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Standby Systems with Backups

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Principles of Performance and Reliability Modeling and Evaluation

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

This chapter presents a numerical methodology to model and evaluate reliability, expected mission completion time, and expected total mission cost of 1-out-of-N: G standby sparing systems subject to periodic or non-periodic backup actions. The backups are performed to facilitate effective system recovery in the case of the occurrence of an online operating element failure. The methodology is applicable to dynamic data backup and retrieval times as well as nonidentical system elements with different time-to-failure distributions, different performance, and different standby modes. This chapter also presents applications of the methodology to a set of optimization problems that find the optimal backup distribution and/or element activation sequence, maximizing mission reliability or minimizing expected mission completion time or minimizing total mission cost. Examples are provided to illustrate the presented methodology as well as optimized solutions.

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References

  1. Amari SV, Dill G (2010) Redundancy optimization problem with warm-standby redundancy. In: Proceedings of annual reliability and maintainability symposium, pp 1–6

    Google Scholar 

  2. Amari SV, Misra KB, Pham H (2008) Tampered failure rate load-sharing systems: status and perspectives. In: Misra KB (ed) Chapter 20 in handbook of performability engineering. Springer, pp 291–308

    Google Scholar 

  3. Amari SV, Pham H, Misra RB (2012) Reliability characteristics of k-out-of-n warm standby systems. IEEE Trans Reliab 61:1007–1018

    Article  Google Scholar 

  4. Boddu P, Xing L (2013) Reliability evaluation and optimization of series-parallel systems with k-out-of-n: G subsystems and mixed redundancy types. Proc IMechE Part O, J Risk Reliab 227(2):187–198

    Google Scholar 

  5. Chambari A, Rahmati S, Najafi A, Karimi A (2012) A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies. Comput Industr Eng 63(1):109–119

    Article  Google Scholar 

  6. Chen T-C, You P-S (2005) Immune algorithms-based approach for redundant reliability problems with multiple component choices. Comput Ind 56(2):195–205

    Article  Google Scholar 

  7. Chia LY, Smith AE (2004) An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans Reliab 53(3):417–423

    Article  Google Scholar 

  8. Coit DW (2001) Cold-standby redundancy optimization for non-repairable systems. IIE Trans 33:471–478

    Google Scholar 

  9. Coit DW (2003) Maximization of system reliability with a choice of redundancy strategies. IIE Trans 35(6):535–544

    Article  Google Scholar 

  10. Coit DW, Smith AE (1996) Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Trans Reliab 45(2):254–260

    Article  Google Scholar 

  11. Elerath JG, Pecht M (2009) A highly accurate method for assessing reliability of redundant arrays of inexpensive disks (RAID). IEEE Trans Comput 58(3):289–299

    Article  MathSciNet  Google Scholar 

  12. Fyffe DE, Hines WW, Lee NK (1968) System reliability allocation and a computation algorithm. IEEE Trans Reliab 17:64–69

    Article  Google Scholar 

  13. Hsieh C, Hsieh Y (2003) Reliability and cost optimization in distributed computing systems. Comput Oper Res 30:1103–1119

    Article  MathSciNet  MATH  Google Scholar 

  14. Johnson BW (1989) Design and analysis of fault tolerant digital systems. Addison-Wesley (1989)

    Google Scholar 

  15. Kuo W, Wan R (2007) Recent advances in optimal reliability allocation. IEEE Trans Syst Man Cybern Part A Syst Hum 37(2):143–156

    Article  Google Scholar 

  16. Levitin G (2006) Genetic algorithms in reliability engineering. Guest editorial. Reliab Eng Syst Saf 91(9):975–976 (2006)

    Google Scholar 

  17. Levitin G, Xing L, Dai Y (2013) Optimal sequencing of warm standby elements. Comput Ind Eng 65:570–576

    Article  Google Scholar 

  18. Levitin G, Xing L, Dai Y (2013) Cold-standby sequencing optimization considering mission cost. Reliab Eng Syst Saf 118:28–34

    Article  MATH  Google Scholar 

  19. Levitin G, Xing L, Dai Y (2013) Sequencing optimization in\( k\)-out-of-\(n\) cold-standby systems considering mission cost. Int J Gen Syst 42(8):870–882

    Article  MathSciNet  MATH  Google Scholar 

  20. Levitin G, Xing L, Dai Y (2014) Minimum mission cost cold-standby sequencing in non-repairable multi-phase systems. IEEE Trans Reliab 63(1):251–258

    Article  MathSciNet  Google Scholar 

  21. Levitin G, Xing L, Dai Y (2014) Mission cost and reliability of 1-out-of-N warm standby systems with imperfect switching mechanisms. IEEE Trans Syst Man Cybern Syst 44(9):1262–1271

    Article  Google Scholar 

  22. Levitin G, Xing L, Dai Y (2015) Reliability of non-coherent warm standby systems with reworking. IEEE Trans Reliab 64(1):444–453

    Article  Google Scholar 

  23. Levitin G, Xing L, Johnson BW, Dai Y (2015) Mission reliability, cost and time for cold standby computing systems with periodic backup. IEEE Trans Comput 64(4):1043–1057

    Article  MathSciNet  Google Scholar 

  24. Levitin G, Xing L, Dai Y (2015) Optimal backup distribution in 1-out-of-N cold standby systems. IEEE Trans Syst Man Cybern Syst 45(4):636–646

    Article  Google Scholar 

  25. Levitin G, Xing L, Dai Y (2015) Heterogeneous 1-out-of-N warm standby systems with dynamic uneven backups. IEEE Trans Reliab 64(4):1325–1339

    Google Scholar 

  26. Levitin G, Xing L, Zhai Q, Dai Y (in press) Optimization of full vs. incremental periodic backup policy. IEEE Trans Dependable Secure Comput, doi:10.1109/TDSC.2015.2413404

    Google Scholar 

  27. Misra KB (1972) Reliability optimization of a series-parallel system. IEEE Trans Reliab R-21(4):230–238

    Google Scholar 

  28. Misra KB, Sharma U (1991) An efficient algorithm to solve integer programming problems arising in system-reliability design. IEEE Trans Reliab 40(1):81–91

    Article  MATH  Google Scholar 

  29. Nakagawa T (2007) Shock and damage models in reliability theory, Chapter 9. Springer, London (Springer series in reliability engineering)

    Google Scholar 

  30. Onishi J, Kimura S, James RJW, Nakagawa Y (2007) Solving the redundancy allocation problem with a mix of components using the improved surrogate constraint method. IEEE Trans Reliab 56(1):94–101

    Article  Google Scholar 

  31. Papageorgiou E, Kokolakis G (2010) Reliability analysis of a two-unit general parallel system with warm standbys. Eur J Oper Res 201(3):821–827

    Article  MathSciNet  MATH  Google Scholar 

  32. Qian C, Huang Y, Zhao X, Nakagawa T (2010) Optimal backup interval for a database system with full and periodic incremental backup. J Comput 5(4):557–564

    Article  Google Scholar 

  33. Ruiz-Castro JE, Fernández-Villodre G (2012) A complex discrete warm standby system with loss of units. Eur J Oper Res 218(2):456–469

    Article  MathSciNet  MATH  Google Scholar 

  34. Sandoh H, Kaio N, Kawai H (1992) On backup policies for hard computer disks. Reliab Eng Syst Saf 37(1):29–32

    Article  Google Scholar 

  35. Sinaki G (1994) Ultra-reliable fault tolerant inertial reference unit for spacecraft. In: Proceedings of the annual rocky mountain guidance and control conference. Univelt Inc., San Diego, CA, pp 239–248

    Google Scholar 

  36. Tannous Q, Xing L, Dugan JB (2011) Reliability analysis of warm standby systems using sequential BDD. In: Proceedings of the 57th annual reliability and maintainability symposium, FL, USA

    Google Scholar 

  37. Tannous O, Xing L, Peng R, Xie M, Ng SH (2011) Redundancy allocation for series-parallel warm-standby systems. In: Proceedings of the IEEE international conference on industrial engineering and engineering management, Singapore

    Google Scholar 

  38. Wang C, Xing L, Amari SV (2012) A fast approximation method for reliability analysis of cold-standby systems. Reliab Eng Syst Saf 106:119–126

    Article  Google Scholar 

  39. Xing L, Tannous O, Dugan JB (2012) Reliability analysis of non-repairable cold-standby systems using sequential binary decision diagrams. IEEE Trans Syst Man Cybern Part A Syst Hum 42(3):715–726

    Article  Google Scholar 

  40. Yang X, Wang Z, Xue J, Zhou Y (2012) The reliability wall for exascale supercomputing. IEEE Trans Comput 61(6):767–779

    Article  MathSciNet  Google Scholar 

  41. Zhang T, Xie M, Horigome M (2006) Availability and reliability of k-out-of-(M+N): G warm standby systems. Reliab Eng Syst Saf 91(4):381–387

    Article  Google Scholar 

  42. Zhao R, Liu B (2004) Redundancy optimization problems with uncertainty of combining randomness and fuzziness. Eur J Oper Res 157(3):716–735

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhao R, Liu B (2005) Standby redundancy optimization problems with fuzzy lifetimes. Comput Ind Eng 49(2):318–338

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. The Israel Electric Corporation, P.O. Box 10, 31000, Haifa, Israel

    Gregory Levitin

  2. University of Massachusetts Dartmouth, 285 Old Westport Road, Dartmouth, MA, 02747, USA

    Liudong Xing

Authors
  1. Gregory Levitin
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  2. Liudong Xing
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Correspondence to Gregory Levitin .

Editor information

Editors and Affiliations

  1. University of Massachusetts Dartmou, Dartmouth, Massachusetts, USA

    Lance Fiondella

  2. Università degli studi di Messina, Messina, Italy

    Antonio Puliafito

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Levitin, G., Xing, L. (2016). Standby Systems with Backups. In: Fiondella, L., Puliafito, A. (eds) Principles of Performance and Reliability Modeling and Evaluation. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30599-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-30599-8_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30597-4

  • Online ISBN: 978-3-319-30599-8

  • eBook Packages: EngineeringEngineering (R0)

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