Skip to main content
Log in

Review and classification of reliability measures for multistate and continuum models

  • Published:
IIE Transactions

Abstract

In this paper we examine a variety of customer-centered reliability measures, generalized to multistate and continuum contexts. A classification scheme is proposed for these measures, and a new measure based on customer-usage patterns is defined. In each case, reliability measures are defined such that they are equally valid for binary, multistate, continuum, and mixed systems. Techniques which facilitate the use of continuum models are discussed, and time-dynamic, infinite-time, and partial-information modeling considerations are also addressed.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Birnbaum, Z.W., Esary, J.D. and Saunders, S.C. (1961) Multicomponent systems and structures and their reliability. Technometrics, 3, 55–77.

    Google Scholar 

  2. Kapur, K.C. and Lamberson, L.R. (1977) Reliability in Engineering Design, Wiley, New York.

    Google Scholar 

  3. Høyland, A. and Rausand, M. (1994) System Reliability Theory, Wiley, New York.

    Google Scholar 

  4. El-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. Journal of Applied Probability, 15, 675–688.

    Google Scholar 

  5. Barlow, R.E. and Wu, A.S. (1978) Coherent systems with multistate components. Mathematics of Operations Research, 3, 275–281.

    Google Scholar 

  6. Hudson, J.C. and Kapur, K.C. (1983) Reliability analysis for multistate systems with multistate components. IIE Transactions, 15, 127–135.

    Google Scholar 

  7. Natvig, B., Srmo, S., Holen, A.T. and Hgåsen, G. (1986) Multistate reliability theory – a case study. Advances in Applied Probability, 18, 921–932.

    Google Scholar 

  8. Boedigheimer, R.A. and Kapur, K.C. (1994) Customer-driven reliability models for multistate coherent systems. IEEE Transactions on Reliability, 43, 46–50.

    Google Scholar 

  9. Block, H.W. and Savits, T.H. (1984) Continuous multistate structure functions. Operations Research, 32, 703–714.

    Google Scholar 

  10. Baxter, L.A. (1984) Continuum structures I. Journal of Applied Probability, 21, 802–815.

    Google Scholar 

  11. Baxter, L.A. (1986) Continuum structures II. Mathematical Proceedings of the Cambridge Philosophical Society, 99, 331–338.

    Google Scholar 

  12. Baxter, L.A. and Kim, C. (1986) Bounding the stochastic performance of continuum structure functions I. Journal of Applied Probability, 23, 660–669.

    Google Scholar 

  13. Montero, J., Tejada, J. and Yáñez, J. (1990) Structural properties of continuum systems. European Journal of Operational Research, 45, 231–240.

    Google Scholar 

  14. Yang, K. and Xue, J. (1996) Continuous state reliability analysis, in Proceedings of the Annual Reliability and Maintainability Symposium, IEEE, Piscataway, NJ, pp. 251–257.

    Google Scholar 

  15. Trivedi, K.S., Muppala, J.K., Woolet, S.P. and Haverkort, B.R. (1992) Composite performance and dependability analysis. Performance Evaluation, 14, 239–242.

    Google Scholar 

  16. Boedigheimer, R.A. and Kapur, K.C. (1993) Involving the customer in the development and evaluation of multistate reliability models, in Proceedings of the Annual Reliability and Maintainability Symposium, IEEE, Piscataway, NJ, pp. 250–255.

    Google Scholar 

  17. Aven, T. (1993) On performance measures for multistate monotone systems. Reliability Engineering and System Safety, 41, 259–266.

    Google Scholar 

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

    Google Scholar 

  19. Brunelle, R. and Kapur, K.C. (1997) Customer-centered reliability methodology, in Proceedings of the Annual Reliability and Maintainability Symposium, IEEE, Piscataway, NJ, pp. 286–292.

    Google Scholar 

  20. Phadke, M. (1989) Quality Engineering Using Robust Design, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  21. Feller, W. (1971) An Introduction to Probability Theory and Its Applications, 2nd edn, Vol. 2, Wiley, New York.

    Google Scholar 

  22. Parzen, E. (1962) Stochastic Processes, Holden-Day, San Francisco, CA.

    Google Scholar 

  23. Jenny, J.A. (1969) The effect of partial failure modes on reliability analysis. IEEE Transactions on Reliability, 18, 175–180.

    Google Scholar 

  24. Boedigheimer, R.A. (1992) Customer-driven reliability models for multistate coherent systems. Ph.D. thesis, University of Oklahoma, Norman, OK.

    Google Scholar 

  25. Brunelle, R. and Kapur, K.C. (1998) Continuous-state system reliability: an interpolation approach. IEEE Transactions on Reliability, 47, 181–187.

    Google Scholar 

  26. Alfeld, P. (1989) Scattered data interpolation in three or more variables, in Mathematical Methods in Computer Added Geometric Design, Academic Press, Boston, MA, pp. 1–33.

    Google Scholar 

  27. Wolfram, S. (1996) The Mathematica Book, Cambridge University Press, Reading, MA.

    Google Scholar 

  28. Hartless, G. and Leemis, L. (1996) Computational algebra applications in reliability theory. IEEE Transactions on Reliability, 45, 393–399.

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

BRUNELLE, R.D., KAPUR, K.C. Review and classification of reliability measures for multistate and continuum models. IIE Transactions 31, 1171–1180 (1999). https://doi.org/10.1023/A:1007600314061

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007600314061

Keywords

Navigation