Advances in System Reliability Analysis Under Uncertainty

Chapter
First Online:

Abstract

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

Keywords

Performance Function System Reliability Direct Monte Carlo Simulation Series System Much Probable Failure Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. Au SK, Beck JL (1999) A new adaptive importance sampling scheme for reliability calculations. Struct Saf 21(2):135–158CrossRefGoogle Scholar
  2. Breitung K (1984) Asymptotic approximations for multinormal integrals. ASCE J Eng Mech 110(3):357–366CrossRefGoogle Scholar
  3. Ditlevsen O (1979) Narrow reliability bounds for structural systems. J Struct Mech 7(4):453–472CrossRefGoogle Scholar
  4. Ferson S, Kreinovich LRGV, Myers DS, Sentz K (2003) Constructing probability boxes and Dempster–Shafer structures. Technical report SAND2002-4015, Sandia National Laboratories, Albuquerque, NMGoogle Scholar
  5. Foo J, Wan X, Karniadakis GE (2008) The multi-element probabilistic collocation method (ME-PCM): error analysis and applications. J Comput Phys 227:9572–9595MathSciNetCrossRefMATHGoogle Scholar
  6. Foo J, Karniadakis GE (2010) Multi-element probabilistic collocation method in high dimensions. J Comput Phys 229:1536–1557MathSciNetCrossRefMATHGoogle Scholar
  7. Fu G, Moses F (1988) Importance sampling in structural system reliability. In: Proceedings of ASCE joint specialty conference on probabilistic methods, Blacksburg, VA, pp 340–343Google Scholar
  8. Ganapathysubramanian B, Zabaras N (2007) Sparse grid collocation schemes for stochastic natural convection problems. J Comput Phys 225(1):652–685MathSciNetCrossRefMATHGoogle Scholar
  9. Ghanem RG, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer, New YorkCrossRefMATHGoogle Scholar
  10. Grestner T, Griebel M (2003) Dimension-adaptive tensor-product quadrature. Computing 71(1):65–87MathSciNetCrossRefGoogle Scholar
  11. Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New YorkGoogle Scholar
  12. Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. ASCE J Eng Mech Div 100(1):111–121Google Scholar
  13. Hu C, Youn BD (2011) An asymmetric dimension-adaptive tensor-product method for reliability analysis. Struct Saf 33(3):218–231MathSciNetCrossRefGoogle Scholar
  14. Hurtado JE (2007) Filtered importance sampling with support vector margin: a powerful method for structural reliability analysis. Struct Saf 29(1):2–15CrossRefGoogle Scholar
  15. Karamchandani A (1987) Structural system reliability analysis methods. Report no. 83, John A. Blume Earthquake Engineering Center, Stanford University, Stanford, CAGoogle Scholar
  16. Klimke A (2006) Uncertainty modeling using fuzzy arithmetic and sparse grids. PhD thesis, Universität Stuttgart, Shaker Verlag, AachenGoogle Scholar
  17. Lee CY (1959) Representation of switching circuits by binary-decision programs. Bell Syst Tech J 38:985–999CrossRefGoogle Scholar
  18. Liang JH, Mourelatos ZP, Nikolaidis E (2007) A single-loop approach for system reliability-based design optimization. ASME J Mech Des 126(2):1215–1224CrossRefGoogle Scholar
  19. Mahadevan S, Raghothamachar P (2000) Adaptive simulation for system reliability analysis of large structures. Comput Struct 77(6):725–734CrossRefGoogle Scholar
  20. Möller B, Beer M (2004) Fuzzy randomness: uncertainty in civil engineering and computational mechanics. Springer, BerlinCrossRefGoogle Scholar
  21. Naess A, Leira BJ, Batsevych O (2009) System reliability analysis by enhanced Monte Carlo simulation. Struct Saf 31(5):349–355CrossRefGoogle Scholar
  22. Nguyen TH, Song J, Paulino GH (2010) Single-loop system reliability-based design optimization using matrix-based system reliability method: theory and applications. ASME J Mech Des 132(1):011005(11)CrossRefGoogle Scholar
  23. Rahman S, Xu H (2004) A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Prob Eng Mech 19:393–408CrossRefGoogle Scholar
  24. Ramachandran K (2004) System reliability bounds: a new look with improvements. Civil Eng Environ Syst 21(4):265–278CrossRefGoogle Scholar
  25. Rubinstein RY (1981) Simulation and the Monte Carlo method. Wiley, New YorkCrossRefMATHGoogle Scholar
  26. Smolyak S (1963) Quadrature and interpolation formulas for tensor product of certain classes of functions. Sov Math Doklady 4:240–243Google Scholar
  27. Song J, Der Kiureghian A (2003) Bounds on systems reliability by linear programming. J Eng Mech 129(6):627–636CrossRefGoogle Scholar
  28. Swiler LP, Giunta AA (2007) Aleatory and epistemic uncertainty quantification for engineering applications. Sandia technical report SAND2007-2670C, Joint Statistical Meetings, Salt Lake City, UTGoogle Scholar
  29. Thoft-Christensen P, Murotsu Y (1986) Application of structural reliability theory. Springer, BerlinCrossRefMATHGoogle Scholar
  30. Tvedt L (1984) Two second-order approximations to the failure probability. Section on structural reliability. Hovik: A/S Vertas ResearchGoogle Scholar
  31. Wang P, Hu C, Youn BD (2011) A generalized complementary intersection method for system reliability analysis and design. J Mech Des 133(7):071003(13)CrossRefGoogle Scholar
  32. Wiener N (1938) The homogeneous chaos. Am J Math 60(4):897–936MathSciNetCrossRefGoogle Scholar
  33. Xi Z, Youn BD, Hu C (2010) Effective random field characterization considering statistical dependence for probability analysis and design. ASME J Mech Des 132(10):101008(12)CrossRefGoogle Scholar
  34. Xiao Q, Mahadevan S (1998) Second-order upper bounds on probability of intersection of failure events. ASCE J Eng Mech 120(3):49–57Google Scholar
  35. Xiong F, Greene S, Chen W, Xiong Y, Yang S (2010) A new sparse grid based method for uncertainty propagation. Struct Multidisc Optim 41(3):335–349MathSciNetCrossRefMATHGoogle Scholar
  36. Xiu D, Karniadakis GE (2002) The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644MathSciNetCrossRefMATHGoogle Scholar
  37. Xu H, Rahman S (2004) A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics. Int J Numer Methods Eng 61:1992–2019CrossRefMATHGoogle Scholar
  38. Youn BD, Choi KK, Du L (2007a) Integration of possibility-based optimization and robust design for epistemic uncertainty. ASME J Mech Des 129(8):876–882. doi: 10.1115/1.2717232 CrossRefGoogle Scholar
  39. Youn BD, Xi Z, Wang P (2008) Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis. Struct Multidisc Optim 37(1):13–28MathSciNetCrossRefMATHGoogle Scholar
  40. Youn BD, Wang P (2009) Complementary intersection method for system reliability analysis. ASME J Mech Des 131(4):041004(15)CrossRefGoogle Scholar
  41. Youn BD, Xi Z (2009) Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method. Struct Multidisc Optimiz 37(5):474–492MathSciNetGoogle Scholar
  42. Youn BD, Wang P (2009) Complementary intersection method for system reliability analysis. ASME Journal of Mechanical Design 131(4):041004(15)Google Scholar
  43. Zhou L, Penmetsa RC, Grandhi RV (2000) Structural system reliability prediction using multi-point approximations for design. In: Proceedings of 8th ASCE specialty conference on probabilistic mechanics and structural Reliability, PMC2000-082Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Maryland College ParkCollege ParkUSA
  2. 2.Department of Industrial and Manufacturing EngineeringWichita State UniversityWichitaUSA
  3. 3.Seoul National UniversitySeoulSouth Korea

Personalised recommendations