Multilevel design of experiments for statistical moment and probability calculation

Structural and Multidisciplinary Optimization

Volumn 37, Issue 1, 2008, Pages 57-70

  Lee, S H ^a   Choi, H S ^b   Kwak, B M ^c  

^a Northwestern University   (United States)

^b Agency for Defence Development   (South Korea)

^c Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Design of experiments; Numerical integration; Pearson system; Statistical moment; Structural reliability

Indexed keywords

DENSITY (OPTICAL); DESIGN; DESIGN OF EXPERIMENTS; DIFFRACTIVE OPTICAL ELEMENTS; EXPERIMENTS; FRUITS; IMAGE SEGMENTATION; INTEGRATION; METHOD OF MOMENTS; NUMERICAL ANALYSIS; OPTICAL PROPERTIES; PROBABILITY; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; RELIABILITY ANALYSIS; STATISTICS;

ANALYSIS METHODS; EMPIRICAL DISTRIBUTIONS; FACTORIAL DESIGNS; NUMERICAL INTEGRATION; OPTIMAL LEVELS; PEARSON SYSTEM; PEARSON SYSTEMS; PROBABILITY CALCULATIONS; STATISTICAL MOMENT; STATISTICAL MOMENTS; STRUCTURAL RELIABILITY; SYSTEM RESPONSE FUNCTIONS;

RELIABILITY;

EID: 55849083116     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0215-2     Document Type: Article

References (24)

1. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions, 10th edn. Dover, New York
2. Creveling CM (1997) Tolerance design, a handbook for developing optimal specifications. Addison-Wesley, Reading
3. JR D'Errico NA Zaino 1988 Statistical tolerancing using a modification of Taguchi's method Technometrics 30 397 405
4. Engels H (1980) Numerical quadrature and qubature. Academic, New York
5. DH Evans 1967 An application of numerical integration techniques to statistical tolerancing Technometrics 9 441 456
6. T Gerstner M Griebel 1998 Numerical integration using sparse grids Numer Algorithms 18 209 232
7. Ghanem RG, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer, Berlin Heidelberg New York
8. Hahn GJ, Shapiro SS (1967) Statistical models in engineering. Wiley, New York
9. AM Hasofer NC Lind 1974 Exact and invariant second-moment code format J Eng Mech ASCE 100 111 121
10. M Hohenbichler R Rackwitz 1981 Nonnormal dependent vectors in structural reliability J Eng Mech ASCE 107 1127 238
11. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, 2nd edn. Wiley, New York
12. AD Kiureghian 1996 Structural reliability methods for seismic safety assessment: a review Eng Struct 18 412 424
13. AD Kiureghian T Dakessian 1998 Multiple design points in first and second-order reliability Struct Saf 20 37 49
14. Kleiber M, Hien TD (1992) The stochastic finite element method. Wiley, Chichester
15. Krylov VI (1962) Approximate calculation of integrals. Macmillan, New York (translated by Stroud AH)
16. SH Lee BM Kwak 2006 Response surface augmented moment method for efficient reliability analysis Struct Saf 28 261 272
17. Madsen HO, Krenk S, Lind NC (2006) Methods of structural safety. Dover, Mineola, NY
18. R Rackwitz B Fiessler 1978 Structural reliability under combined random load sequences Comput Struct 9 489 494
19. HS Seo BM Kwak 2002 Efficient statistical tolerance analysis for general distributions using three-point information Int J Prod Res 40 931 944
20. Stoer J, Bulirsch R (2002) Introduction to numerical analysis, 3rd edn. Springer, Berlin Heidelberg New York
21. G Taguchi 1978 Performance analysis design Int J Prod Res 16 521 530
22. T-Christensen P, Baker MJ (1982) Structural reliability theory and its application. Springer, Berlin Heidelberg New York
23. CC Wu Z Chen GR Tang 1998 Component tolerance design for minimum quality loss and manufacturing cost Comput Ind 35 223 232
24. H Xu S Rahman 2004 A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics Int J Numer Methods Eng 61 1992 2019