Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 913–923 | Cite as

Reliability analysis for k-out-of-n systems with shared load and dependent components

RESEARCH PAPER
  • 123 Downloads

Abstract

Many structural systems require a minimal number of components to be operational, and predicting the reliability of such systems is a challenge because surviving components share the original system workload with higher component loads after the failure of some components. The states of all the components are also dependent. Such dependence, however, is generally neglected in many existing methods. In this study, we develop a new reliability method for systems with dependent components that share the system load equally before and after other components have failed. The components are also subjected to other loads, such as a preload. The new method is based on limit-state functions that predict the states of components, and the First Order Reliability Method is used. The advantage of the proposed method is that it can directly link the system reliability with design variables and random parameters because of the use of a physics-based approach. High accuracy is maintained with the consideration of dependent component states. Two examples are used to demonstrate the good accuracy and efficiency of the proposed method.

Keywords

Reliability k-out-of-n system Limit-state function Simulation 

References

  1. Amari SV, Bergman R (2008) Reliability analysis of k-out-of-n load-sharing systems. In: Reliability and Maintainability Symposium. RAMS 2008. Annual, 2008. IEEE, pp 440–445Google Scholar
  2. Cheng Y, Conrad DC, Du X (2017) Narrower System Reliability Bounds With Incomplete Component Information and Stochastic Process Loading. J Comput Inf Sci Eng 17:041007CrossRefGoogle Scholar
  3. Dolinski K (1982) First-order second-moment approximation in reliability of structural systems: critical review and alternative approach. Struct Saf 1:211–231CrossRefGoogle Scholar
  4. Drezner Z (1994) Computation of the trivariate normal integral. Math Comput 62:289–294MathSciNetCrossRefMATHGoogle Scholar
  5. Drezner Z, Wesolowsky GO (1990) On the computation of the bivariate normal integral. J Stat Comput Simul 35:101–107MathSciNetCrossRefGoogle Scholar
  6. Drignei D, Baseski I, Mourelatos ZP, Kosova E (2016) A Random Process Metamodel Approach for Time-Dependent Reliability. J Mech Des 138:011403CrossRefGoogle Scholar
  7. Du X (2008) Unified uncertainty analysis by the first order reliability method. J Mech Des 130:091401CrossRefGoogle Scholar
  8. Du X, Sudjianto A (2004) First-order saddlepoint approximation for reliability analysis. AIAA J 42Google Scholar
  9. Du X, Sudjianto A, Chen W (2004) An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des 126:562–570CrossRefGoogle Scholar
  10. Du X, Guo J, Beeram H (2008) Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim 35:117–130MathSciNetCrossRefMATHGoogle Scholar
  11. Genz A (2004) Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Stat Comput 14:251–260MathSciNetCrossRefGoogle Scholar
  12. Hu Z, Du X (2017) System reliability prediction with shared load and unknown component design details. AI EDAM 31:223–234Google Scholar
  13. Huamin L (1998) Reliability of a load-sharing k-out-of-n:G system: non-iid components with arbitrary distributions. IEEE Trans Reliab 47:279–284.  https://doi.org/10.1109/24.740502 CrossRefGoogle Scholar
  14. Kong Y, Ye Z (2017) Interval estimation for k-out-of-n load-sharing systems. IISE Trans 49:344–353CrossRefGoogle Scholar
  15. Kuo W, Zuo MJ (2003) Optimal reliability modeling: principles and applications. John Wiley & SonsGoogle Scholar
  16. Lee TW, Kwak BM (1987) A reliability-based optimal design using advanced first order second moment method. J Struct Mech Earthq Eng 15:523–542Google Scholar
  17. Lim J, Lee B, Lee I (2014) Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization International. Int J Numer Methods Eng 100:773–792CrossRefMATHGoogle Scholar
  18. Liu B, Xie M, Kuo W (2016) Reliability modeling and preventive maintenance of load-sharing systemswith degrading components. IIE Trans 48:699–709CrossRefGoogle Scholar
  19. das Neves Carneiro G, Antonio CC (2017) A RBRDO approach based on structural robustness and imposed reliability level. Struct Multidiscip Optim.  https://doi.org/10.1007/s00158-017-1870-6
  20. Ramu P, Kim NH, Haftka RT (2010) Multiple tail median approach for high reliability estimation. Struct Saf 32:124–137CrossRefGoogle Scholar
  21. Taghipour S, Kassaei ML (2015) Periodic inspection optimization of a k-out-of-n load-sharing system. IEEE Trans Reliab 64:1116–1127CrossRefGoogle Scholar
  22. Teng H-W, Kang M-H, Fuh C-D (2015) On spherical Monte Carlo simulations for multivariate normal probabilities. Adv Appl Probab 47:817–836MathSciNetCrossRefMATHGoogle Scholar
  23. Wang Z, Wang P (2016) Accelerated failure identification sampling for probability analysis of rare events. Struct Multidiscip Optim 54:137–149MathSciNetCrossRefGoogle Scholar
  24. Xi Z, Pan H, Yang R-J (2017) Time dependent model bias correction for model based reliability analysis. Struct Saf 66:74–83CrossRefGoogle Scholar
  25. Xie S, Pan B, Du X (2017) High dimensional model representation for hybrid reliability analysis with dependent interval variables constrained within ellipsoids. Struct Multidiscip Optim 56:1493–1505.  https://doi.org/10.1007/s00158-017-1806-1 CrossRefGoogle Scholar
  26. Yang G (2007) Life cycle reliability engineering. John Wiley & SonsGoogle Scholar
  27. Yang R, Gu L (2004) Experience with approximate reliability-based optimization methods. Struct Multidiscip Optim 26:152–159CrossRefGoogle Scholar
  28. Youn BD, Wang P (2008) Bayesian reliability-based design optimization using eigenvector dimension reduction (EDR) method. Struct Multidiscip Optim 36:107–123CrossRefGoogle Scholar
  29. Youn BD, Choi KK, Du L (2005) Enriched performance measure approach for reliability-based design optimization. AIAA J 43:874–884CrossRefGoogle Scholar
  30. Zhang T (2017) An improved high-moment method for reliability analysis. Structural and Multidisciplinary Optimization: 1-8Google Scholar
  31. Zhang Y, Der Kiureghian A (1995) Two Improved Algorithms for Reliability Analysis. In: Rackwitz R, Augusti G, Borri A (eds) Reliability and Optimization of Structural Systems: Proceedings of the sixth IFIP WG7.5 working conference on reliability and optimization of structural systems 1994. Springer US, Boston, pp 297–304.  https://doi.org/10.1007/978-0-387-34866-7_32 CrossRefGoogle Scholar
  32. Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidiscip Optim 31:190–200CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Illinois at ChicagoChicagoUSA
  2. 2.Shenyang University of Chemical TechnologyShenyangChina
  3. 3.Mechanical EngineeringMissouri University of Science and TechnologyRollaUSA

Personalised recommendations