Application of bootstrap method in conservative estimation of reliability with limited samples

Structural and Multidisciplinary Optimization

Volumn 41, Issue 2, 2010, Pages 205-217

  Picheny, Victor ^a   Kim, Nam Ho ^a   Haftka, Raphael T ^a  

^a University of Florida   (United States)

Author keywords

Bootstrap method; Conservative estimation; Probability of failure; Reliability

Indexed keywords

ACCURATE ESTIMATION; BOOTSTRAP APPROACH; BOOTSTRAP METHOD; COMPOSITE PANELS; ESTIMATION METHODS; LOG-NORMAL DISTRIBUTION; LOW PROBABILITY; PROBABILITY OF FAILURE; RELIABILITY BASED OPTIMIZATION; SAMPLE SIZES; SMALL SAMPLE SIZE; SYSTEM RESPONSE; THERMAL LOADINGS;

ESTIMATION; RELIABILITY; SAMPLING;

PROBABILITY;

EID: 77649339915     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-009-0419-8     Document Type: Article

References (25)

1. Acar E, Haftka RT (2005) The effects of uncertainty control measures on the weight saving from composite laminates at cryogenic temperatures. In: ASME-IDECT-2005, Long Beach, California, 24-28 September
2. Ben-Haim Y, Elishakoff I (1990) Convex models of uncertainty in applied mechanics. Elsevier, Amsterdam
3. Chernick MR (1999) Bootstrap methods, a practitioner's guide (Wiley series in probability and statistics). A Wiley-Interscience publication
4. Choi KK, Du L, Youn BD, Gorsich D (2005) Possibility-based design optimization method for design problems with both statistical and fuzzy input data. In: 6th world congress on structural and multidisciplinary optimization, 30 May-3 June
5. Du X, Sudjianto A, Huang B (2005) Reliability-based design under the mixture of random variables. ASME J Mech Des 127(6):1068-1076
6. Du L, Choi KK, Youn BD, Gorsich D (2006) Possibility-based design optimization method for design problems with both statistical and fuzzy input data. ASME J Mech Des 128(4):928-935 (Pubitemid 44123182)
7. Efron B (1982) The jackknife, the bootstrap, and other resampling plans. SIAM, Philadelphia
8. Enevoldsen I, Sørensen J (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169-196
9. Engelund S, Rackwitz R (1993) A benchmark study on importance sampling techniques in structural reliability. Struct Saf 12:255-276
10. Elishakoff IE (1990) An idea on the uncertainty triangle. Shock Vibr Dig 22(1):1-2
11. Haldar A, Mahadevan S (2000) Probability, reliability and statistical methods in engineering design. Wiley, New York
12. Holton GA (2003) Value-at-risk: theory and practice. Academic, New York
13. Kenney JF, Keeping ES (1951) Mathematics of statistics, 2nd edn. Van Nostrand, Princeton
14. Kim NH, Ramu P, Queipo NV (2006) Tail modeling in reliability-based design optimization for highly safe structural systems. In: 47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference
15. Kwon YW, Berner JM (1997) Matrix damage of fibrous composites: effect of thermal residual stresses and layer sequences. Comput Struct 64(1-4):375-382
16. Lee JO, Yang YS, Ruy WS (2002) A comparative study on reliabilityindex and target-performance-based probabilistic structural design optimization. Comput Struct 80(3-4):257-269
17. Melchers RE (1999) Structural reliability analysis and prediction, 2nd edn. Wiley, New York
18. Neal DM, Matthews WT, Vangel MG (1991) Uncertainty in obtaining high reliability fro stress-strength models. In: 9th DOD-/ NASA/FAA conference on fibrous composites in structural design, vol 1. Dept. of Defense, Lake Tahoe, NV, pp 503-521
19. Nikolaidis E, Cudney HH, Chen S, Haftka RT, Rosca R (2004) Comparison of probability and possibility for design against catastrophic failure under uncertainty. ASME J Mech Des 126: 386-394
20. Qu X, Haftka RT (2004) Reliability-based design optimization using probability sufficiency factor. Struct Multidisc Optim 27(5):314-325
21. Qu X, Haftka RT, Venkataraman S, Johnson T (2003) Deterministic and reliability-based optimization of composite laminates for propeller tanks. AIAA J 41(10):2029-2036
22. Rackwitz R (2000) Reliability analysis-past, present and future. In: 8th ASCE specialty conference on probabilistic mechanics and structural reliability, South Bend, IN, USA, PMC 2000-RRR
23. Smarslok BP, Alexander D, Haftka RT, Carraro L, Ginsbourger D (2008) Separable Monte Carlo applied to laminated composite plates reliability. In: 49th AIAA/ASME/ ASCE/AHS/ASC structures, structural dynamics, and materials conference, Schaumburg, Illinois
24. Starnes JH Jr, Haftka RT (1979) Preliminary design of composite wings for bucking, stress and displacement constraints. J Aircr 16:564-570
25. Youn BD, Wang P (2007) Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method. Structural multidisciplinary optimization. Springer, Heidelberg