Skip to main content

Redundancy Optimization Problems with Uncertain Lifetimes

  • Chapter
Computational Intelligence in Reliability Engineering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 39))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Cai KY, Wen CY, Zhang ML (1991) Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets and Systems 42:145-172

    Article  MATH  MathSciNet  Google Scholar 

  • Campos L, González A (1989) A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems 29:145-153

    Article  MATH  MathSciNet  Google Scholar 

  • Castellano G, Fanelli AM, Pelillo M (1997) An iterative pruning algorithm for feedforward neural networks. IEEE Transactions on Neural Network 8:519-537

    Article  Google Scholar 

  • Chanas S, Nowakowski M (1988) Single value simulation of fuzzy variable. Fuzzy Sets and Systems 25:43-57

    Article  MATH  MathSciNet  Google Scholar 

  • Chern CS (1992) On the computational complexity of reliability redundancy allo-cation in the series system. Operations Research Letters 11:309-315

    Article  MATH  MathSciNet  Google Scholar 

  • Coit DW (2001) Cold-standby redundancy optimization for nonrepairable sys-tems. IIE Transactions 33:471-478

    Google Scholar 

  • Coit DW, Smith AE (1996) Reliability optimization of series-parallel systems us-ing a genetic algorithm. IEEE Transactions on Reliability 45:254-260

    Article  Google Scholar 

  • Coit DW, Smith AE (1998) Redundancy allocation to maximize a lower percentile of the system time-to-failure distribution. IEEE Transactions on Reliability 47:79-87

    Article  Google Scholar 

  • Dubois D, Prade H (1987) The mean value of a fuzzy number. Fuzzy Sets and Systems 24:279-300

    Article  MATH  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1988) Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum, New York

    MATH  Google Scholar 

  • Fogel DB (1994) An introduction to simulated evolutionary optimization. IEEE Transactions on Neural Networks 5:3-14

    Article  Google Scholar 

  • Gao J, Liu B (2001) New primitive chance measures of fuzzy random event. In-ternational Journal of Fuzzy Systems 3:527-531

    MathSciNet  Google Scholar 

  • Gen M, Liu B (1995) Evolution program for production plan problem. Engineer-ing Design and Automation 1:199-204

    Google Scholar 

  • Gen M, Liu B (1997) Evolution program for optimal capacity expansion. Journal of Operations Research Society of Japan 40:1-9

    MATH  MathSciNet  Google Scholar 

  • Goldberg DE (1989) Genetic Algorithms in Search. Optimization and Machine Learning, Addison-Wesley

    Google Scholar 

  • González A (1990) A study of the ranking function approach through mean val-ues. Fuzzy Sets and Systems 35:29-41

    Article  MATH  MathSciNet  Google Scholar 

  • Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets and Systems 47:81-86

    Article  MATH  MathSciNet  Google Scholar 

  • Karwowski W, Mital A (1986) Applications of fuzzy set theory in human factors. Elsevier, Amasterdam

    Google Scholar 

  • Kaufmann A (1975) Introduction to the theory offuzzy subsets. Academic Press, New York

    Google Scholar 

  • Kruse R, Meyer KD (1987) Statistics with Vague Data. D. Reidel Publishing Company, Dordrecht

    MATH  Google Scholar 

  • Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimiza-tion. IEEE Transactions on Reliability 49:176-187

    Article  Google Scholar 

  • Kwakernaak H (1978) Fuzzy random variables—I. Information Sciences 15:1-29

    Article  MATH  MathSciNet  Google Scholar 

  • Kwakernaak H (1979) Fuzzy random variables—II. Information Sciences 17:253-278

    Article  MATH  MathSciNet  Google Scholar 

  • Levitin G, Lisnianski A, Ben-Haim H, Elmakis D (1998) Redundancy optimiza-tion for series-parallel multi-state system. IEEE Transactions on Reliability 47:165-172

    Article  Google Scholar 

  • Liu B (1998) Minimax chance constrained programming models for fuzzy deci-sion systems. Information Sciences 112:25-38

    Article  MATH  MathSciNet  Google Scholar 

  • Liu B (1999) Dependent-chance programming with fuzzy decision. IEEE Transac-tions on Fuzzy Systems 7:354-360

    Article  Google Scholar 

  • Liu B (1999) Uncertain Programming. John Wiley & Sons, New York

    Google Scholar 

  • Liu B (1999) Dependent-chance programming with fuzzy decisions. IEEE Trans-actions on Fuzzy Systems 7:354-360

    Article  Google Scholar 

  • Liu B (2000) Dependent-chance programming in fuzzy environments. Fuzzy Sets and Systems 109:97-106

    Article  MATH  MathSciNet  Google Scholar 

  • Liu B (2001) Fuzzy random chance-constrained programming. IEEE Transactions on Fuzzy Systems 9:713-720

    Article  Google Scholar 

  • Liu B (2001) Fuzzy random dependent-chance programming. IEEE Transactions on Fuzzy Systems 9:721-726

    Article  Google Scholar 

  • Liu B (2002) Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg

    MATH  Google Scholar 

  • Liu B (2004) Uncertainty Theory: An Introduction to Its Axiomatic Foundations. Springer-Verlag, Berlin

    MATH  Google Scholar 

  • Liu B, Iwamura K (1998) Chance-constrained programming with fuzzy parame-ters. Fuzzy Sets and Systems 94:227-237

    Article  MATH  MathSciNet  Google Scholar 

  • Liu B, Iwamura K (1998) A note on chance-constrained programming with fuzzy coefficients. Fuzzy Sets and Systems 100:229-233

    Article  MATH  MathSciNet  Google Scholar 

  • Liu B, Liu Y (2002) Expected value of fuzzy variable and fuzzy expected value model. IEEE Transactions on Fuzzy Systems 10:445-450

    Article  Google Scholar 

  • Liu Y, Gao J (2005) The independence of fuzzy variables in credibility theory and its applications. Technical Report

    Google Scholar 

  • Liu Y, Liu B (2002) Random fuzzy programming with chance measures defined by fuzzy integrals, Mathematical and Computer Modelling 36:509-524

    Article  MATH  MathSciNet  Google Scholar 

  • Liu Y, Liu B (2003) Expected value operator of random fuzzy variable and ran-dom fuzzy expected value models. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 11:195-215

    Article  MATH  Google Scholar 

  • Liu Y, Liu B (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optimization and Decision Making 2:143-160

    Article  MathSciNet  Google Scholar 

  • Liu Y, Liu B (2005) On minimum-risk problems in fuzzy random decision sys-tems, Computers & Operations Research 32:257-283

    Article  MATH  MathSciNet  Google Scholar 

  • Michalewicz Z (1992) Genetic Algorithms + Data Structures = Evolution Pro-grams. Springer-Verlag, New York

    Google Scholar 

  • Nahmias S (1978) Fuzzy variables. Fuzzy Sets and Systems 1:97-110

    Article  MATH  MathSciNet  Google Scholar 

  • Prasad VR, Kuo W, Kim KMO (1999) Optimal allocation of s-identical, multi-functional redundant elements in a series system. IEEE Transactions on Reli-ability 47:118-126

    Article  Google Scholar 

  • Puri ML, Ralescu DA (1985) The concept of normality for fuzzy random vari-ables. Ann. probab. 13:1371-1379

    Article  MathSciNet  Google Scholar 

  • Puri ML, Ralescu DA (1986) Fuzzy random variables. Journal of Mathematical Analysis and Applications 114:409-422

    Article  MATH  MathSciNet  Google Scholar 

  • Shitaishi N, Furuta H (1983) Reliability analysis based on fuzzy probability. Jour-nal of Engineering Mechanism 109:1445-1459

    Google Scholar 

  • Venkatech S (1992) Computation and learning in the context of neural network capacity. Neural Networks for Perception 2:173-327

    Google Scholar 

  • Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. In-formation Sciences 24:143-161

    MATH  MathSciNet  Google Scholar 

  • Yager RR (1992) On the specificity of a possibility distribution. Fuzzy Sets and Systems 50:279-292

    Article  MATH  MathSciNet  Google Scholar 

  • Yager RR (1993) On the completion of qualitative possibility measures. IEEE Transactions on Fuzzy Systems 1:184-193

    Article  MathSciNet  Google Scholar 

  • Yager RR (2002) On the evaluation of uncertain courses of action. Fuzzy Optimization and Decision Making 1:13-41

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Sys-tems 1:3-28

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1979) A theory of approximate reasoning. In: Hayes J, Michie D and Throll DM (eds): Mathematical Frontiers of the Social and Policy Sciences. Westview Press, Boulder Cororado, pp 69-129

    Google Scholar 

  • Zhao R, Liu B (2003) Stochastic programming models for general redundancy op-timization problems. IEEE Transactions on Reliability 52:181-192

    Article  Google Scholar 

  • Zhao R, Liu B (2004) Redundancy optimization problems with uncertainty of combining randomness and fuzziness. European Journal of Operational Re-search 157: 716-735

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao R, Liu B (2005) Standby Redundancy Optimization Problems with Fuzzy Lifetimes. Computer & Industrial Engineering 49: 318-338

    Article  Google Scholar 

  • Zhao R, Song K, Zhu J (2001) Redundancy Optimization Problems with Fuzzy Random Lifetimes. IEEE International Conference on Fuzzy Systems: 288-291

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zhao, R., Tang, W. (2007). Redundancy Optimization Problems with Uncertain Lifetimes. In: Levitin, G. (eds) Computational Intelligence in Reliability Engineering. Studies in Computational Intelligence, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37368-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-37368-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37367-4

  • Online ISBN: 978-3-540-37368-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics