis D. Design for six sigma: in technology and product development (2003), Prentice Hall, New Jersey
14. Helton J.C. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. J Statist Comput Simul 57 1-4 (1997) 3-76
15. Rowe W.D. Understanding uncertainty. Risk Anal 14 5 (1994) 743-750
16. van Asselt M.B.A., and Rotmans J. Uncertainty in integrated assessment modeling. Climatic Change 54 1 (2002) 75-105
17. Regan H.M., Colyvan M., and Burgman M.A. A taxonomy and treatment of uncertainty for ecology and conservation biology. Ecol Appl 12 2 (2002) 618-628
18. Helton J.C., Johnson J.D., and Oberkampf W.L. An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliab Eng Syst Safety 85 1-3 (2004) 39-71
19. Helton J.C. Treatment of uncertainty in performance assessments for complex systems. Risk Anal 14 4 (1994) 483-511
20. Hoffman F.O., and Hammonds J.S. Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Anal 14 5 (1994) 707-712
21. Parry G.W., and Winter P.W. Characterization and evaluation of uncertainty in probabilistic risk analysis. Nucl Safety 22 1 (1981) 28-42
22. Paté-Cornell M.E. Uncertainties in risk analysis: six levels of treatment. Reliab Eng Syst Safety 54 2-3 (1996) 95-111
23. Ding K., Zhou Z., and Liu C. Latin hypercube sampling used in the calculation of the fracture probability. Reliab Eng Syst Safety 59 (1998) 239-242
24. Helton J.C., and Davis F.J. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Safety 81 (2003) 23-69
25. Moarefzadeh M.R., and Melchers R.E. Directional importance sampling for ill-proportioned spaces. Struct Safety 21 1 (1999) 1-22
26. Dey A., and Mahadevan S. Ductile structural system reliability analysis using adaptive importance sampling. Struct Safety 20 2 (1998) 137-154
27. Mckay M.D., Conover W.J., and Beckman R.J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21 2 (1979) 239-245
28. Youn B.D., and Choi K.K. Selecting probabilistic approaches for reliability-based design optimization. AIAA J 42 1 (2004) 124-131
29. Hasofer A.M., and Lind N.C. Exact and invariant second-moment code format. ASCE J Eng Mech Division 100 EM1 (1974) 111-121
30. Zhao Y.G., Alfredo H.S., and Ang H.M. System reliability assessment by method of moments. ASCE J Struct Eng 129 10 (2003) 1341-1349
31. Wang L, Beeson D, Wiggs G. Efficient and accurate point estimate method for moments and probability distribution. In: 10th AIAA/ISSMO Multidisciplinary analysis and optimization conference. Albany, New York, 2004.
32. Breitung K. Asymptotic approximations for multinomial integrals. J Eng Mech 110 3 (1984) 357-367
33. Hohenbichler M., Gollwitzer S., Kruse W., and Rackwitz R. New light on first- and second-order reliability methods. Struct Safety 4 (1987) 267-284
34. Du X., and Sudjianto A. First order saddlepoint approximation for reliability analysis. AIAA J 42 6 (2004) 1199-1207
35. Daniels H.E. Saddlepoint approximations in statistics. Ann Math Statist 25 (1954) 631-650
36. Dennis J.E., and Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations (1983), Prentice-Hall, Englewood Cliffs
37. Rosenblatt M. Remarks on a multivariate transformation. Ann Math Statist 23 (1952) 470-472
38. Thoft-Christensen P., and Baker M.J. Structural reliability theory and its application (1982), Springer, Berlin Heidelberg, New York
39. Bain LJ, Engelhardt M. Introduction to probability and mathematical statistics (Duxbury classic series), 2nd ed. Thomson Learning; 1991.
40. Johnson N.L., and Kotz S. Continuous univariate distributions-2 (1970), Wiley, New York
41. Jensen J.L. Saddlepoint approximations (1995), Clarendon Press, Oxford
42. Wang S. General saddlepoint approximations in the bootstrap. Statist Probab Lett 13 (1992) 61-66
43. Kuonen D. Computer-intensive statistical methods: saddlepoint approximations with applications in bootstrap and robust inference. PhD thesis, Swiss Federal Institute of Technology, 2001.
44. Reid N. Saddlepoint methods and statistical inference (with discussion). Statist Sci 3 (1988) 213-238
45. Gouits C., and Casella G. Explaining the saddlepoint approximation. Am Statist 53 3 (1999) 216-224
46. Huzurbazar S. Practical saddlepoint approximations. Am Statist 53 3 (1999) 225-232
47. Gatto R., and Ronchetti E. General saddlepoint approximations of marginal densities and tail probabilities. J Am Statist Assoc 91 433 (1996) 666-673
48. Lugannani R., and Rice S.O. Saddlepoint approximation for the distribution of the sum of independent random variables. Adv Appl Probab 12 (1980) 475-490
49. Sciuva M.D., and Lomario D. A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure. Compos Struct 59 (2003) 155-162
50. Wu Y.-T., Millwater H.R., and Cruse T.A. Advanced probabilistic structural analysis method for implicit performance functions. AIAA J 28 9 (1990) 1663-1669
51. Wu Y.-T. Computational methods for efficient structural reliability and reliability Sensitivity analysis. AIAA J 32 8 (1994) 1717-1723