Skip to main content
SpringerLink
Log in

New Models and Measures for Reliability of Multi-state Systems

  • Chapter
Handbook of Performability Engineering

Abstract

This chapter descibes some new reliability models and measures for multistate systems. Equivalent classes and lower/upper boundary points are used for deriving the structure function for multistate system with multistate components. In addition to the static multistate reliability measures, several dynamic reliability measures are also introduced. Two stochastic models, Markov process and non-homogeneous continuous time Markov process are applied to formulate the probability that the system is in each state. With Non-homogeneous continuous time Markov, the age effect of the system is considered. Utility functions and disutility functions are incorporated with the stochastic models for the customer-centered reliability measures. Couple of potential applications are introduced and used to illustrate these reliability models and measures.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
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

  1. Andersen PK. Multi-state models in survival analysis: A study of nephropathy and mortality in diabetes. Statistics in Medicine 1988; 7: 661–670.

    Article  Google Scholar 

  2. Aven T, Jensen U. Stochastic models in reliability. Springer, New York, 1999.

    MATH  Google Scholar 

  3. Barlow RE, Wu AS. Coherent systems with multistate components. Mathematics of Operations Research 1978; 3(4): 275–281.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bell MGH, Iida Y. Transportation network analysis. Wiley, New York, 1997.

    Google Scholar 

  5. Boedigheimer R, Kapur KC. Customer driven reliability models for multistate coherent systems. IEEE Transactions on Reliability 1994; 43(1): 46–50.

    Article  Google Scholar 

  6. Boutsikas MV, Koutras MV. Generalized reliability bounds for coherent structures. Journal of Applied Probability 2000; 37: 778–794.

    Article  MATH  MathSciNet  Google Scholar 

  7. Brunelle RD, Kapur KC. Customer-center reliability methodology. Proceedings of the Annual Reliability and Maintainability Symposium, IEEE, New Jersey, 1997; 286–292.

    Google Scholar 

  8. Camerer CF. Recent tests of generalized expected utility theories. In: Edwards W, editor. Utility theories: Measurement and applications. Cambridge University Press, 1992.

    Google Scholar 

  9. Chen A,Yang H, Lo HK, Tang WH. A capacity related teliability for transportation network. Journal of Advanced Transportation. 1999; 33: 183–200.

    Article  Google Scholar 

  10. Chen A, Yang H, Lo HK, Tang WH. Capacity reliability of a road network: An assessment methodology and numerical results. Transportation Research, Part B 2002; 36: 225–252.

    Article  Google Scholar 

  11. Chen P, Bernard EJ, Sen PK. A Markov chain model used in analyzing disease history applied to a stroke study. Journal of Applied Statistics 1999; 26(4): 413–422.

    Article  MATH  Google Scholar 

  12. Cowen ME, Chartrand M, Weitzel WF. A Markov model of the natural history of prostate cancer. Journal of Clinical Epidemiology 1994; 47(1): 3–21.

    Article  Google Scholar 

  13. Davis D, Holt C. Experimental economics. Princeton University Press 1993.

    Google Scholar 

  14. Fossa S, Kaasa S, Calais da Silva F, Suciu S, Hengeveld M. Quality of life in prostate cancer patients. Prostate 1992; 4(Suppl): 145–148.

    Article  Google Scholar 

  15. Fleming TR, Harrington DP. Counting process and survival analysis. Wiley, New York, 1991.

    Google Scholar 

  16. Fowler FJ, Barry MJ, Lu-Yao G, Wasson J, Roman A, Wennberg J. Effect of radical prostatectomy for prostate cancer on patient quality of life: results from a Medicare survey. Urology 1995; 45(6): 905–1089.

    Article  Google Scholar 

  17. Ganz PA, Schag CAC, Lee JJ, Sim MS. The CARES: A generic measure of health-related quality of life for patients with cancer. Quality of Life Research 1992; 1: 19–29.

    Article  Google Scholar 

  18. Hudson JC, Kapur KC. Reliability analysis for multistate systems with multistate components. IIE Transactions 1983; 15(2): 127–135.

    Article  Google Scholar 

  19. Hudson JC, Kapur KC. Reliability bounds for multistate systems with multistate components. Operations Research 1985; 33(1): 153–160.

    MATH  Google Scholar 

  20. Iida Y. Basic concepts and future directions of road network reliability analysis. Journal of Advanced Transportation 1999; 32: 125–134.

    Google Scholar 

  21. Kapur KC, Lamberson LR. Reliability in engineering design, Wiley, New York, 1997.

    Google Scholar 

  22. Kapur KC. Quality evaluation systems for reliability. Reliability Review 1986; June, 6(2).

    Google Scholar 

  23. Kim M, Moon J, song H. Techniques improving the transmission reliability in high-rate wireless LANs. IEEE Transactions on Consumer Electronics 2004; 50: 64–72.

    Article  Google Scholar 

  24. Li D, Dolezal T, Haimes YY. Capacity reliability of water distribution networks. Reliability Engineering and System Safety 1993; 42: 29–38.

    Article  Google Scholar 

  25. Lisnianski A, Levitin G. Multi-state system reliability: assessment, optimization and application. World Scientific, Singapore, 2003.

    MATH  Google Scholar 

  26. Litwin MS, Hays RD, Fink A, Ganz PA, Leake B, Leach GE, et al., Quality-of-life outcomes in men treated for localized prostate cancer. JAMA 1995; 273(2): 129–135.

    Article  Google Scholar 

  27. Liu H, Ban J, Ran B, Mirchandani P. An analytical dynamic traffic assignment model with stochastic network and travelers’ perceptions. Journal of Transportation Research Board 2002; 1783:125–133.

    Google Scholar 

  28. Liu Y, Kapur KC. Reliability measures for dynamic multi-state systems and their applications for system design and evaluation. IIE Transactions 2006;38(6): 511–520.

    Article  Google Scholar 

  29. McClean S, Montgomery E, Ugwuowo F. Non-Homogeneous continuous-time Markov and semi-Markov manpower models. Applied Stochastic Models and Data Analysis 1998;13:191–198.

    Article  MathSciNet  Google Scholar 

  30. Natvig B. Two suggestions of how to define a multistate coherent system. Advanced Applied Probability 1982; 14: 434–455.

    Article  MATH  MathSciNet  Google Scholar 

  31. Natvig B, March HWH. An application of multistate reliability theory to an offshore gas pipeline network. International Journal of Reliability, Quality and Safety Engineering 2003;10:361–381.

    Article  Google Scholar 

  32. Nicholson W. Microeconomics theory: Basic principles and extensions, 7th edition, Dryden Press, Harcourt Brace College Publishers, 1998.

    Google Scholar 

  33. Ross SM. Multivalued state component systems. The Annals of Probability 1979; 7(2):379–383.

    Article  MATH  MathSciNet  Google Scholar 

  34. Ross SM. Stochastic processes, 2nd edition, Wiley, 1996.

    Google Scholar 

  35. Sargent TJ. Macroeconomics theory, 2nd edition, Academic Press, New York, 1987.

    Google Scholar 

  36. Satitsatian S, Kapur KC. Multi-state reliability model for the evaluation of supply chain network. Proceedings of the International Conference on Manufacturing Excellence, Melboune, Australia, Oct. 13–15, 2003.

    Google Scholar 

  37. Satitsatian S, Kapur KC. Performance evaluation of infrastructure networks with multi-state reliability analysis. International Journal of Performability Engineering 2006; 2(2): 103–121.

    Google Scholar 

  38. Satitsatian S, Kapur KC. An algorithm for lower reliability bounds of multistate two-terminal networks. IEEE Transactions of Reliability 2006; 55(2): 199–206.

    Article  Google Scholar 

  39. Sharp JW. Expanding the definition of quality of life for prostate cancer. Cancer 1993; 71(Suppl): 1078–1082.

    Article  Google Scholar 

  40. Shooman, M.L. Reliability of computer systems and networks: fault tolerance, analysis and design, Wiley, New York, 2002.

    Google Scholar 

  41. Song, J. and Kiureghian, A.D. Bounds on system reliability by linear programming. Journal of Engineering Mechanics. ASCE. 2003; 129(6), 627–636.

    Article  Google Scholar 

  42. Steinberg GD, Bales GT, Brendler CB. An analysis of watchful waiting for clinically localized prostate cancer. Journal of Urology. 1998; 159(5):1431–1436.

    Article  Google Scholar 

  43. Tatineni M, Boyce DE, Mirchandani P. Comparisons of deterministic and stochastic traffic loading models. Transportation Research Record 1997; 1607: 16–23.

    Article  Google Scholar 

  44. Vassiliou P-CG. The evolution of the theory of non-homogeneous Markov system. Applied Stochastic Models and Data Analysis. 1998; 13: 159–176.

    Article  MathSciNet  Google Scholar 

  45. Xu C, Goulter IC. Reliability-based optimal design of water distribution networks. Journal of Water Resources Planning and Management 1999; 125: 352–362.

    Article  Google Scholar 

  46. Xue J, Yang K. Dynamic reliability analysis of coherent multistate systems. IEEE Transactions on Reliability 1995; 44(4): 683–688.

    Article  Google Scholar 

  47. Yang K, Xue J. Dynamic reliability measures and life distribution models for multistate systems. Internaltional Journal of Reliability, Quality and Safety Engineering 1995; 2(1): 79–102.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Michigan in Dearborn, Michigan, USA

    Yung-Wen Liu

  2. University of Washington in Seattle, Washington, USA

    Kailash C. Kapur

Authors
  1. Yung-Wen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kailash C. Kapur
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMS Consultants, 71 Vrindaban Vihar, Ajmer Road, Jaipur (Rajasthan), 302019, India

    Krishna B. Misra (Principal Consultant) (Principal Consultant)

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag London Limited

About this chapter

Cite this chapter

Liu, YW., Kapur, K.C. (2008). New Models and Measures for Reliability of Multi-state Systems. In: Misra, K.B. (eds) Handbook of Performability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-131-2_28

Download citation

  • DOI: https://doi.org/10.1007/978-1-84800-131-2_28

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-130-5

  • Online ISBN: 978-1-84800-131-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation