Reliability sensitivity analysis with random and interval variables

International Journal for Numerical Methods in Engineering

Volumn 78, Issue 13, 2009, Pages 1585-1617

  Guo, Jia ^a   Du, Xiaoping ^a  

^a University of Missouri Rolla   (United States)

Author keywords

Intervals; Reliability; Sensitivity analysis

Indexed keywords

DISTRIBUTION PARAMETERS; ENGINEERING APPLICATIONS; FIRST ORDER RELIABILITY METHODS; FUNCTION CALLS; INTERVAL VARIABLE; INTERVALS; RELIABILITY BASED DESIGN; RELIABILITY SENSITIVITY; SENSITIVITY INDICES; UNCERTAIN VARIABLES;

QUALITY ASSURANCE; RANDOM PROCESSES; RANDOM VARIABLES; SENSITIVITY ANALYSIS;

RELIABILITY ANALYSIS;

EID: 67649554284     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2543     Document Type: Article

References (46)

1. Du X, Sudjianto A. The first order saddlepoint approximation for reliability analysis. AIAA Journal 2004; 42(6):1199-1207.
2. Melchers RE. Structural Reliability Analysis and Prediction. Wiley: New York, 1999.
3. Huang HZ. Reliability analysis method in the presence of fuzziness attached to operating time. Microelectronics Reliability 1995; 35(12):1483-1487.
4. Du X, Sudjianto A, Huang B. Reliability-based design under the mixture of random and interval variables. Journal of Mechanical Design (ASME) 2005; 127(6):1068-1076.
5. Liang J, Mourelatos ZP, Tu J. A single-loop method for reliability-based design optimisation. International Journal of Product Development 2008; 5(1/2):76-92.
6. Huang HZ, Tian ZG, Zuo MJ. Intelligent interactive multiobjective optimization method and its application to reliability optimization. IIE Transactions 2005; 37(11):983-993.
7. Wang L, Grandhi RV, Hopkins DA. Structural reliability optimization using an efficient safety index calculation procedure. International Journal for Numerical Methods in Engineering 1995; 38(10):1721-1738.
8. Turanyi T. Sensitivity analysis of complex kinetic systems: tools and applications. Journal of Mathematic Chemistry 1990; 5(3):203-248.
9. Cacuci DG. Sensitivity and Uncertainty Analysis, Volume 1: Theory. CRC Press: Boca Raton, FL, 2003.
10. Saltelli A, Chan K, Scott EM. Sensitivity Analysis. Wiley: New York, 2000.
11. Wu YT. Computational methods for efficient structural reliability and reliability sensitivity analysis. AIAA Journal 1994; 32(8):1717-1723.
12. Mohanty S, Wu YT. CDF sensitivity analysis technique for ranking influential parameters in the performance assessment of the proposed high-level waste repository at Yucca Mountain, Nevada, U.S.A. Reliability Engineering and System Safety 2001; 73:167-176.
13. Mavris D, Roth B, Macsotai N. A method for probabilistic sensitivity analysis of commercial aircraft engines. Presented at the 14th ISABE, Florence, Italy, 1999.
14. Kern D, Du X, Sudjianto A. Forecasting manufacturing quality during design using process capability data. Proceedings of the IMECE '03, ASME 2003 International Mechanical Engineering Congress and Exposition, Washington, DC, 2003.
15. Liu H, Chen W, Sudjianto A. Relative entropy based method for probabilistic sensitivity analysis in engineering design. Journal of Mechanical Design (ASME) 2006; 128(2):326-336.
16. Ferson S, Joslyn CA, Helton JC, Oberkampf WL, Sentz K. Summary from the epistemic uncertainty workshop: consensus amid diversity. Reliability Engineering and System Safety 2004; 85(1-3):355-369.
17. Helton JC, Johnson JD, Oberkampf WL. An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliability Engineering and System Safety 2004; 85(1-3):39-71.
18. Bayarri MJ, Berger JO, Higdon D, Kennedy MC, Kottas A, Paulo R, Sacks J, Cafeo JA, Cavendish J, Lin CH, Tu J. A framework for validation of computer models. Foundations for Verification and Validation in the 21st Century Workshop, John Hopkins University/Applied Physics Laboratory, Laurel, MD, 2000.
19. Bae H-R, Grandhi RV, Canfield RA. Epistemic uncertainty quantification techniques including evidence theory for large-scale structures. Computers and Structures 2004; 82(13-14):1101-1112.
20. Gu X, Renaud JE, Batill SM. An investigation of multidisciplinary design subject to uncertainties. Seventh AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis and Optimization Symposium, St. Louis, MO, 1998; 309-319.
21. Du X, Chen W. An integrated methodology for uncertainty propagation and management in simulation-based systems design. AIAA Journal 2000; 38(8):1471-1478.
22. Rao SS, Cao L. Optimum design of mechanical systems involving interval parameters. Journal of Mechanical Design (ASME) 2002; 124(3):465-472.
23. Pownuk A. Efficient method of solution of large scale engineering problems with interval parameters. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 2004; 3015-3016.
24. Modares M, Mullen R, Muhanna RL, Zhang H. Buckling analysis of structures with uncertain properties and loads using an interval finite element method. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 2004; 317-328.
25. Pereira SC, Mello UT, Ebecken NMAD, Muhanna RL. Uncertainty in thermal basin modeling: an interval finite element approach. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 2004; 371-390.
26. Wang Y. Solving interval constraints in computer-aided design. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 15-17 September 2004; 251-267.
27. Hall J, Lawry J. Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis. Second International Symposium on Imprecise Probabilities and their Applications, Ithaca, New York, 2001.
28. Starks SA, Kreinovich V, Longpre L, Ceberio M, Xiang G, Araiza R, Beck J, Kandathi R, Nayak A, Torres R. Towards combining probabilistic and interval uncertainty in engineering calculations. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 2004; 193-213.
29. Kreinovich V, Beck J, Ferregut C, Sanchez A, Keller GR, Averill M, Starks SA. Monte-Carlo-type techniques for processing interval uncertainty, and their engineering applications. Proceedings of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, 2004; 139-160.
30. Penmetsa RC, Grandhi RV. Efficient estimation of reliability for problems with uncertain intervals. Computers and Structures 2002; 80(12):1103-1112.
31. Tonon F. Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliability Engineering and System Safety 2004; 85(1-3):169-181.
32. Agarwal H, Renaud JE, Preston EL, Padmanabhan D. Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering and System Safety 2004; 85(1-3):281-294.
33. Fetz T, Oberguggenberger M. Propagation of uncertainty through multivariate functions in the framework of sets of probability measures. Reliability Engineering and System Safety 2004; 85(1-3):73-87.
34. Kreinovich V, Lakeyev A, Rohn J, Kahl P. Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer: Dordrecht, 1997.
35. Bae HR, Grandhi RV, Canfield RA. Uncertainty quantification of structural response using evidence theory. Forty-third AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, 22-25 April 2002.
36. Bae HR, Grandhi RV, Canfield R. Sensitivity analysis of structural response uncertainty propagation using evidence theory. Structural and Multidisciplinary Optimization 2006; 31:270-291.
37. Helton JC, Johnson JD, Oberkampf WL, Sallaberry CJ. Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty. Reliability Engineering and System Safety 2006; 91(10-11):1414-1434.
38. Guo J, Du X. Sensitivity analysis with mixture of epistemic and aleatory uncertainties. AIAA Journal 2007; 45(9):2337-2349.
39. Du X. Unified uncertainty analysis by the first order reliability method. Journal of Mechanical Design (ASME) 2008; 130(9):091401-091410.
40. Hasofer AM, Lind NC. Exact and invariant second-moment code format. Journal of Engineering Mechanics Division (ASCE) 1974; 100(EM1):111-121.
41. Haldar A, Mahadevan S. Probability, Reliability, and Statistical Methods in Engineering Design. Wiley: New York, 2000.
42. Mahadevan S. Physics-based reliability models. In Reliability-based Mechanical Design, Cruse TA (ed.). Dekker: New York, 1997.
43. Der Kiureghian A. First- and second-order reliability methods. In Engineering Design Reliability Handbook, Nikolaidis E, Ghiocel D, Singhl S (eds). CRC Press LLC: Boca Raton, FL, 2005.
44. Du X. Interval reliability analysis. Proceedings of ASME 2007 International Design Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, Nevada, 2007.
45. Budynas RG, Nisbett JK. Shigley's Mechanical Engineering Design. McGraw-Hill: New York, 2006.
46. Ferson S, Tucker WT. Sensitivity in risk analyses with uncertain numbers. SAND Report 2006-2801, Applied Biomathematics, Setauket, New York, 2006.