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.
Similar content being viewed by others
References
Birnbaum, Z.W., Esary, J.D. and Saunders, S.C. (1961) Multicomponent systems and structures and their reliability. Technometrics, 3, 55–77.
Kapur, K.C. and Lamberson, L.R. (1977) Reliability in Engineering Design, Wiley, New York.
Høyland, A. and Rausand, M. (1994) System Reliability Theory, Wiley, New York.
El-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. Journal of Applied Probability, 15, 675–688.
Barlow, R.E. and Wu, A.S. (1978) Coherent systems with multistate components. Mathematics of Operations Research, 3, 275–281.
Hudson, J.C. and Kapur, K.C. (1983) Reliability analysis for multistate systems with multistate components. IIE Transactions, 15, 127–135.
Natvig, B., Srmo, S., Holen, A.T. and Hgåsen, G. (1986) Multistate reliability theory – a case study. Advances in Applied Probability, 18, 921–932.
Boedigheimer, R.A. and Kapur, K.C. (1994) Customer-driven reliability models for multistate coherent systems. IEEE Transactions on Reliability, 43, 46–50.
Block, H.W. and Savits, T.H. (1984) Continuous multistate structure functions. Operations Research, 32, 703–714.
Baxter, L.A. (1984) Continuum structures I. Journal of Applied Probability, 21, 802–815.
Baxter, L.A. (1986) Continuum structures II. Mathematical Proceedings of the Cambridge Philosophical Society, 99, 331–338.
Baxter, L.A. and Kim, C. (1986) Bounding the stochastic performance of continuum structure functions I. Journal of Applied Probability, 23, 660–669.
Montero, J., Tejada, J. and Yáñez, J. (1990) Structural properties of continuum systems. European Journal of Operational Research, 45, 231–240.
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.
Trivedi, K.S., Muppala, J.K., Woolet, S.P. and Haverkort, B.R. (1992) Composite performance and dependability analysis. Performance Evaluation, 14, 239–242.
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.
Aven, T. (1993) On performance measures for multistate monotone systems. Reliability Engineering and System Safety, 41, 259–266.
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.
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.
Phadke, M. (1989) Quality Engineering Using Robust Design, Prentice-Hall, Englewood Cliffs, NJ.
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, 2nd edn, Vol. 2, Wiley, New York.
Parzen, E. (1962) Stochastic Processes, Holden-Day, San Francisco, CA.
Jenny, J.A. (1969) The effect of partial failure modes on reliability analysis. IEEE Transactions on Reliability, 18, 175–180.
Boedigheimer, R.A. (1992) Customer-driven reliability models for multistate coherent systems. Ph.D. thesis, University of Oklahoma, Norman, OK.
Brunelle, R. and Kapur, K.C. (1998) Continuous-state system reliability: an interpolation approach. IEEE Transactions on Reliability, 47, 181–187.
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.
Wolfram, S. (1996) The Mathematica Book, Cambridge University Press, Reading, MA.
Hartless, G. and Leemis, L. (1996) Computational algebra applications in reliability theory. IEEE Transactions on Reliability, 45, 393–399.
Xue, J. and Yang, K. (1995) Dynamic reliability analysis of coherent multistate systems. IEEE Transactions on Reliability, 44, 683–688.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1007600314061